# An analysis of factors impacting team strengths in the Australian Football
League using time-variant Bradley-Terry models

Carlos Rafael González Soffner  Manuele Leonelli

###### Abstract

Australian Rules Football is a field invasion game where two teams attempt to
score the highest points to win. Complex machine learning algorithms have been
developed to predict match outcomes post-game, but their lack of
interpretability hampers an understanding of the factors that affect a team’s
performance. Using data from the male competition of the Australian Football
League, seasons 2015 to 2023, we estimate team strengths and the factors
impacting them by fitting flexible Bradley-Terry models. We successfully
identify teams significantly stronger or weaker than the average, with
stronger teams placing higher in the previous seasons’ ladder and leading the
activity in the Forward 50 zone, goal shots and scoring over their opponents.
Playing at home is confirmed to create an advantage regardless of team
strengths. The ability of the model to predict game results in advance is
tested, with models accounting for team-specific, time-variant features
predicting up to 71.5% of outcomes. Therefore, our approach can provide an
interpretable understanding of team strengths and competitive game
predictions, making it optimal for data-driven strategies and training.

###### keywords:

Australian football , Bradley-Terry models , Feature selection , Sports
analytics

organization=School of Science and Technology, IE University,city=Madrid,
country=Spain

##  1 Introduction

Australian Rules Football (AF) is a field invasion game played by two teams of
18 players each through four consecutive twenty-minute quarters. Teams score
by sending the ball (football or footy) in between the opposite team’s four
goalposts: teams score a goal (worth 6 points) if the ball is kicked through
the central posts, and a behind (worth 1 point) if it goes through a centre
and a side post, touches the post or is touched by an opponent. The team with
the highest score by the end of the fourth quarter wins the game, with draws
if both teams have the same score.

Players can move the football by running and bouncing it or kicking and
handballing (punching the ball towards a teammate) to dispose of it. Opponents
attempt to seize the ball by interrupting disposals, tackling (forcing the
player holding the ball to dispose of it) or taking a mark (catching a
football that was kicked in the air, awarding a free kick). The playing ground
has an oval shape and can be divided into three zones: Defensive (50 metres
closest to a team’s goalposts), Forward 50 (50 metres closest to the
opponent’s goalposts) and Midfield (area in between).

The male Australian Football League (AFL) is the prime AF competition,
gathering 18 teams across Australia. They compete against each other every
week in a Home-and-Away season, usually made up of 23 or 24 rounds, and are
ranked on a ladder based on their game outcomes: wins award 4 points, draws 2
points and losses no points. The top 8 teams in the ladder progress to a
Finals Series, where losers are progressively eliminated until the Grand
Final. The winner of the Grand Final is referred to as the season Premier.

There is extensive research about the use of data collected during AF games to
model outcomes, players’ performance or network effects, most of them using
data from AFL games as these are publicly available on different websites.
Researchers have successfully predicted game winners and score margins using
counts of actions like handballs or disposals (Robertson et al., 2016; Young
et al., 2019a), network measures (Braham and Small, 2018; Fransen et al.,
2022; Sargent et al., 2022; Young et al., 2020) or features of the game
itself, like playing home or away (Robertson and Joyce, 2018).

Most of the studies modelling game outcomes take a post-game approach, aiming
to predict the winner or the scores through their in-game performance. While
often resulting in well-performing models (Robertson et al., 2016; Young et
al., 2019a, 2020), any derived conclusion cannot give information about a
team’s future performance beyond what went wrong during a game or what
strategies worked best. On the other hand, research efforts to model outcomes
pre-game, while achieving worse-performing models (Fahey-Gilmour et al., 2019;
Manderson et al., 2018; Sargent et al., 2022), do confirm the viability of
this approach, whereby teams’ performance in their past games can be
predictive of their future performance.

Additionally, even though complex machine learning models have performed best
(Fahey-Gilmour et al., 2019; Manderson et al., 2018; Young et al., 2019a,
2020), in the context of sports they can be problematic since their
interpretation must be comprehensible enough for teams to modify their
training and strategies accordingly. Thus, there is a tradeoff between
advanced predictive methods and the need to understand what makes a team more
likely to win a game before it takes place.

We explore the performance of various, flexible Bradley-Terry (BT) models (see
e.g. Agresti, 2012) to estimate teams’ strength and predict AF games’ outcomes
using pre-game features. The BT model is designed to model pairwise
comparisons, which are extremely common in sports like AF since each team is
pitted against another. For a game between two hypothetical teams $i$ and $j$,
the model calculates the probability of team $i$ winning as a measure of the
strength of team $i$ relative to the combined strength of teams $i$ and $j$.
While the original model formulation assumes that the values for the strengths
are fixed in time, Tsokos et al. (2019) describes expansions of the model to
include time-variant features. Moreover, the BradleyTerry2 R package further
adapts the model to game and team-specific features that can vary with time
(Firth and Turner, 2012). This is the first paper to attempt using the BT
model to predict outcomes in AF, despite its satisfactory performance in other
sports, such as football (Tsokos et al., 2019), cricket (Dewart and Gillard,
2019), and tennis (Fayomi et al., 2022).

Our aim is to determine how well various BT models can predict AF match
outcomes with features only available before the game takes place. The games
predicted are those from the male competition of the AFL, seasons 2015 to
2023, as the majority of the research efforts to date have concentrated on
this competition. BT models of increasing complexity are fitted progressively,
from its simplest specification, which only considers binomial counts of
outcomes, to the most complex, which predicts games with time-variant
predictors. Our approach deviates from others in its encoding of some of the
features to account for a team’s cumulative performance over a whole season or
the last 4 games. Furthermore, we fit models over different windows of seasons
to investigate whether a higher sample size of past seasons improves the fit
and predictive ability.

The paper is organised as follows. Section 2 reviews the state of the art in
the features, models and techniques used to predict AFL game outcomes. Section
3 describes the data collection and feature engineering processes, the BT
models and the experiment design. The significant features and models’
performance are presented in Section 4, along with a discussion in Section 5
on the implications for strength estimation in the AFL. Section 6 concludes
the paper.

##  2 Related work

###  2.1 Game features

The different movement and scoring possibilities in AF, along with the complex
fixture design of the AFL, result in a broad pool of possible features to
model game outcomes. Most research efforts have concentrated on variables
relating to the fixture (e.g.: location of the game, playing home or away) or
the team totals of actions of individual players (e.g.: total kicks, total
goals), although there is a growing body of research about team-specific
features represented as network effects.

Following Fahey-Gilmour et al. (2019), this section identifies ‘strength’ and
‘match difficulty’ features. The former refers to the variables potentially
identifying that a team is stronger than another regardless of fixed effects
like the location of the game. The latter covers the features impacting the
odds of winning regardless of how strong a team is compared to their opponent
(e.g.: playing away, travelling).

####  2.1.1 Technical strength

Technical features are the individual and aggregated actions of the players
and the results of the teams. The most prolific ones in the literature are
Performance Indicators (PIs), the actions individual players perform during a
game that can be aggregated into team totals. Modelling game outcomes based on
the absolute counts of the indicators (say, total kicks of a team during a
game) is discouraged as it dismisses the performance of the opponent
(Robertson et al., 2016). Indeed, Young et al. (2019a) confirmed that PIs in
their relative form were significantly more explanatory of game outcomes and
score margins than PIs in their absolute form.

Achieving higher relative counts of kicks and goal conversions during the game
appears to be indicative of winning. More specifically, during the 2013
season, 81% of the teams recording kick differentials higher or equal to $-1$
won their games, while 90% of the teams with higher additional kicks and a
goal conversion 4.2% higher than their opponents also won their games
(Robertson et al., 2016). Furthermore, it is natural that teams with more
activity in the Forward 50, the zone closest to the opponent’s goalposts, are
more likely to score. Indeed, Robertson et al. (2016) mentioned that
differentials in the inside 50s (entries into the Forward 50), marks in the
Forward 50, regular marks and contested possessions were all influential
variables for in-game outcomes. The findings of Young et al. (2019a) confirmed
the effect of all previous indicators, along with the differentials in
disposals, time in possession and metres gained, the last two being more
important than any other indicator.

Notably, most research about PIs is descriptive, with the outcomes or score
margins modelled with the features observed in such a game. While still
relevant for post-game analyses, there is a research gap on the predictive
ability of cumulative PIs before the game takes place. This is particularly
striking considering that the evolution of these indicators over the season or
a window of past games is the simplest indicator of a team’s relative strength
to another.

In terms of the individual players’ strength, it has been found that older and
heavier teams, that is, with a higher average player age and weight, are
significantly (yet slightly) more likely to win their games (Lazarus et al.,
2018). It is theorised that older players’ experience may compensate for any
physical deterioration.

While most research efforts have concentrated on understanding a team’s
strength as the aggregate of their players, some studies have focused on team-
level strength indicators. One of these indicators is the team’s performance
over past games. The wins over a window of the past 4 games, known as
‘momentum’ or ‘form’, were found to significantly increase the likelihood of
winning a game (Robertson and Joyce, 2018). Furthermore, the difference in the
ladder position was also associated with a slightly higher chance of winning
(Robertson and Joyce, 2018), along with differentials in the ladder rank from
the previous season (Fahey-Gilmour et al., 2019; Robertson and Joyce, 2018).

Finally, differentials in higher rankings in player-based team ratings, Elo
ratings (ratings of players or teams in two-player games, updated based on
wins and losses and the rating of the opponent) and the availability of the
Top 10 best-performing players were significant predictors of game outcomes
(Fahey-Gilmour et al., 2019). However, while being calculated before the game
takes place, except for the Elo team ratings, there is no consensus over a
standardised way to rank players that all teams can use.

####  2.1.2 Tactical strength

Predictions of game outcomes based on the aggregation of individual PIs have
lately been reexamined in favour of approaches modelling AF as Social Networks
built over the players’ interactions, often referred to as a ‘tactical’
analysis.

In one of the earliest tactical analyses of AF, Sargent and Bedford (2013)
modelled games as passing networks, with edges representing passes between
players, and concluded that higher values for a team’s connectedness were
predictive of the score margin, to the point that they could estimate the
impact of important players missing and recommend potential substitutes.
Sargent and Bedford (2013) therefore suggests that it is possible to predict
the outcome of a game once the lineup is revealed. Braham and Small (2018)
built similar ‘passing networks’, confirming that stronger teams tend to show
higher network values. More specifically, the average values for a team’s
betweenness and out-degree were important predictors of game outcomes, along
with the mean betweenness for the previous game and the previous four games
(Braham and Small, 2018).

Young et al. (2019b), however, found no significant differences in the
betweenness centrality between winning and losing teams. While the other
network measures remained significant, they were slightly to moderately
correlated with the score margin. It could be possible that network measures
might explain playing strategies that remain stable throughout a season but
change from season to season, perhaps to compensate for bad results or reflect
changes in coaching strategies or adaptations to rules. Furthermore, just like
with PIs, absolute values of network measures may not fully capture their
effect, if any, on game outcomes.

Modelling approaches combining tactical and technical features are currently
limited and inconclusive. Reasons for this include the difficulty of finding
network data from free sources and the significant effort to calculate network
measures for every team at every game. Moreover, the variety of possible
actions in AF opens the door for different network designs, with the resulting
network measures representing different aspects of the game. Consequently, the
same measures can have different significance in different models. Indeed,
Young et al. (2020) drew mixed conclusions from a combined approach, stating
that tactical features were slightly more important than technical PIs while
not improving the classification accuracy of winning and losing teams.

However, after encoding a passing network’s interactions in three types of
metrics (receiving the football as indegree, distributing as outdegree and
mutual passes as connectedness), Fransen et al. (2022) found that one-unit
increases in the connectedness increased the probability of winning the game
by 5.3%, further arguing that tactical features explained 14% to 27% of the
variance in the result and that their effects were stable across seasons.
Consequently, the research around the inclusion of tactical features to model
game outcomes might be at a stage too early to decide on a specific network
design and encoding strategy.

####  2.1.3 Match difficulty

Match difficulty features are pre-game fixed effects impacting the winning
probability for all teams regardless of their strengths. Accounting for these
factors is important in AF, as teams sometimes travel long distances with
changing rest days between games (Sargent et al., 2022).

One significant condition is the Home and Away team designations. It is common
for teams to play games in shared home venues (say, North Melbourne and Saint
Kilda share the Marvel Stadium) or grounds with no teams in the AFL (mostly in
the Northern Territory and Tasmania). Robertson et al. (2016) found that teams
playing away were less likely to win the game, especially if they had
travelled to another state, an effect that Lazarus et al. (2018) confirmed to
be significant yet small. The effect of playing at home or as the Home Team
has been explored widely in other sports, with some researchers pointing to
the positive effects of emotional support from fans (Leitner et al., 2023).

Regarding the travelling effect, it is also possible that players rest less,
especially considering the different time zones in Australia and the impact it
can have on physical performance. While it has been confirmed that playing
interstate games decreases the sleep of players, there are no studies
analysing the effect of poor sleep on game outcomes (Sargent et al., 2022).

###  2.2 Eras in AFL

Like any long-running sport, AF has experienced changes in its rules and style
of play. The current game is faster, with heavier and taller players (Woods et
al., 2017). Scoring has also declined in the latest seasons (Lane et al.,
2020). While PIs and strategies remain stable throughout the same seasons, a
growing body of research argues that changes to the game can be appreciated in
the medium term, to the point of identifying groups of seasons or ‘eras’ in
the AFL where the indicators are significantly different from each other.

Woods et al. (2017) confirmed how the totals of PIs varied in different
seasons, possibly reflecting changing strategies or adaptation to new rules of
the game. More specifically, they identified an era where possessing the
football was prioritised (2005-09 seasons), followed by a defensive era
(2010-13), and an era focusing on repossession and turnovers (2014-onwards).
Likewise, Lane et al. (2020) identified an era where offensive strategies
predominated (until 2007-08), followed by an increasingly defensive game
(2007-11) with more tackles and disposals and lower scoring.

Identifying eras raises doubts about the effectiveness of a historical model
making no distinction between seasons. If PIs change between eras, modelling
all seasons could imply trying to fit one model to different strategies of the
same game. Similar concerns were voiced by Young et al. (2019a), as the lack
of proper consensus on the methods for identifying these periods complicated
the modelling and validation processes. Indeed, while there is not a unique
strategy for identifying eras, the findings do warrant a model that is either
season-specific or assigns heavier weights to the most recent seasons or
rounds.

###  2.3 Machine learning models

Research shows that non-linear models often perform better when modelling
outcomes in the AFL, especially if they perform feature selection (Fahey-
Gilmour et al., 2019). Such models are common in team invasion sports and
feature selection is necessary before or during modelling given the high
number of possible predictors. In the context of pre-game outcome predictions,
black-box and complex machine learning models are not appropriate as their
predictive power does not compensate for the lack of interpretability.

Research often centres on classification models to predict binary outcomes
(wins or losses), excluding draws since they are rare in AF. However, the
scoring dynamics of the sport have drawn attention to models predicting score
margins. Strangely enough, research about modelling the number of goals or
behinds, jointly or separately, is sparse.

Models based on decision trees often yield good results, which follows the
notion that values above a threshold in differential PIs can successfully
identify winning teams. Young et al. (2020) used a decision tree to model wins
and losses with technical and tactical indicators, achieving a classification
accuracy of about 89%. Similarly, random forest models achieved accuracies
between 85% and 89% when modelling outcomes in different eras (Young et al.,
2019a).

Generalised linear models (GLMs) often outperform other techniques. Young et
al. (2020) confirmed that GLMs achieved a classification accuracy of 93.2%
when modelling wins and losses, and an RMSE of 6.9 points when modelling the
score margin. GLMs have also been used to predict outcomes in advance.
Specifically, training a GLM with elastic net regularisation on features known
before the game, Fahey-Gilmour et al. (2019) reported an accuracy of 73.3% on
the 2018 season games and 71.6% during cross-validation (seasons 2013-17).

Finally, Manderson et al. (2018), arguing that the number of goals and the
number of behinds each followed a Skellam distribution, used a Bayesian
hierarchical model to produce pre-game predictions on the two scoring types,
identifying the team with the highest aggregated points as the winner. They
correctly predicted 132 games (around two-thirds), performing slightly worse
than betting markets.

All the literature on machine learning approaches for AF reviewed above is
further summarized in A.

##  3 Methodology

###  3.1 The data

Data was fetched through the fitzRoy R package, which offers different
functions to fetch official AFL data from various sources, including the AFL,
AFL Tables, FootyWire and Squiggle (Nguyen et al., 2021). It is currently the
most comprehensive, non-commercial tool to access AFL data and has been used
in previous research (Fahey-Gilmour et al., 2019). Match results from seasons
2015 to 2023 were retrieved from AFL Tables through fitzRoy. Ladder results
from the same seasons were retrieved from the AFL official website, also
through the package. The ladder result from the last round of the Home-and-
Away season, combined with the placement at the Finals Series, was retrieved
manually from the AFL Website. Finally, fitzRoy was used to retrieve
performance indicator data for each game in those seasons from the AFL
Website. Network data was not retrieved as it was not publicly available,
thereby discarding the use of tactical features.

Data from 1826 games from seasons 2015 to 2023 was used to fit the models.
These amounted to 207 games per season except for 2015 (206 as one game was
cancelled), 2020 (162 since the season was cut short due to Covid) and 2023
(216 games due to the addition of one round). Following Fahey-Gilmour et al.
(2019) and Fransen et al. (2022), draws were excluded as they amounted to only
14 games. A glossary with the details of all features used to predict games’
outcomes is given in B, while C summarizes the data pipelines used to create
the required dataframes to fit the models.

The code to extract the data and replicate the experiments can be found at
https://github.com/charlieceratops/AFL_BradleyTerry.

###  3.2 The Bradley-Terry model

The Bradley-Terry (BT) model is a GLM used to model pairwise comparisons, like
those in AF, where two teams compete against each other for the win. Following
the explanation in Tsokos et al. (2019), AF outcomes can be modelled like:

$Y_{ijr}=\left\\{\begin{array}[]{lc}1,&\mbox{if team }i\mbox{ beats team
}j\mbox{ at round }r,\\\ 0,&\mbox{if team }j\mbox{ beats team }i\mbox{ at
round }r,\\\ \end{array}\right.$

for $i,j=1,\dots,18$, $i\neq j$, since there are 18 teams in the AFL, and
$r=1,\dots,N$, where $N$ is the total number of rounds. The BT model takes the
probability of Team $i$ winning against Team $j$ in round $r$ as:

$P(Y_{ijr}=1)=\frac{\pi_{ir}}{\pi_{ir}+\pi_{jr}},$

where $\pi_{ir}=\exp(\lambda_{ir})$ and $\lambda_{ir}$ is the strength of Team
$i$ in round $r$ (Tsokos et al., 2019). This formulation simplifies the
understanding of a game outcome as proportional to how strong a team compares
to the other, thereby leading to more understandable explanations of team
performance.

####  3.2.1 Standard Bradley-Terry

The initial formulation of the BT model assumes strengths and features to be
time-invariant (Tsokos et al., 2019). Teams’ strengths to depend only on game
outcomes, excluding any contest or team-specific predictors. Assuming
independence of games, the standard BT models a binomial target (Team $i$,
Team $j$) based on each team’s wins for each pairing (Firth and Turner, 2012).
The resulting coefficients are the logarithms of the strengths of each team.
The probability of Team $i$ winning in round $r$ against Team $j$ is therefore
calculated as

$\textnormal{logit}(P(Y_{ijr}=1))=\lambda_{i}-\lambda_{j},$

where we dropped the $r$ subscript since strengths are constant throughout a
season.

####  3.2.2 Contest-specific, time-invariant Bradley-Terry

The contest-specific, time-invariant BT model expands the standard one to
allow for ‘order effects’, which are biases in favour of a particular team,
thereby extending the model to

$\textnormal{logit}(P(Y_{ijr}=1))=\lambda_{i}-\lambda_{j}+\delta Z$

where $\delta$ is the value of the bias and $Z=1$ if $i$ has the advantage,
$-1$ otherwise (Firth and Turner, 2012).

In the AFL, the only effect that is specific to all contest pairs and constant
over time is whether or not the team is designated as Home or Away. Other
possible features will be specific to the teams or time-variant (PIs and past
performance). Moreover, since teams can be designated as Home in games outside
their home venue and state, it is not possible to derive order effects from
these features.

The model estimates the order effect along with the team strengths, which are
independent of it. Conceptually, team strengths are still derived from the
frequency of wins since there are no other team-specific features.

####  3.2.3 Team-specific, time-variant Bradley-Terry

This final expansion allows the introduction of features with values specific
to the competing teams (e.g.: the number of wins through the season), with the
strength of the team being calculated as

$\lambda_{ir}=\sum_{k=1}^{p}\beta_{k}X_{ik}+\varepsilon_{i},$

where $\varepsilon_{i}\sim N(0,\sigma^{2})$ are Gaussian independent errors,
$X_{i1},\dots,X_{ip}$ are independent features to predict Team $i$ strength,
and $\beta_{1},\dots,\beta_{p}$ are the features coefficients.

Following the literature review, time-invariant features will not be included
in the modelling. This is because most of the strength features, as described
below, are taken as differentials, meaning their value changes for each game
relative to the opposite team. Moreover, measures of game difficulty beyond
the AT_HOME effect are all player-specific and time-variant. Consequently,
because team strength is dependent on player-specific features that change for
each game, the BT model will no longer return fixed estimates of team
abilities, as these are not explained by the binomial counts of outcomes but
by predictors.

###  3.3 Construction of features

The ladder position, that is the position after the previous game, is firstly
added to the game results. The value is transformed into differentials
following Robertson and Joyce (2018) as it is more predictive of game outcomes
compared to the absolute value. As in Fahey-Gilmour et al. (2019) and
Robertson and Joyce (2018), the differentials of the ladder position of the
last year are also calculated for both teams.

Team form features are used to assess short and long-term performance
throughout the season. These include whether a team won their last game, the
number of games won over the last 4 games, the cumulative wins over the season
and the consecutive wins and losses. Only the differential from the cumulative
wins is taken.

Differentials for the points in favour, points against and the percentage
ratio of the first variable to the latter are calculated as the absolute
difference. PIs are aggregated for each game and team, summed to be taken as
cumulatives over the season and the last 4 games, and calculated as
differentials. Essentially, the past performance of two competing teams is
compared.

Finally, variables to assess match difficulty are calculated, particularly
binary variables assessing whether the team is playing at home, at their home
ground or if they have travelled interstate.

###  3.4 Description of the experiments

####  3.4.1 Experiment 1: Standard Bradley-Terry

The BradleyTerry2 R package was used to fit the standard BT specification on
each season and an additional dataset containing all games from seasons 2015
to 2023. The model was further trained on windows of 2, 3 and 4 seasons to
explore cross-seasonal variations in team strengths. The target variable (WIN)
indicated whether the team won the game (1) or not (0), excluding draws as
explained before. The goodness of fit was assessed with the Akaike Information
Criterion (AIC). To simplify the interpretation of the results, for each
window of seasons, the reference team/level was chosen as the team which had
an ’average performance’ (half wins/half losses).

Classification accuracy was calculated for each model on the predicted
probability of the Home Team winning in the training dataset and the test
dataset for the following season. For the models trained on more than one
season, the predicted season was the following to the last season in the
training data. A team was predicted to win whenever their probability was
higher than 0.5. Figure 3. summarises the training and testing strategy for
this experiment.

####  3.4.2 Experiment 2: Contest-specific effects

This experiment makes no changes to the model training and testing explained
in Section 3.4.1, with the difference of the added AT_HOME effect, estimated
as a parameter separate from the team strengths.

####  3.4.3 Experiment 3: Team-specific, time-variant features

In this experiment, models are trained on games for each season and used to
predict all the games in the following, using windows of one or two seasons.
The target variable remains the same and the predictive ability is estimated
with the classification accuracy.

The features used for training can be divided into three categories: Match
Difficulty (e.g.: playing home or away), PIs and Form (measures teams’
performance e.g.: wins over last 4 games). Models are further trained on two
sets of features: one with the cumulative performance over the season, and the
other with the cumulative performance over the last four games.

Following the recommendations in the literature to perform feature selection
(Fahey-Gilmour et al., 2019), a model is trained on one season or window of
seasons for each individual feature which, if found to be significant at the
5% level, is added to a set of final features. A final model is trained on the
significant features, performing backward elimination of the feature that has
the highest p-value above 0.05 until all the remaining features are
significant. The features included in the final model are recorded along with
the features that were found to be significant individually, although these
are not part of the model used for predictions. Figure 4 illustrates the
training process.

####  3.4.4 Experiment 4: Round-by-round predictions

This experiment expands on the previous models, changing the prediction
strategy. The reason behind it is that, in a real scenario, models can be
retrained throughout the season with updated information, instead of
predicting the full season in advance with historical data. We now predict
games in the test season, updating the models throughout the testing process,
which is the closest simulation of a BT model that would allow for time-
varying coefficients. Predictions are made round-by-round instead of game-by-
game since it is common for AFL games to overlap each other.

We test four different strategies to perform round-by-round predictions. The
Addition strategy trains a model on a single season and tests the model on the
first round of the following season. Once the games are predicted, data from
that round is added to the training data and the model is retrained. The model
is tested and retrained for each round until the Grand Final. The Substitution
strategy is similar, although the data from the corresponding round of the
previous season is discarded during the retrain to give more weight to the
current season.

In the Incremental strategy, the first three rounds of the test data are
predicted with the model trained on the previous season since most of the
differential features will amount to 0. From the third round onwards, a model
is built on the tested rounds: if no significant features are found, the
predictions will be those from the previous season model; otherwise, the model
with significant features will be used to predict the subsequent rounds.
Figures 5-7 illustrate the three strategies.

Finally, the Majority Voting strategy combines the predictions from these
three strategies along with the models in Experiments 2 and 3, making a final
prediction by majority voting. A team is predicted to win if at least three of
the predictions from the chosen models predict it to win.

##  4 Results

###  4.1 Team Strengths Based on Game Outcomes (Experiment 1)

The estimated strength coefficients for the standard BT model trained on
windows of one season are summarised in Table 1. TABLES 12 to 14. display the
coefficients for the models trained on windows of two, three and four seasons.

Table 1: Estimated strength coefficients with the standard Bradley-Terry
model, fitted to single seasons (2015-2023) and all available data.
Coefficients found to be significant at the 5% level are in bold and
underlined. The coefficient for the reference team is 0.00.

Team | Season
---|---
| 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2015-23
Adelaide | 0.14 | 1.55 | 1.15 | 0.04 | -0.29 | -1.58 | -0.77 | -1.07 | 0.00 | 0.00
Brisbane Lions | -2.34 | -2.08 | -1.27 | -1.74 | 0.72 | 1.80 | 0.75 | 0.78 | 1.31 | -0.09
Carlton | -2.26 | -0.94 | -1.00 | -3.03 | -0.99 | -0.28 | -0.56 | 0.04 | 0.61 | -0.63
Collingwood | -0.79 | -0.21 | -0.26 | 0.66 | 0.81 | 0.43 | -0.95 | 0.82 | 1.75 | 0.25
Essendon | -1.57 | -2.12 | 0.06 | 0.10 | 0.09 | -0.40 | -0.06 | -0.95 | -0.13 | -0.35
Fremantle | 1.03 | -1.55 | -0.53 | -0.91 | -0.43 | -0.28 | -0.13 | 0.76 | -0.36 | -0.16
Gold Coast | -2.20 | -1.35 | -1.17 | -2.27 | -2.02 | -0.74 | -0.76 | -0.58 | -0.48 | -0.95
Geelong | 0.00 | 1.86 | 0.90 | 0.20 | 0.84 | 1.22 | 1.14 | 1.68 | -0.10 | 0.66
Greater Western Sydney | -0.67 | 1.58 | 0.89 | 0.40 | 0.56 | 0.00 | 0.39 | -1.20 | 0.45 | 0.24
Hawthorn | 0.92 | 1.63 | -0.07 | 0.41 | 0.08 | -0.87 | -0.65 | -0.96 | -0.97 | 0.00
Melbourne | -1.36 | -0.01 | 0.17 | 0.42 | -1.32 | 0.28 | 2.04 | 0.83 | 0.73 | 0.20
North Melbourne | 0.20 | 0.75 | -1.09 | -0.25 | -0.16 | -1.58 | -1.48 | -2.83 | -2.25 | -0.66
Port Adelaide | 0.02 | 0.00 | 0.46 | 0.00 | 0.00 | 1.80 | 1.36 | -0.36 | 0.96 | 0.39
Richmond | 0.31 | -0.49 | 1.09 | 1.33 | 1.25 | 1.67 | -0.13 | 0.07 | -0.21 | 0.49
Saint Kilda | -1.60 | 0.44 | 0.07 | -1.86 | -0.68 | 0.61 | 0.00 | 0.00 | 0.15 | -0.22
Sydney | 0.50 | 1.82 | 0.60 | 0.44 | -0.70 | -0.87 | 0.75 | 0.96 | 0.14 | 0.36
Western Bulldogs | 0.05 | 1.76 | 0.00 | -0.93 | 0.12 | 0.43 | 1.21 | 0.05 | 0.09 | 0.26
West Coast | 1.05 | 1.38 | 0.29 | 1.15 | 0.70 | 0.96 | -0.17 | -2.79 | -2.22 | 0.14

Not all strength coefficients in Table 1 are significant in each season, with
seasons like 2017 having no teams being significantly stronger or weaker than
the reference (average) team. The direction of the coefficients is also not
constant: notice how the significant strengths in 2015 are all negative while
those in 2020 are positive. Finally, while the window of outcomes from 2015 to
2023 does mark the strengths of teams that have “historically” performed worse
(Gold Coast) or better (Geelong) as significant, it estimates the strengths of
teams with an evolving performance (Brisbane Lions or West Coast) close to 0.

The significance of strength estimates varies when considering windows of more
than one season. Windows of two seasons (Table 12) will show Richmond being
significantly stronger from 2017 to 2020 while, in the previous analysis, they
were only significant in 2020; or Carlton, who were consistently weaker from
2015 to 2019, and not just in 2015 and 2018. Windows covering three (Table 13)
or four (Table 14) seasons support the previous findings, confirming some
teams a significantly stronger than others throughout the window (Richmond,
Geelong) and capturing changing results in others (Brisbane Lions).

Table 2 shows the AIC and classification accuracy of the fitted models. As to
the goodness of fit, the AIC is similar within windows, except for the 2020
season, where it decreases, while increasing for windows of more seasons. The
classification accuracy over the season where the model was trained is lowest
at 65.38% for 2017 and highest at 78.38% for 2016. The metric progressively
decreases with the windows of more seasons (Table 15).

The classification accuracy over the tested seasons is lower than that in the
training set, ranging around 60% for windows of one season and 60.98% for all
available data. On average it decreases as the windows become larger (Table
15), although this changes for some seasons like 2018 (65.76%) and 2023
(65.26%), with the highest accuracies achieved with a window of three seasons.

Table 2: AIC and classification accuracy for the standard Bradley-Terry model,
fitted to windows of one season (2015-2023).

Window: 1 season
---
Train Season | Test Season | Train AIC | Train Accuracy | Test Accuracy
2015 | 2016 | 237.07 | 71.20% | 61.20%
2016 | 2017 | 224.21 | 78.38% | 57.46%
2017 | 2018 | 269.16 | 65.38% | 63.04%
2018 | 2019 | 233.99 | 75.54% | 60.54%
2019 | 2020 | 269.21 | 69.73% | 63.83%
2020 | 2021 | 196.88 | 74.83% | 60.22%
2021 | 2022 | 254.23 | 70.33% | 58.15%
2022 | 2023 | 237.35 | 75.00% | 61.58%
2023 |  | 261.10 | 72.90% |

###  4.2 Effect of home team designation (Experiment 2)

The AT_HOME effect was estimated along with the strength coefficients of each
team. The results are summarised in Table 3 and Tables 17 to 19. While not
significant in all seasons, the AT_HOME effect was significant and positive
when considering all available data, which translates as an advantage to the
Home Team under the BT model. There are no major changes to the strength
estimates. AT_HOME becomes significant for all training sets from the windows
of three seasons onwards.

Table 4 shows the AIC and classification accuracy of the fitted models. The
AIC slightly decreases compared to the models in Experiment 1, denoting an
increase of fit, with the classification accuracy over train showing a slight
increase for all available data (61.92%, Table 20). The classification
accuracy also improves over most test seasons, reaching highs of 67.37% for
the 2023 season.

Table 3: Estimated AT_HOME Coefficient with the Bradley-Terry expansion for
contest-specific effects, fitted to single seasons (2015-2023) and all
available data. Significant coefficients at the 5% level are in bold.

Season | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2015-23
---|---|---|---|---|---|---|---|---|---|---
Feature (AT_HOME) | 0.15 | 0.63 | 0.43 | 0.25 | 0.35 | 0.35 | 0.08 | 0.62 | 0.37 | 0.29

Table 4: AIC and classification accuracy for the Bradley-Terry expansion for
contest-specific effects, fitted to windows of one season (2015-2023).

Window: 1 season
---
Train Season | Test Season | Train AIC | Train Accuracy | Test Accuracy
2015 | 2016 | 238.33 | 72.28% | 63.93%
2016 | 2017 | 214.80 | 75.68% | 62.43%
2017 | 2018 | 263.75 | 65.93% | 62.50%
2018 | 2019 | 233.93 | 77.17% | 59.46%
2019 | 2020 | 266.42 | 68.65% | 63.12%
2020 | 2021 | 195.64 | 76.22% | 60.77%
2021 | 2022 | 255.98 | 71.98% | 58.70%
2022 | 2023 | 227.32 | 78.80% | 67.37%
2023 |  | 257.97 | 72.43% |

###  4.3 Effect of team-specific, time-variant features (Experiment 3)

The features from the trained team-specific, time-variant BT expansions, along
with those features that were found to be individually significant, yet
excluded from the final models, are summarised in Table 5 and Tables 21 to 23.

Match difficulty features are significant in most seasons at the individual
level, with at least one of them being included in the model except in 2018
and 2021. INTERSTATE and AT_HOME are included in the model trained in all
available data with strong negative and positive coefficients respectively,
suggesting that teams playing interstate or away are at a disadvantage.
HOMEGROUND is not included in this model, although it appears to be
individually significant here and for individual seasons with a strong
positive value, and it is included in four of the models in windows of two
seasons. The coefficients remain similar in the models using cumulative
features from the last four games and the full season. Interaction effects
between AT_HOME and the other difficulty features were tested although they
were not found to be significant except for season 2015, and were thereby
excluded from the following experiments.

The coefficients of the features of teams’ form do not change significantly
between the models using PIs of the last four games or the season. The
differential in the ladder position at the time of the game
(LADDER_POSITION_DIFF) appears to be individually significant across seasons
with a positive coefficient, although it is never included in the model.
Moreover, the differentials in the previous season’s final ladder position
(LADDERLY_POSITION_DIFF) are included in more of the final models with a
positive estimate, especially those trained on individual seasons with
cumulatives from the previous four games. The indicator is often included in
the models trained in windows of two seasons but only until 2020-21.

The differentials in the percentage (PERCENTAGE_DIFF) are often significant
but not included in the final models. Differentials in the points in favour
(POINTSFOR_DIFF) and points against (POINTSAGAINST_DIFF) appear in models
trained in windows of one and two seasons and both sets of cumulatives, also
being included in the model trained on all data with a positive coefficient.

Whether or not a team won their previous game (LG_WON) was included in the
2023 model with a strong, positive coefficient, and it was individually
significant in the model trained on all seasons, although it was not
significant for the rest of the seasons and windows. The cumulative number of
wins (WINS_CUMULATIVE_DIFF) is significant at the individual level with a
positive coefficient for some seasons, although it is included in some final
models with a negative coefficient.

As to the performance indicators, most of them are significant at the
individual level when considering all available data regardless of the window
and encoding.

When considering PIs in their cumulative form over the previous four games,
there are no major changes to their significance between windows. The
differentials in the entries into the Forward 50 (INSIDE50_L4_CSUM_DIFF) are
only included in some of the models of the single-season windows with a
positive coefficient, while being individually significant consistently when
considering windows of two seasons. Likewise, differentials in goal shots
(GOALS_SHOTS_L4_CSUM_DIFF) are significant with a positive coefficient between
2018-20, being included in the 2019 model, and this is further confirmed in
the windows of two seasons.

Differentials in the contested possessions won at ground level over the
previous four games (GETS_GROUNDBALL50_L4_CSUM_DIFF) become significant since
2020 when considering windows of two seasons, being included in some of the
final models with a positive coefficient. The differential in intercepts
(INTERCEPTS_L4_CSUM_DIFF) is consistently significant although not included in
the final model between the 2021-23 seasons, with a positive coefficient.

Additional features that are significant when considering windows of two
seasons include the differentials in metres gained
(METRES_GAINED_L4_CSUM_DIFF), individually significant between 2016-19 with a
positive coefficient; contested possessions
(POSSESSIONS_CONTESTED_L4_CSUM_DIFF), individually between 2018-22 with a
positive coefficient; and tackles in the Forward 50 area
(TACKLES_INSIDE50_L4_CSUM_DIFF) between 2020-22 with a positive coefficient.
Likewise, differentials in the score launches (SCORE_LAUNCHES_L4_CSUM_DIFF)
are consistently significant at the individual level since 2018 and are
included in the model for the seasons 2022-23 with a positive coefficient.

When modelled as season cumulatives, the differential in cumulative goal shots
(GOALS_SHOTS_CSUM_DIFF) is significant with a positive coefficient in almost
every season from 2018 to 2022, for windows of both one and two seasons,
although it is included in the model trained in the 2017 season with a
negative coefficient. Differentials in the indicators of actions in the
Forward 50 often appear significant individually and in models for both
windows, including entries (INSIDE50_CSUM_DIFF) and marks
(MARKS_INSIDE50_CSUM_DIFF) with a positive coefficient. Differentials in
rebounds (REBOUND_INSIDE50S_CSUM_DIFF) are significant for some seasons with a
negative coefficient for both windows. Differentials in the score launches
(SCORE_LAUNCHES_CSUM_DIFF) are often significant and included in models with a
positive coefficient.

When modelled as season cumulatives, the differential in cumulative goal shots
(GOALS_SHOTS_CSUM_DIFF) is significant with a positive coefficient in almost
every season from 2018 to 2022, for windows of both one and two seasons,
although it is included in the model trained in the 2017 season with a
negative coefficient. Differentials in the indicators of actions in the
Forward 50 often appear significant individually and in models for both
windows, including entries (INSIDE50_CSUM_DIFF) and marks
(MARKS_INSIDE50_CSUM_DIFF) with a positive coefficient. Differentials in
rebounds (REBOUND_INSIDE50S_CSUM_DIFF) are significant for some seasons with a
negative coefficient for both windows. Differentials in the score launches
(SCORE_LAUNCHES_CSUM_DIFF) are often significant and included in models with a
positive coefficient.

When considering windows of two seasons, the differentials in the lost
opportunities to get the ball (CONTEST_DEFENSIVE_LOSS_CSUM_DIFF) appear to be
consistently significant at the individual level with a negative coefficient
between 2018-21. Likewise, differentials in the contested possessions at the
ground level of the Forward 50 (GETS_GROUNDBALL50_CSUM_DIFF) are individually
significant, with a positive coefficient, for almost all windows between
2016-22. Finally, both the differentials in the metres gained
(METRES_GAINED_CSUM_DIFF) and tackles (TACKLES_CSUM_DIFF,
TACKLES_INSIDE50_CSUM_DIFF) are significant and with a positive coefficient,
although the former indicator does not appear to be significant beyond the
2018-19 window.

Table 5: Estimated coefficients for the time-variant Bradley-Terry fitted to
windows of one season and with PIs encoded as cumulatives over the previous
four games (2015-2023). Significant coefficients are in bold and underlined.
Significant coefficients at the individual level only are in italics.

| Season
---|---
FEATURE | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2015-23
| MATCH DIFFICULTY
AT_HOME |  | 0.609 | 0.404 |  | 0.303 |  |  | 0.521 | 0.527 | 0.187
HOMEGROUND | 0.381 | 0.438 |  |  | 0.615 |  |  | 0.716 | 0.409 | 0.363
INTERSTATE | -0.545 | -0.443 | -0.469 |  | -0.530 | -0.705 |  | -0.515 | -0.437 | -0.268
| FORM
CONSECUTIVE_LOSSES |  |  |  |  |  |  | 0.416 |  | -0.164 | -0.139
CONSECUTIVE_WINS |  |  |  |  |  |  |  |  |  | 0.106
L4G_WINS |  |  |  |  |  |  | -0.280 |  | 0.230 | 0.299
LADDER_POSITION_DIFF | 0.039 | 0.061 | 0.038 | 0.030 |  | 0.029 |  | 0.050 |  | 0.044
LADDERLY_POSITION_DIFF | 0.047 | 0.058 | 0.025 | 0.045 | 0.031 | 0.040 | 0.036 |  | 0.045 | 0.026
LG_WON |  |  |  |  |  |  |  |  | 0.557 | 0.278
PERCENTAGE_DIFF |  |  | 0.009 | 0.007 |  |  | 0.011 | 0.012 |  | 0.009
POINTSAGAINST_DIFF |  |  | 0.002 |  |  |  | 0.002 | 0.002 | 0.001 | 0.001
POINTSFOR_DIFF | 0.001 |  |  | 0.002 | 0.003 | 0.003 |  | 0.002 | 0.001 | 0.001
| PIs
BOUNCES_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.004
CLANGERS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
CLEARANCES_CENTRE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.009
CLEARANCES_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.006
CLEARANCES_STOPPAGE_L4_CSUM_DIFF |  |  |  |  |  |  | 0.012 |  |  | 0.005
CONTEST_DEFENSIVE_LOSS_L4_CSUM_DIFF |  |  |  |  | -0.018 |  |  |  |  |
CONTEST_DEFENSIVE_LOSS_RATE_L4_CSUM_DIFF |  |  |  |  | -0.023 |  |  |  |  | -0.008
CONTEST_OFFENSIVE_WIN_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.013
CONTEST_OFFENSIVE_WIN_RATE_L4_CSUM_DIFF |  |  |  |  |  |  |  | 0.025 |  |
DISPOSALS_EFFECTIVE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
DISPOSALS_EFFICIENCY_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
DISPOSALS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.001
FREES_AGAINST_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
GETS_GROUNDBALL_L4_CSUM_DIFF |  |  |  |  |  |  | 0.006 |  |  | 0.002
GETS_GROUNDBALL50_L4_CSUM_DIFF |  |  |  |  |  |  | 0.018 | 0.014 |  | 0.012
GOALS_ACCURACY_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
GOALS_SHOTS_L4_CSUM_DIFF |  |  |  | 0.020 | 0.016 | 0.015 |  |  |  | 0.013
HANDBALLS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
HITOUTS_ADVANTAGE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  | -0.013 |
HITOUTS_ADVANTAGE_RATE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.005
HITOUTS_WIN_RATE_L4_CSUM_DIFF | 0.005 |  |  |  |  |  |  |  | -0.006 | 0.002
INSIDE50_L4_CSUM_DIFF |  | 0.013 |  | 0.014 |  |  |  |  | 0.009 | 0.004
INTERCEPTS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.005
KICK2HANDBALL_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.400
KICKS_EFFECTIVE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.001
KICKS_EFFICIENCY_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
KICKS_L4_CSUM_DIFF |  |  |  | 0.004 |  |  |  |  |  | 0.002
MARKS_CONTESTED_L4_CSUM_DIFF |  |  |  | 0.017 |  |  |  |  |  | 0.010
MARKS_INSIDE50_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.010
MARKS_INTERCEPT_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.009
MARKS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
MARKS_ONLEAD_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
METRES_GAINED_L4_CSUM_DIFF |  |  |  | 0.000 |  |  |  |  |  | 0.000
ONE_PERCENTERS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.002
POSSESSIONS_CONTESTED_L4_CSUM_DIFF |  |  |  |  |  |  |  | 0.008 |  | 0.004
POSSESSIONS_CONTESTED_RATE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.019
POSSESSIONS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.001
POSSESSIONS_UNCONTESTED_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
PRESSURE_DEFENSEHALF_L4_CSUM_DIFF |  | -0.002 |  | -0.003 |  |  |  |  |  | -0.002
PRESSURE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
REBOUND_INSIDE50S_L4_CSUM_DIFF | -0.009 |  |  |  |  |  |  |  |  | -0.006
SCORE_LAUNCHES_L4_CSUM_DIFF |  |  |  | 0.016 | 0.012 |  |  |  | 0.012 | 0.014
SPOILS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
TACKLES_INSIDE50_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.009
TACKLES_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
TURNOVERS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |  |

Table 6 summarises the classification accuracies for the trained models,
tested on all games of the following season. Compared to the models in the
previous experiment, it seems that the fit is better, at least considering all
available data, with the classification accuracy over the trained seasons
reaching 68.54% for both encodings (Table 24). The fit for individual seasons
or windows is often worse than that of the models in Experiment 2. At the
season level, both encodings achieve similar accuracies over the training data
in both windows. As to the classification accuracy over the test seasons, the
encoding for the last four games is only better until 2019 for windows of one
season, where it is surpassed by the models with the season cumulatives,
reaching accuracies as high as 69.38% for 2020. For windows of two seasons,
both encodings achieve similar accuracies over the test data, although some of
these models improve the accuracy of those trained on single seasons.

Table 6: Classification accuracy for the Bradley-Terry team-specific, time-
variant expansion, fitted to windows of one season (2015-2023) with both
encodings of PIs.

Window: 1 season
---
|  | Last 4 games cumulative | Season cumulative
Train Season | Test Season | Train Accuracy | Test Accuracy | Train Accuracy | Test Accuracy
2015 | 2016 | 71.08% | 67.15% | 67.16% | 62.80%
2016 | 2017 | 71.50% | 60.29% | 74.40% | 59.31%
2017 | 2018 | 62.75% | 66.02% | 70.10% | 46.60%
2018 | 2019 | 71.36% | 61.84% | 65.53% | 59.00%
2019 | 2020 | 70.05% | 65.62% | 66.18% | 69.38%
2020 | 2021 | 68.75% | 62.25% | 73.12% | 65.20%
2021 | 2022 | 68.63% | 61.17% | 66.67% | 58.25%
2022 | 2023 | 72.82% | 64.02% | 72.33% | 64.95%
2023 |  | 70.56 |  | 69.16% |

###  4.4 Round-by-Round Prediction Accuracy (Experiment 4)

Table 7 compares the classification accuracy of the strategies mentioned
Section 3.4.4 with the results obtained from the already discussed models.
When encoding PIs as cumulatives of the last four games, the Majority Voting
strategy achieves the highest classification accuracy in seasons 2017, 2021
and 2022, and a high of 69.57% for 2016. The Addition strategy achieves the
best accuracies in seasons 2018, 2019 and 2019, while the highest accuracy
(70.05%) is achieved by the Incremental model in season 2015, although it
performs considerably worse for the remaining seasons. The Substitution and
Contest-Specific models never achieve the highest accuracies.

Table 7: Classification accuracy for the Bradley-Terry team-specific, time-
variant (TS-TV) expansion, fitted to windows of one season (2015-2023) with
both encodings of PIs. The highest accuracies for each season are underlined
and in bold.

|  |  | Last 4 games cumulative
---|---|---|---
Train Season | Test Season | Contest-Specific | TS-TV | Addition | Substitution | Incremental | Majority Voting
2015 | 2016 | 63.93% | 67.15% | 66.18% | 67.15% | 70.05% | 69.57%
2016 | 2017 | 62.43% | 60.29% | 61.76% | 59.31% | 51.96% | 63.76%
2017 | 2018 | 62.50% | 66.02% | 67.48% | 61.65% | 64.56% | 64.56%
2018 | 2019 | 59.46% | 61.84% | 66.18% | 62.80% | 58.94% | 65.70%
2019 | 2020 | 63.12% | 65.62% | 65.00% | 60.00% | 55.63% | 61.88%
2020 | 2021 | 60.77% | 62.25% | 61.27% | 60.78% | 57.85% | 63.73%
2021 | 2022 | 58.70% | 61.17% | 61.65% | 60.68% | 60.68% | 65.05%
2022 | 2023 | 67.37% | 64.02% | 67.76% | 64.49% | 53.27% | 64.49%
|  |  | Season cumulative
Train Season | Test Season | Contest-Specific | TS-TV | Addition | Substitution | Incremental | Majority Voting
2015 | 2016 | 63.93% | 62.80% | 67.15% | 64.25% | 71.50% | 65.22%
2016 | 2017 | 62.43% | 59.31% | 57.35% | 61.27% | 50.49% | 60.29%
2017 | 2018 | 62.50% | 46.60% | 65.53% | 58.74% | 66.50% | 64.08%
2018 | 2019 | 59.46% | 59.90% | 64.25% | 62.32% | 57.49% | 64.25%
2019 | 2020 | 63.12% | 69.38% | 68.12% | 61.88% | 60.63% | 66.25%
2020 | 2021 | 60.77% | 65.20% | 60.29% | 55.39% | 50.49% | 60.78%
2021 | 2022 | 58.70% | 58.25% | 66.99% | 65.06% | 63.11% | 67.96%
2022 | 2023 | 67.37% | 64.95% | 62.62% | 61.21% | 60.75% | 62.62%

In the season cumulative encoding, the Majority Voting model achieves worse
results, although it performs the best for 2019 and 2022. Models predicting
the full season perform best in four seasons, with the model from Experiment 3
performing better than any model from the previous encoding in seasons 2020
and 2021. The Incremental strategy achieves the highest accuracy for season
2015 (71.5%) while also performing the worst in season 2021 with 50.49%.

The number of correctly predicted matches in the Finals Series was also
computed and summarised in Table 25. With some exceptions for seasons 2019 and
2022, it seems that the models struggle to predict these games compared to
those in the Home-and-Away season.

As to the teams, the models can correctly predict most of the outcomes for
some of the weakest and strongest teams. For instance, predictions for North
Melbourne are particularly more accurate than for other teams between 2021-23,
a period where the team only won nine games in total. This is also the case
for the Brisbane Lions (2015-18) and Richmond (2018-19). However, there are
cases where the predictions for the ‘average’ teams are more accurate, meaning
that, at this stage, the ability of these expansions to predict some teams
better than others is inconclusive (Table 26).

##  5 Discussion

###  5.1 Summary and discussion of findings

The findings for the standard BT model confirm that, while game outcomes alone
are not enough to explain why a team is significantly stronger than another,
the BT model can successfully identify teams that are significantly stronger
or weaker than the average. For instance, it is able to capture North
Melbourne’s poor performance between 2021-23, the Brisbane Lions’ evolution
from poor to better results, and the best and worst teams in the 2023 season.
Increasing the windows to cover more seasons captures performances that are
significantly better in the medium term, like Richmond’s between seasons
2017-20, although windows with a higher number of seasons risk averaging out
evolving performances, like those of the Brisbane Lions or West Coast. This
implies that team strengths change gradually in the medium term, possibly in a
window of three seasons, and that advantages for weaker teams in the draft are
not necessarily reflected in the subsequent seasons.

The worsening predictive ability of the standard BT model as the windows
enlarge is natural given that the model only considers outcomes, thereby
missing cross-seasonal changes in teams’ performance which might be continued
in the predicted season.

The significance of the AT_HOME effect echoes the findings in Lazarus et al.
(2018) and Robertson and Joyce (2018), meaning playing as the Home Team
creates a positive advantage for the team. Since the inclusion of the effect
results in slight changes to the strength estimates, it is safe to assume that
Home teams enjoy the advantage regardless of their strength. The increase in
accuracy for both the train and test seasons confirms that the AT_HOME
advantage is explanatory and predictive of game outcomes.

The significance of the other difficulty features in Experiment 3 regardless
of the encoding of other features suggests that they are independent from
other effects. In particular, playing at their home venue creates an advantage
for the team, while playing interstate results in a significant disadvantage,
supporting the findings in Robertson and Joyce (2018).

In terms of form, while the difference in the ladder position is estimated to
grant an advantage to teams placing higher on the ladder at the time of the
game, the effect of the differential in the last ladder position of the
previous season seems to grant a stronger advantage, coinciding with the
findings of Robertson and Joyce (2018) and Fahey-Gilmour et al. (2019). This
was expected after Experiments 1 and 2 confirmed that strengths change
gradually, meaning the previous season’s performance will still be somehow
predictive of the current season. Having the advantage on the points in favour
and against are both associated with higher chances of winning, indicating a
team’s offensive and defensive strength respectively.

The significance of the majority of the performance indicators regardless of
their encoding in the model trained on all available data hints that the
cumulative differentials in performance indicators are significantly different
for winning and losing teams, even if they are not significant in multivariate
models. The findings contribute to the literature on the predictive ability of
these indicators encoded as differentials for forward game prediction.

In particular, having an advantage over the activity in the Forward 50 area,
both during the season and the last four games, is indicative of a team having
greater chances of winning. Indeed, a team with more entries, possessions,
marks and tackles in the Forward 50 can be considered stronger as it is more
likely to get close to the opponent’s goal posts, get the football or take a
mark (and its consequent free kick) and turn that into a goal or a behind.
Moreover, teams that have an advantage in the shots at goal and scoring chains
are naturally more likely to win since they are more likely than the other
team to score. Other significant performance indicators were the metres
gained, hinting that teams where players move more are more likely to win,
perhaps because it is indicative of them moving across the field into the
Forward 50; and the rebounds, with weaker teams having higher rebounds
possibly because they are more likely to have moved the ball from their
Defensive area to the Midfield, indicating they were pressured by the opposing
team.

###  5.2 Changing coefficients and eras

Something noticeable about the results in Experiment 3 is that the effect of
some performance indicators seems to change direction or are counterintuitive.
For instance, having the advantage over the cumulative wins was associated
with a decrease in the winning chance for seasons 2017, 2018 and the 2019-20
and 2022-23 windows. This can be partly explained by the modelling strategy
and the fixtures in the AFL.

It is possible that the early stages of the seasons, where the team
differentials are lower, are skewing the results. Moreover, if a strong team
by the end of the season loses a game, their advantage in their differentials
will also distort the direction of the performance indicator. Indeed, it may
well be possible that a losing team has the advantage in cumulative wins if it
faced weaker teams in the earlier rounds, or their opponent faced stronger
teams.

Moreover, the inclusion of the Finals Series in the modelling, where only the
strongest teams face each other might also contribute to the changing
coefficients, especially if the teams that placed lower on the ladder manage
to make it far into the Series.

The findings also contribute to the discussion of ‘eras’ presented in the
literature review. In particular, it seems that teams with an advantage in
scoring (points in favour, goal shots, score launches) were more likely to win
their subsequent matches between seasons 2018-20. This implies that weaker
teams in this era are more likely to win over stronger teams if they have an
advantage in scoring differentials.

Furthermore, being able to pressure the opponent in the Forward 50 seems to
gain relevance from season 2020 onwards, with stronger teams having the
advantage in the entries and groundballs, along with higher season cumulative
in marks and tackles in this area. Both ‘eras’ potentially identify teams
prioritising offensive strategies, with the first one focusing on scoring and
the second one favouring a stronger presence in the Forward 50.

###  5.3 Predictive ability of the Bradley-Terry expansions

When considering all available data, the fit of the Bradley-Terry model
significantly improves with the inclusion of team-specific, time-variant
features known before the game. Their predictive ability also improves
compared to the standard specification and the expansion allowing for contest-
specific effects, hinting that, in the AFL, outcomes can be predicted by a
team’s strength as explained by its form, cumulative performance indicators
and match difficulty.

Although dependent on the season and the prediction strategy, the Bradley-
Terry expansions can successfully predict up to 71.5% of the games. Predicting
games round-by-round, allowing for models to be updated or trained iteratively
on the predicted season, often results in higher accuracies over the predicted
games, although the models predicting the full season, whether it is with
contest-specific effects or team-specific, time-variant features, still
perform the best on some occasions. Strategies combining the previous models
by majority voting result in stable accuracies above 60%, reaching up to
67.96%.

In conclusion, it appears that interpretable models like BT models might be
feasible to predict game results in advance and design data-driven strategies
in the AFL.

###  5.4 Limitations and future lines of research

The results are limited to the male competition of the AFL, seasons 2015 to
2023, and it could be possible that the features found to be significant do
not correspond to those in earlier seasons, the female competition (AFLW) or
national leagues of football.

Moreover, the worsening accuracy in the Finals Series might imply that the
inclusion of these games for modelling is not optimal: the Series pitches the
strongest teams, so it might not be representative of an average game.
However, given that the Finals only account for nine games, it is complicated
to model them separately without experiencing the disadvantages of a reduced
sample size.

Given the better predictive performance on significantly stronger and weaker
teams, it would be interesting to confirm whether the BT model with team-
specific, time-variant features struggles to predict games pitching teams that
are not significantly stronger or weaker. So far, results are inconclusive
because they might not be related to the overall strength of the team but due
to inter-seasonal changes in strengths (e.g.: teams performing significantly
different than in the season before) or even winning and losing streaks.
Clarifying this aspect would help review the modelling approaches or encoding
of variables so that the models can predict teams equally well regardless of
their strength.

Regarding the use of the BT models, it would be rational to study their
performance on the backward prediction of games, this is, predicting game
outcomes after the match takes place, so as to compare the model with the
existing ones in the literature. Moreover, the results of the fitted models
are promising enough to study the performance of the BT expansions with other
combinations of predictions beyond majority voting, or new features from
commercial providers, like network data. Finally, it would also be interesting
to replicate the analysis in this thesis with other machine learning models to
confirm if the same features are found to be significant and compare their
predictive performance. From a more technical point of view, it would also be
interesting to investigate the use of more general BT models, for instance
those that embed model selection using LASSO regularization (for instance,
using the BTLLasso R package of Schauberger and Tutz, 2019), or mixed-effect
models.

On another note, the BT expansions are limited to modelling game outcomes. AF,
however, differs from other sports in the scoring, as teams can reach well
beyond 100 points in a game, with score margins also ranging from a few points
to dozens. BT models simply ignore this granularity in the results, so it
would be interesting to model the score margin or the number of goals and
behinds with pre-game variables. Hierarchical Bayesian (Manderson et al.,
2018) and Poisson (Tsokos et al., 2019) models have already been applied to
predict scoring and margins in sports, so it would be worth examining whether
these features can be predicted before the game and whether they improve our
results.

##  6 Conclusions

Our findings showcase that the various BT models can be used to predict games’
outcomes in the AFL using only pre-game data. Furthermore, they provide an
interpretable understanding of team strengths and the impact of different pre-
game features on match outcomes.

The model can identify the teams that are significantly stronger or weaker,
both in single years and windows of multiple seasons. The significance of
strengths across these windows, along with the advantage generated by a higher
ladder position in the season before, suggests that team performance does not
change drastically year-to-year, but gradually in a window of about three
years.

Match difficulty features are confirmed to affect the winning chances of a
team independently of its strength, with playing as the Home Team and in the
home ground increasing them and playing interstate decreasing them. Teams with
the advantage over the points in favour and against are also considered
stronger. Finally, the differentials in cumulatives of performance indicators
can be indicative of winning teams, in particular, leading the activity in the
Forward 50, goal shots and scoring.

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##  Appendix A Summary of works on machine learning approaches in AF

Work |  Models |  Features |  Data |  Comments
---|---|---|---|---
Braham and Small (2018) |  Linear Regression |  Differentials in mean betweenness last 4 games, outdegree |  2014 AFL Season (207 games). From Champion Data |  Games of AF can be modelled as passing networks, with players as nodes and weighted edges as passes
Fahey-Gilmour et al. (2019) |  GLM with elastic net regularization |  Differentials ladder position last season, player-based and team-based rating. Pre-game features |  2013-18 AFL Season (1,241 games). From fitzRoy package. Player data from Champion Data |  Classify features as team-related and game-related. Non-linear models and approaches including feature selection perform better
Fransen et al. (2022) |  Binomial generalized linear mixed effects regression |  Linear combinations of network variables representing connectedness, in-degree variability, out-degree variability |  Network data from Champion Data (1,629 observations) |  Combine network measures of passing networks as connectedness, in-degree variability and out-degree variability. One-unit increases in connectedness increase the probability of winning by 5.3%
Lane et al. (2020) |  Calculate z-scores of offensive and defensive variables |  Offensive (inside 50s, metres gained, etc.) and defensive features (tackles, rebound 50s, clangers, etc.) |  Performance Indicator Data from AFL seasons 1999-2019 |  Identify eras in the AFL with significant differences in PIs. They identify an era of an offensive game (2007-08) moving to a defensive game (until 2011) with more tackles and disposals but lower scores
Lazarus et al. (2018) |  Logistic mixed-effect regression |  Playing Home/Away, travelling, age and weight differentials, days between games. |  Data for AFL seasons 2000-13 (5,109 games). From AFL Tables |  Older and heavier teams are found to have significantly yet slightly higher chances of winning. Playing as the away team significantly yet slightly decreases the chances of winning
Manderson et al. (2018) |  Bayesian hierarchical model with Skellam distribution |  Score, goals and behinds for each team. |  Home-and-Away data from AFL seasons 2013-15. From Footywire |  Pre-game prediction of the number of goals and behinds separately. It performed slightly worse in the last games of the season
Robertson et al. (2016) |  Logistic regression |  Differentials in Performance Indicators (kicks, goal conversions, inside 50s, etc.) |  Performance Indicator data from AFL 2013-14 Season (396 games). Unspecified freely available sources |  81% of teams with a kick differential above -1 won their games. 90% of teams with higher additional kicks and goal conversion won their games. Differentials in the inside 50s, marks, marks inside 50s and contested possessions were the most important predictors.
Robertson and Joyce (2018) |  Logistic regression |  Number of wins over the past 4 games, and differentials in ladder rankings from the current and previous seasons |  AFL difficulty factors from the 2014 pre-season (198 games). From Champion Data and AFL Stats |  Teams playing away show decreased chances of winning, especially if they play interstate
Sargent and Bedford (2013) |  Linear regression |  Team ratings based on eigenvector centrality |  Games from AFL 2011 season, Geelong Football Club |  Higher team connectedness increases the score margin. The score margin can be predicted with pre-game connectedness values, to the point that the individual impact of players can be estimated
Sargent et al. (2022) |  Linear mixed effects model |  Sleep time, sleep efficiency, time between sleeping and waking up |  Sleep data from 37 male AFL players |  Confirm that players sleep less when playing interstate. Mention the lack of studies relating poorer sleep to game outcomes
Woods et al. (2017) |  Non-metric multidimensional scaling |  Handballs, disposals, uncontested possessions, clangers, marks |  Performance Indicators from AFL 2001-15 seasons. From Champion Data |  Identify eras in the AFL: a ‘possession’ era (2005-09 seasons), a ‘defensive’ era (2010-13) and a ‘repossession’ (2014-onwards)
Young et al. (2019b) |  Parametric tests for network measures |  Edge count, edge density, average path length, degree centrality, eigenvector centrality, betweenness centrality, transitivity |  Games from AFL 2009-16 seasons (1,516 games). From Champion Data |  Create passing networks based on player interactions. No significant differences are found in the betweenness centrality. Other network measures were significant but only slightly correlated to the score margin.
Young et al. (2019a) |  Random Forest |  Differentials in the time in possession and meters gained, along with relative disposals, Inside 50s, Marks Inside 50, along the regular Marks and Contested Possessions |  Performance Indicator data from AFL 2001-16 seasons. From Champion Data |  Raise concerns about the lack of consensus on the identification of eras in the AFL
Young et al. (2020) |  Decision trees and GLMs |  Differentials in metres gained, time in possession, kicks |  Performance Indicator data (52 PIs) from AFL 2009-16 seasons (1,516 games). From Champion Data. 14 Tactical Indicators form event data representing passes |  Tactical features are more important but they do not increase accuracy

##  Appendix B Glossary of the used features

Table 8: Glossary of the used features - Part I.

Type |  Variable |  Description
---|---|---
TARGET |  WIN |  Indicates whether the team won (1) or lost (0)
TARGET |  AWAY_WIN |  Indicates whether the Away team won (1) or lost (0)
TARGET |  HOME_WIN |  Indicates whether the Home team won (1) or lost (0)
MATCH DIFFICULTY |  AT_HOME |  Indicates whether the team was designated as the Home Team (1) or the Away Team (0)
MATCH DIFFICULTY |  HOMEGROUND |  Indicates whether the team was played at their Home Ground (1) or not (0)
MATCH DIFFICULTY |  INTERSTATE |  Indicates whether the team was played outside their State (1) or not (0)
FORM |  CONSECUTIVE_LOSSES |  Number of consecutive losses
FORM |  CONSECUTIVE_WINS |  Number of consecutive wins
FORM |  L4G_WINS |  Number of wins over the previous 4 games
FORM |  LADDER_POSITION_DIFF |  Differential in ladder position compared to the other team at the time of the game
FORM |  LADDERLY_POSITION_DIFF |  Differential in ladder position of last year compared to the other team
FORM |  LG_WON |  Indicates whether the team won their previous game (1) or not (0)
FORM |  PERCENTAGE_DIFF |  Differential in Points For to Points Against ratio compared to the other team
FORM |  POINTSAGAINST_DIFF |  Differential in cumulative points scored against the team compared to the other team
FORM |  POINTSFOR_DIFF |  Differential in cumulative points scored in favour of the team compared to the other team
FORM |  WINS_CUMULATIVE_DIFF |  Differential in cumulative wins compared to the other team
PI |  BOUNCES_L4_CSUM_DIFF |  Differential in the cumulative sum of bounces over the previous 4 games, compared to the other team
PI |  CLANGERS_L4_CSUM_DIFF |  Differential in the cumulative sum of clangers (mistakes) over the previous 4 games, compared to the other team
PI |  CLEARANCES_CENTRE_L4_CSUM_DIFF |  Differential in the cumulative sum of centre clearances (clearing the centre area) over the previous 4 games, compared to the other team
PI |  CLEARANCES_L4_CSUM_DIFF |  Differential in the cumulative sum of clearances (clearing the centre or stoppage area) over the previous 4 games, compared to the other team
PI |  CLEARANCES_STOPPAGE_L4_CSUM_DIFF |  Differential in the cumulative sum of stoppage clearances (clearing the stoppage area) over the previous 4 games, compared to the other team
PI |  CONTEST_DEFENSIVE_LOSS_L4_CSUM_DIFF |  Differential in the cumulative losses of one-to-one contests (moments where two opposing players can get the ball) over the previous 4 games, compared to the other team
PI |  CONTEST_DEFENSIVE_LOSS_RATE_L4_CSUM_DIFF |  Differential in the rate of losses of one-to-one contests (moments where two opposing players can get the ball) over the previous 4 games, compared to the other team
PI |  CONTEST_OFFENSIVE_WIN_L4_CSUM_DIFF |  Differential in the cumulative wins of one-to-one contests (moments where two opposing players can get the ball) over the previous 4 games, compared to the other team
PI |  CONTEST_OFFENSIVE_WIN_RATE_L4_CSUM_DIFF |  Differential in the rate of wins of one-to-one contests (moments where two opposing players can get the ball) over the previous 4 games, compared to the other team
PI |  DISPOSALS_EFFECTIVE_L4_CSUM_DIFF |  Differential in the cumulative sum of successful disposals (kicks and handballs) over the previous 4 games, compared to the other team
PI |  DISPOSALS_EFFICIENCY_L4_CSUM_DIFF |  Differential in the rate of successful disposals (kicks and handballs) over the previous 4 games, compared to the other team
PI |  DISPOSALS_L4_CSUM_DIFF |  Differential in the cumulative sum of disposals (kicks and handballs) over the previous 4 games, compared to the other team
PI |  FREES_AGAINST_L4_CSUM_DIFF |  Differential in the cumulative sum of free kicks against the team over the previous 4 games, compared to the other team
PI |  GETS_GROUNDBALL_L4_CSUM_DIFF |  Differential in the cumulative sum of contested possessions won in the ground over the previous 4 games, compared to the other team
PI |  GETS_GROUNDBALL50_L4_CSUM_DIFF |  Differential in the cumulative sum of contested possessions won in the ground of the Forward 50 area over the previous 4 games, compared to the other team
PI |  GOALS_ACCURACY_L4_CSUM_DIFF |  Differential in the goals-to-goal shots ratio over the previous 4 games, compared to the other team

Table 9: Glossary of the used features - Part II.

Type |  Variable |  Description
---|---|---
PI |  GOALS_SHOTS_L4_CSUM_DIFF |  Differential in the cumulative sum of goals over the previous 4 games, compared to the other team
PI |  HANDBALLS_L4_CSUM_DIFF |  Differential in the cumulative sum of handballs over the previous 4 games, compared to the other team
PI |  HITOUTS_ADVANTAGE_L4_CSUM_DIFF |  Differential in the cumulative sum of hitouts to advantage (knocking the ball to a teammate in a contest after a stoppage) over the previous 4 games, compared to the other team
PI |  HITOUTS_ADVANTAGE_RATE_L4_CSUM_DIFF |  Differential in the ratio of hitouts to advantage to hitouts over the previous 4 games, compared to the other team
PI |  HITOUTS_WIN_RATE_L4_CSUM_DIFF |  Differential in the ratio of contests with a hitout win to contests over the previous 4 games, compared to the other team
PI |  INSIDE50_L4_CSUM_DIFF |  Differential in the cumulative sum of entries into the Forward 50 area over the previous 4 games, compared to the other team
PI |  INTERCEPTS_L4_CSUM_DIFF |  Differential in the cumulative sum of intercepts (taking the ball from the other team) over the previous 4 games, compared to the other team
PI |  KICK2HANDBALL_L4_CSUM_DIFF |  Differential in the ratio of kicks to handballs over the previous 4 games, compared to the other team
PI |  KICKS_EFFECTIVE_L4_CSUM_DIFF |  Differential in the cumulative sum of successful kicks over the previous 4 games, compared to the other team
PI |  KICKS_EFFICIENCY_L4_CSUM_DIFF |  Differential in the ratio of effective kicks to all kicks over the previous 4 games, compared to the other team
PI |  KICKS_L4_CSUM_DIFF |  Differential in the cumulative sum of kicks over the previous 4 games, compared to the other team
PI |  MARKS_CONTESTED_L4_CSUM_DIFF |  Differential in the cumulative sum of marks taken under pressure over the previous 4 games, compared to the other team
PI |  MARKS_INSIDE50_L4_CSUM_DIFF |  Differential in the cumulative sum of marks taken in the Forward 50 area over the previous 4 games, compared to the other team
PI |  MARKS_INTERCEPT_L4_CSUM_DIFF |  Differential in the cumulative sum of marks taken from the opponent over the previous 4 games, compared to the other team
PI |  MARKS_L4_CSUM_DIFF |  Differential in the cumulative sum of marks over the previous 4 games, compared to the other team
PI |  MARKS_ONLEAD_L4_CSUM_DIFF |  Differential in the cumulative sum of marks taken under no pressure over the previous 4 games, compared to the other team
PI |  METRES_GAINED_L4_CSUM_DIFF |  Differential in the cumulative sum of metres gained over the previous 4 games, compared to the other team
PI |  ONE_PERCENTERS_L4_CSUM_DIFF |  Differential in the cumulative sum of one-percenters (defensive but rare actions) over the previous 4 games, compared to the other team
PI |  POSSESSIONS_CONTESTED_L4_CSUM_DIFF |  Differential in the cumulative sum of contested possessions (possessions gained under dispute) over the previous 4 games, compared to the other team
PI |  POSSESSIONS_CONTESTED_RATE_L4_CSUM_DIFF |  Differential in the ratio of possessions won in a dispute to all disputes over the previous 4 games, compared to the other team
PI |  POSSESSIONS_L4_CSUM_DIFF |  Differential in the cumulative sum of possessions over the previous 4 games, compared to the other team
PI |  POSSESSIONS_UNCONTESTED_L4_CSUM_DIFF |  Differential in the cumulative sum of uncontested possessions (possessions gained under no pressure) over the previous 4 games, compared to the other team
PI |  PRESSURE_DEFENSEHALF_L4_CSUM_DIFF |  Differential in the cumulative sum of pressure acts in the Defense Half of the ground over the previous 4 games, compared to the other team
PI |  PRESSURE_L4_CSUM_DIFF |  Differential in the cumulative sum of pressure acts over the previous 4 games, compared to the other team
PI |  REBOUND_INSIDE50S_L4_CSUM_DIFF |  Differential in the cumulative sum of rebound 50s (moving the ball from the Defensive 50 to the midfield) over the previous 4 games, compared to the other team
PI |  SCORE_LAUNCHES_L4_CSUM_DIFF |  Differential in the cumulative sum of score launches (scoring chains after successful clearances, intercepts, free kicks, hitouts) over the previous 4 games, compared to the other team
PI |  SPOILS_L4_CSUM_DIFF |  Differential in the cumulative sum of spoils (preventing opponents from taking a mark) over the previous 4 games, compared to the other team
PI |  TACKLES_INSIDE50_L4_CSUM_DIFF |  Differential in the cumulative sum of tackles in the Forward 50 area over the previous 4 games, compared to the other team
PI |  TACKLES_L4_CSUM_DIFF |  Differential in the cumulative sum of tackles over the previous 4 games, compared to the other team
PI |  TURNOVERS_L4_CSUM_DIFF |  Differential in the cumulative sum of turnovers (losses of possession) over the previous 4 games, compared to the other team

Table 10: Glossary of the used features - Part III.

Type |  Variable |  Description
---|---|---
PI |  BOUNCES_CSUM_DIFF |  Differential in the cumulative sum of bounces over the season, compared to the other team.
PI |  CLANGERS_CSUM_DIFF |  Differential in the cumulative sum of clangers (mistakes) over the season, compared to the other team
PI |  CLEARANCES_CENTRE_CSUM_DIFF |  Differential in the cumulative sum of centre clearances (clearing the centre area) over the season, compared to the other team
PI |  CLEARANCES_CSUM_DIFF |  Differential in the cumulative sum of clearances (clearing the centre or stoppage area) over the season, compared to the other team
PI |  CLEARANCES_STOPPAGE_CSUM_DIFF |  Differential in the cumulative sum of stoppage clearances (clearing the stoppage area) over the season, compared to the other team
PI |  CONTEST_DEFENSIVE_LOSS_CSUM_DIFF |  Differential in the cumulative losses of one-to-one contests (moments where two opposing players can get the ball) over the season, compared to the other team
PI |  CONTEST_DEFENSIVE_LOSS_RATE_CSUM_DIFF |  Differential in the rate of losses of one-to-one contests (moments where two opposing players can get the ball) over the season, compared to the other team
PI |  CONTEST_OFFENSIVE_WIN_CSUM_DIFF |  Differential in the cumulative wins of one-to-one contests (moments where two opposing players can get the ball) over the season, compared to the other team
PI |  CONTEST_OFFENSIVE_WIN_RATE_CSUM_DIFF |  Differential in the rate of wins of one-to-one contests (moments where two opposing players can get the ball) over the season, compared to the other team
PI |  DISPOSALS_CSUM_DIFF |  Differential in the cumulative sum of successful disposals (kicks and handballs) over the season, compared to the other team
PI |  DISPOSALS_EFFECTIVE_CSUM_DIFF |  Differential in the rate of successful disposals (kicks and handballs) over the season, compared to the other team
PI |  DISPOSALS_EFFICIENCY_CSUM_DIFF |  Differential in the cumulative sum of disposals (kicks and handballs) over the season, compared to the other team
PI |  FREES_AGAINST_CSUM_DIFF |  Differential in the cumulative sum of free kicks against the team over the season, compared to the other team
PI |  GETS_GROUNDBALL_CSUM_DIFF |  Differential in the cumulative sum of contested possessions won in the ground over the season, compared to the other team
PI |  GETS_GROUNDBALL50_CSUM_DIFF |  Differential in the cumulative sum of contested possessions won in the ground of the Forward 50 area over the season, compared to the other team
PI |  GOALS_ACCURACY_CSUM_DIFF |  Differential in the goals-to-goal shots ratio over the season, compared to the other team
PI |  GOALS_SHOTS_CSUM_DIFF |  Differential in the cumulative sum of goals over the season, compared to the other team
PI |  HANDBALLS_CSUM_DIFF |  Differential in the cumulative sum of handballs over the season, compared to the other team
PI |  HITOUTS_ADVANTAGE_CSUM_DIFF |  Differential in the cumulative sum of hitouts to advantage (knocking the ball to a teammate in a contest after a stoppage) over the season, compared to the other team
PI |  HITOUTS_ADVANTAGE_RATE_CSUM_DIFF |  Differential in the ratio of hitouts to advantage to hitouts over the season, compared to the other team
PI |  HITOUTS_WIN_RATE_CSUM_DIFF |  Differential in the ratio of contests with a hitout win to contests over the season, compared to the other team
PI |  INSIDE50_CSUM_DIFF |  Differential in the cumulative sum of entries into the Forward 50 area over the season, compared to the other team
PI |  INTERCEPTS_CSUM_DIFF |  Differential in the cumulative sum of intercepts (taking the ball from the other team) over the season, compared to the other team
PI |  KICK2HANDBALL_CSUM_DIFF |  Differential in the ratio of kicks to handballs over the season, compared to the other team
PI |  KICKS_CSUM_DIFF |  Differential in the cumulative sum of kicks over the season, compared to the other team
PI |  KICKS_EFFECTIVE_CSUM_DIFF |  Differential in the cumulative sum of successful kicks over the season, compared to the other team
PI |  KICKS_EFFICIENCY_CSUM_DIFF |  Differential in the ratio of effective kicks to all kicks over the season, compared to the other team
PI |  MARKS_CONTESTED_CSUM_DIFF |  Differential in the cumulative sum of marks taken under pressure over the season, compared to the other team
PI |  MARKS_CSUM_DIFF |  Differential in the cumulative sum of marks over the season, compared to the other team

Table 11: Glossary of the used features - Part IV.

Type |  Variable |  Description
---|---|---
PI |  MARKS_INSIDE50_CSUM_DIFF |  Differential in the cumulative sum of marks taken in the Forward 50 area over the season, compared to the other team
PI |  MARKS_INTERCEPT_CSUM_DIFF |  Differential in the cumulative sum of marks taken from the opponent over the season, compared to the other team
PI |  MARKS_ONLEAD_CSUM_DIFF |  Differential in the cumulative sum of marks taken under no pressure over the season, compared to the other team
PI |  METRES_GAINED_CSUM_DIFF |  Differential in the cumulative sum of metres gained over the season, compared to the other team
PI |  ONE_PERCENTERS_CSUM_DIFF |  Differential in the cumulative sum of one-percenters (defensive but rare actions) over the season, compared to the other team
PI |  POSSESSIONS_CONTESTED_CSUM_DIFF |  Differential in the cumulative sum of contested possessions (possessions gained under dispute) over the season, compared to the other team
PI |  POSSESSIONS_CONTESTED_RATE_CSUM_DIFF |  Differential in the ratio of possessions won in a dispute to all disputes over the season, compared to the other team
PI |  POSSESSIONS_CSUM_DIFF |  Differential in the cumulative sum of possessions over the season, compared to the other team
PI |  POSSESSIONS_UNCONTESTED_CSUM_DIFF |  Differential in the cumulative sum of uncontested possessions (possessions gained under no pressure) over the season, compared to the other team
PI |  PRESSURE_CSUM_DIFF |  Differential in the cumulative sum of pressure acts over the season, compared to the other team
PI |  PRESSURE_DEFENSEHALF_CSUM_DIFF |  Differential in the cumulative sum of pressure acts in the Defense Half of the ground over the season, compared to the other team
PI |  REBOUND_INSIDE50S_CSUM_DIFF |  Differential in the cumulative sum of rebound 50s (moving the ball from the Defensive 50 to the midfield) over the season, compared to the other team
PI |  SCORE_LAUNCHES_CSUM_DIFF |  Differential in the cumulative sum of score launches (scoring chains after successful clearances, intercepts, free kicks, hitouts) over the season, compared to the other team
PI |  SPOILS_CSUM_DIFF |  Differential in the cumulative sum of spoils (preventing opponents from taking a mark) over the previous 4 games, compared to the other team
PI |  TACKLES_CSUM_DIFF |  Differential in the cumulative sum of tackles over the season, compared to the other team
PI |  TACKLES_INSIDE50_CSUM_DIFF |  Differential in the cumulative sum of tackles in the Forward 50 area over the season, compared to the other team
PI |  TURNOVERS_CSUM_DIFF |  Differential in the cumulative sum of turnovers (losses of possession) over the season, compared to the other team

##  Appendix C Data preparation

Following Firth and Turner (2012), game outcomes were turned into binomial
frequencies, where each entry pairs the Home and the Away Team retrieving the
absolute frequencies of wins for each team against the other. For instance,
for the AFL data used in this thesis, there is an entry pairing the Brisbane
Lions as the Home Team against Collingwood as the Away Team, and the number of
wins each team achieved against the other with this pairing. Likewise, there
will be another entry with Collingwood as the Home Team and the Brisbane Lions
as the Away Team. Since the AFL pairs 18 teams through less than 30 rounds for
our limited number of seasons, the binomial frequencies are expected to be low
for all pairs. FIGURE B.2.1. summarises the data processing for this
expansion. The data is also expanded to include an AT_HOME effect, which will
be 1 for the Home Team and 0 for the Away Team, keeping the data design as
binomial counts. This process is reflected in 1.

Figure 1: Data processing for standard and contest-specific Bradley-Terry
models.

For models fitted using time-variant features, the data has to be structured
in the form of three data frames, since contests cannot be grouped by the Home
and Away pairs: one with a set of teams playing Home, their features and
results; another with the set of Away teams; and a third dataset with time-
invariant features which, for this expansion, are none. All datasets were
complete and contained no missing values.

Figure 2: Data processing for the team-specific, time-variant Bradley-Terry
model. Data from games, merge_away and merge_PIs_complete contains entries
from both Home and Away teams. Data from PIs, PIs_sorted, ladder and last
ladder position contains entries by round and team.

##  Appendix D Description of Experiments

Figure 3: Examples of training and testing of models in Experiment 1. In the
first example, a model is trained on 2015 results and predicts all the games
in 2016. In the example below, a model is trained on a window of 4 seasons,
from 2017 to 2020, to predict all the games in 2021. Figure 4: Process for
training models in Experiment 3.  Figure 5: Example of the Addition strategy.
The model trained on 2019 games is used to predict Round 1 of the 2020 season.
Then, the model is retrained with that season and used to predict Round 2. The
process continues until the Grand Final. Figure 6: Example of the Substitution
strategy. The model trained on 2019 games is used to predict Round 1 of the
2020 season. Then, the first round of 2019 is discarded, and the model is
retrained with the remaining rounds and the first round of 2020 and used to
predict Round 2. The process continues until the Grand Final. Figure 7:
Example of the Incremental strategy. The model trained on 2019 games is used
to predict the first three rounds of the 2020 season. If the model fitted to
those rounds has no significant features, the process is repeated for the
following round. Otherwise, the newly trained model is used to predict the
subsequent rounds.

##  Appendix E Result Tables

Table 12: Estimated Strength Coefficients with the Standard Bradley-Terry
Model, Fitted to Windows of Two Seasons (2015-2023). Coefficients found to be
significant at the 5% level are in bold and underlined. The coefficient for
the reference team is 0.00.

Team | Season
---|---
| 2015-16 | 2016-17 | 2017-18 | 2018-19 | 2019-20 | 2020-21 | 2021-22 | 2022-23
Adelaide | 0.83 | 0.96 | 0.42 | -0.03 | -0.58 | -1.13 | -0.83 | -0.50
Brisbane Lions | -1.97 | -1.75 | -1.63 | -0.20 | 1.20 | 1.00 | 0.81 | 0.94
Carlton | -1.40 | -1.11 | -1.92 | -1.58 | -0.50 | -0.49 | -0.21 | 0.30
Collingwood | -0.40 | -0.45 | 0.02 | 0.84 | 0.72 | -0.36 | -0.02 | 1.14
Essendon | -1.61 | -0.93 | -0.13 | 0.22 | 0.00 | -0.28 | -0.42 | -0.53
Fremantle | 0.00 | -1.11 | -0.84 | -0.50 | -0.21 | -0.26 | 0.34 | 0.21
Gold Coast | -1.50 | -1.29 | -1.75 | -1.87 | -1.24 | -0.81 | -0.57 | -0.53
Geelong | 0.84 | 0.97 | 0.35 | 0.59 | 1.00 | 0.96 | 1.30 | 0.67
Greater Western Sydney | 0.49 | 0.85 | 0.44 | 0.55 | 0.43 | 0.10 | -0.27 | -0.30
Hawthorn | 1.17 | 0.44 | 0.00 | 0.32 | -0.20 | -0.81 | -0.70 | -0.96
Melbourne | -0.57 | -0.12 | 0.13 | -0.21 | -0.44 | 1.06 | 1.33 | 0.72
North Melbourne | 0.37 | -0.48 | -0.81 | -0.06 | -0.55 | -1.57 | -1.91 | -2.49
Port Adelaide | 0.05 | 0.06 | 0.08 | 0.10 | 0.79 | 1.34 | 0.54 | 0.29
Richmond | -0.02 | 0.17 | 0.94 | 1.34 | 1.42 | 0.55 | 0.06 | -0.04
Saint Kilda | -0.47 | 0.00 | -0.87 | -0.99 | 0.03 | 0.18 | 0.00 | 0.00
Sydney | 1.04 | 0.84 | 0.29 | 0.00 | -0.60 | -0.00 | 0.85 | 0.50
Western Bulldogs | 0.88 | 0.54 | -0.58 | -0.28 | 0.33 | 0.72 | 0.59 | 0.04
West Coast | 1.17 | 0.46 | 0.45 | 1.00 | 0.87 | 0.21 | -1.05 | -2.45

Table 13: Estimated Strength Coefficients with the Standard Bradley-Terry
Model, Fitted to Windows of Three Seasons (2015-2023). Coefficients found to
be significant at the 5% level are in bold and underlined. The coefficient for
the reference team is 0.00.

Team | Season
---|---
| 2015-17 | 2016-18 | 2017-19 | 2018-20 | 2019-21 | 2020-22 | 2021-23
Adelaide | 0.94 | 0.59 | 0.18 | -0.40 | -0.65 | -1.10 | -0.56
Brisbane Lions | -1.58 | -1.73 | -0.70 | 0.22 | 0.93 | 0.84 | 0.87
Carlton | -1.13 | -1.55 | -1.51 | -1.15 | -0.52 | -0.37 | 0.07
Collingwood | -0.24 | -0.14 | 0.29 | 0.64 | 0.15 | -0.07 | 0.50
Essendon | -0.82 | -0.66 | -0.04 | 0.00 | -0.06 | -0.55 | -0.32
Fremantle | -0.10 | -1.06 | -0.66 | -0.46 | -0.21 | 0.02 | 0.14
Gold Coast | -1.20 | -1.53 | -1.72 | -1.49 | -1.05 | -0.73 | -0.55
Geelong | 0.89 | 0.61 | 0.48 | 0.62 | 0.89 | 1.03 | 0.79
Greater Western Sydney | 0.68 | 0.61 | 0.45 | 0.33 | 0.31 | -0.37 | -0.06
Hawthorn | 0.82 | 0.35 | 0.00 | -0.02 | -0.38 | -0.87 | -0.77
Melbourne | -0.20 | 0.04 | -0.26 | -0.13 | 0.30 | 0.85 | 1.04
North Melbourne | 0.00 | -0.43 | -0.57 | -0.42 | -0.86 | -1.93 | -1.97
Port Adelaide | 0.28 | 0.00 | 0.05 | 0.44 | 0.87 | 0.66 | 0.63
Richmond | 0.42 | 0.43 | 1.02 | 1.24 | 0.83 | 0.34 | -0.01
Saint Kilda | -0.16 | -0.53 | -0.76 | -0.54 | 0.00 | 0.00 | 0.00
Sydney | 0.94 | 0.61 | 0.00 | -0.27 | -0.13 | 0.24 | 0.58
Western Bulldogs | 0.66 | 0.04 | -0.35 | -0.14 | 0.52 | 0.36 | 0.40
West Coast | 0.86 | 0.58 | 0.53 | 0.88 | 0.45 | -0.60 | -1.36

Table 14: Estimated Strength Coefficients with the Standard Bradley-Terry
Model, Fitted to Windows of Four Seasons (2015-2023). Coefficients found to be
significant at the 5% level are in bold and underlined. The coefficient for
the reference team is 0.00.

Team | Season
---|---
| 2015-18 | 2016-19 | 2017-20 | 2018-21 | 2019-22 | 2020-23
Adelaide | 0.73 | 0.38 | 0.00 | -0.43 | -0.67 | -0.75
Brisbane Lions | -1.54 | -0.93 | -0.13 | 0.34 | 0.88 | 0.92
Carlton | -1.38 | -1.31 | -1.10 | -0.93 | -0.33 | -0.06
Collingwood | 0.02 | 0.12 | 0.40 | 0.27 | 0.27 | 0.40
Essendon | -0.55 | -0.42 | 0.00 | 0.00 | -0.24 | -0.38
Fremantle | -0.24 | -0.85 | -0.47 | -0.34 | 0.04 | 0.00
Gold Coast | -1.34 | -1.54 | -1.35 | -1.22 | -0.82 | -0.62
Geelong | 0.72 | 0.65 | 0.64 | 0.70 | 1.04 | 0.77
Greater Western Sydney | 0.63 | 0.56 | 0.44 | 0.31 | 0.00 | -0.12
Hawthorn | 0.73 | 0.26 | -0.05 | -0.12 | -0.47 | -0.83
Melbourne | 0.03 | -0.23 | -0.07 | 0.34 | 0.42 | 0.81
North Melbourne | 0.00 | -0.37 | -0.59 | -0.60 | -1.18 | -1.90
Port Adelaide | 0.26 | 0.00 | 0.44 | 0.63 | 0.58 | 0.74
Richmond | 0.64 | 0.62 | 1.14 | 0.87 | 0.69 | 0.25
Saint Kilda | -0.44 | -0.52 | -0.38 | -0.36 | 0.00 | 0.05
Sydney | 0.82 | 0.31 | -0.06 | 0.00 | 0.16 | 0.25
Western Bulldogs | 0.34 | 0.04 | -0.10 | 0.19 | 0.39 | 0.33
West Coast | 0.92 | 0.61 | 0.68 | 0.62 | -0.10 | -0.87

Table 15: AIC and classification accuracy for the standard Bradley-Terry
model, fitted to windows of two to four seasons (2015-2023) and all available
data.

Window: 2 seasons
---
Train Seasons | Test Season | Train AIC | Train Accuracy | Test Accuracy
2015-16 | 2017 | 400.55 | 72.05% | 58.79%
2016-17 | 2018 | 418.26 | 67.30% | 62.70%
2017-18 | 2019 | 424.11 | 70.96% | 60.54%
2018-19 | 2020 | 415.88 | 69.29% | 56.64%
2019-20 | 2021 | 397.24 | 66.16% | 54.14%
2020-21 | 2022 | 387.31 | 68.52% | 60.22%
2021-22 | 2023 | 413.76 | 69.13% | 63.68%
2022-23 |  | 422.02 | 70.86% |
Window: 3 seasons
Train Seasons | Test Season | Train AIC | Train Accuracy | Test Accuracy
2015-17 | 2018 | 540.34 | 67.71% | 65.76%
2016-18 | 2019 | 535.43 | 67.82% | 58.38%
2017-19 | 2020 | 562.96 | 68.55% | 56.64%
2018-20 | 2021 | 522.77 | 65.43% | 50.83%
2019-21 | 2022 | 535.23 | 65.16% | 58.15%
2020-22 | 2023 | 521.41 | 67.26% | 65.26%
2021-23 |  | 548.09 | 69.06% |
Window: 4 seasons
Train Seasons | Test Season | Train AIC | Train Accuracy | Test Accuracy
2015-18 | 2019 | 632.71 | 66.94% | 57.30%
2016-19 | 2020 | 653.18 | 65.99% | 53.19%
2017-20 | 2021 | 645.30 | 65.80% | 57.46%
2018-21 | 2022 | 634.16 | 65.17% | 59.67%
2019-22 | 2023 | 641.68 | 64.44% | 63.30%
2020-23 |  | 634.52 | 68.10% |
Window: All Available Data
Train Seasons | Test Season | Train AIC | Train Accuracy | Test Accuracy
2015-23 |  | 978.62 | 60.98% |

Table 16: Estimated strength and AT_HOME coefficients with the Contest-
Specific Bradley-Terry model, fitted to single seasons (2015-2023) and all
available data. Coefficients found to be significant at the 5% level are in
bold and underlined. The coefficient for the reference team is 0.00.

Team | Season
---|---
| 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2015-23
Adelaide | 0.16 | 1.61 | 1.06 | 0.05 | -0.30 | -1.65 | -0.77 | -1.12 | 0.00 | 0.00
Brisbane Lions | -2.35 | -2.22 | -1.32 | -1.72 | 0.70 | 1.73 | 0.74 | 0.90 | 1.35 | -0.09
Carlton | -2.29 | -0.98 | -1.01 | -3.01 | -1.02 | -0.31 | -0.57 | 0.06 | 0.63 | -0.63
Collingwood | -0.80 | -0.28 | -0.27 | 0.68 | 0.84 | 0.51 | -0.95 | 0.99 | 1.73 | 0.26
Essendon | -1.58 | -2.28 | 0.07 | 0.08 | 0.08 | -0.45 | -0.06 | -1.05 | -0.15 | -0.35
Fremantle | 1.03 | -1.71 | -0.58 | -0.93 | -0.45 | -0.39 | -0.13 | 0.79 | -0.37 | -0.17
Gold Coast | -2.21 | -1.50 | -1.20 | -2.29 | -2.08 | -0.86 | -0.75 | -0.57 | -0.46 | -0.96
Geelong | 0.00 | 1.79 | 0.84 | 0.24 | 0.85 | 1.25 | 1.14 | 1.67 | -0.11 | 0.67
Greater Western Sydney | -0.67 | 1.60 | 0.94 | 0.44 | 0.60 | 0.00 | 0.39 | -1.30 | 0.49 | 0.26
Hawthorn | 0.94 | 1.73 | -0.06 | 0.41 | 0.08 | -0.90 | -0.66 | -0.96 | -0.95 | 0.01
Melbourne | -1.36 | -0.03 | 0.18 | 0.43 | -1.36 | 0.25 | 2.02 | 0.80 | 0.76 | 0.20
North Melbourne | 0.21 | 0.76 | -1.09 | -0.23 | -0.18 | -1.64 | -1.47 | -3.10 | -2.26 | -0.66
Port Adelaide | 0.01 | 0.00 | 0.48 | 0.00 | 0.00 | 1.75 | 1.34 | -0.40 | 0.98 | 0.39
Richmond | 0.30 | -0.58 | 1.13 | 1.35 | 1.23 | 1.71 | -0.13 | 0.12 | -0.21 | 0.50
Saint Kilda | -1.59 | 0.47 | 0.09 | -1.87 | -0.70 | 0.59 | 0.00 | 0.00 | 0.16 | -0.21
Sydney | 0.50 | 1.81 | 0.64 | 0.45 | -0.72 | -0.93 | 0.75 | 1.03 | 0.20 | 0.37
Western Bulldogs | 0.05 | 1.97 | 0.00 | -0.94 | 0.16 | 0.45 | 1.22 | 0.04 | 0.13 | 0.29
West Coast | 1.03 | 1.48 | 0.34 | 1.13 | 0.71 | 0.93 | -0.17 | -2.85 | -2.23 | 0.14
Feature (AT_HOME) | 0.15 | 0.63 | 0.43 | 0.25 | 0.35 | 0.35 | 0.08 | 0.62 | 0.37 | 0.29

Table 17: Estimated strength and AT_HOME coefficients with the Contest-
Specific Bradley-Terry model, fitted to windows of two seasons (2015-2023).
Coefficients found to be significant at the 5% level are in bold and
underlined. The coefficient for the reference team is 0.00.

Team | Season
---|---
| 2015-16 | 2016-17 | 2017-18 | 2018-19 | 2019-20 | 2020-21 | 2021-22 | 2022-23
Adelaide | 0.88 | 0.91 | 0.39 | -0.03 | -0.60 | -1.13 | -0.84 | -0.52
Brisbane Lions | -1.99 | -1.86 | -1.67 | -0.22 | 1.18 | 0.99 | 0.82 | 1.00
Carlton | -1.44 | -1.15 | -1.93 | -1.61 | -0.52 | -0.48 | -0.21 | 0.32
Collingwood | -0.41 | -0.49 | 0.04 | 0.85 | 0.78 | -0.34 | -0.02 | 1.18
Essendon | -1.65 | -1.00 | -0.14 | 0.21 | 0.00 | -0.27 | -0.43 | -0.56
Fremantle | 0.00 | -1.19 | -0.88 | -0.53 | -0.25 | -0.27 | 0.34 | 0.22
Gold Coast | -1.54 | -1.38 | -1.78 | -1.91 | -1.31 | -0.82 | -0.58 | -0.52
Geelong | 0.84 | 0.91 | 0.35 | 0.61 | 1.02 | 0.98 | 1.31 | 0.67
Greater Western Sydney | 0.51 | 0.87 | 0.47 | 0.59 | 0.46 | 0.12 | -0.28 | -0.31
Hawthorn | 1.25 | 0.44 | 0.00 | 0.33 | -0.18 | -0.80 | -0.72 | -0.96
Melbourne | -0.58 | -0.14 | 0.14 | -0.22 | -0.46 | 1.05 | 1.29 | 0.73
North Melbourne | 0.40 | -0.52 | -0.82 | -0.07 | -0.56 | -1.55 | -1.92 | -2.59
Port Adelaide | 0.05 | 0.01 | 0.08 | 0.10 | 0.78 | 1.32 | 0.53 | 0.31
Richmond | -0.01 | 0.17 | 0.95 | 1.33 | 1.44 | 0.57 | 0.07 | -0.01
Saint Kilda | -0.47 | 0.00 | -0.88 | -1.02 | 0.03 | 0.19 | 0.00 | 0.00
Sydney | 1.06 | 0.86 | 0.30 | 0.00 | -0.62 | 0.00 | 0.86 | 0.56
Western Bulldogs | 0.94 | 0.58 | -0.60 | -0.28 | 0.37 | 0.75 | 0.61 | 0.05
West Coast | 1.18 | 0.48 | 0.45 | 1.00 | 0.88 | 0.21 | -1.7 | -2.51
Feature (AT_HOME) | 0.35 | 0.47 | 0.35 | 0.29 | 0.34 | 0.18 | 0.29 | 0.47

Table 18: Estimated strength and AT_HOME coefficients with the Contest-
Specific Bradley-Terry model, fitted to windows of three seasons (2015-2023).
Coefficients found to be significant at the 5% level are in bold and
underlined. The coefficient for the reference team is 0.00.

Team | Season
---|---
| 2015-17 | 2016-18 | 2017-19 | 2018-20 | 2019-21 | 2020-22 | 2021-23
Adelaide | 0.94 | 0.58 | 0.16 | -0.40 | -0.66 | -1.12 | -0.58
Brisbane Lions | -1.63 | -1.78 | -0.73 | 0.21 | 0.91 | 0.83 | 0.88
Carlton | -1.16 | -1.56 | -1.54 | -1.17 | -0.53 | -0.37 | 0.07
Collingwood | -0.26 | -0.12 | 0.31 | 0.67 | 0.16 | -0.06 | 0.49
Essendon | -0.84 | -0.67 | -0.04 | 0.00 | -0.06 | -0.57 | -0.33
Fremantle | -0.12 | -1.09 | -0.69 | -0.48 | -0.22 | 0.00 | 0.13
Gold Coast | -1.25 | -1.58 | -1.76 | -1.53 | -1.08 | -0.76 | -0.55
Geelong | 0.87 | 0.62 | 0.48 | 0.64 | 0.91 | 1.04 | 0.79
Greater Western Sydney | 0.70 | 0.65 | 0.48 | 0.36 | 0.32 | -0.37 | -0.05
Hawthorn | 0.85 | 0.38 | 0.00 | 0.00 | -0.38 | -0.88 | -0.79
Melbourne | -0.22 | 0.07 | -0.27 | -0.14 | 0.29 | 0.81 | 1.02
North Melbourne | 0.00 | -0.43 | -0.59 | -0.43 | -0.86 | -1.95 | -1.99
Port Adelaide | 0.26 | 0.00 | 0.05 | 0.43 | 0.85 | 0.63 | 0.62
Richmond | 0.43 | 0.46 | 1.02 | 1.25 | 0.84 | 0.35 | 0.00
Saint Kilda | -0.16 | -0.52 | -0.78 | -0.54 | 0.00 | 0.00 | 0.00
Sydney | 0.95 | 0.64 | 0.00 | -0.28 | -0.14 | 0.24 | 0.60
Western Bulldogs | 0.69 | 0.09 | -0.36 | -0.12 | 0.54 | 0.38 | 0.42
West Coast | 0.87 | 0.61 | 0.54 | 0.88 | 0.45 | -0.63 | -1.39
Feature (AT_HOME) | 0.35 | 0.39 | 0.34 | 0.30 | 0.24 | 0.30 | 0.32

Table 19: Estimated strength and AT_HOME coefficients with the Contest-
Specific Bradley-Terry model, fitted to windows of four seasons (2015-2023).
Coefficients found to be significant at the 5% level are in bold and
underlined. The coefficient for the reference team is 0.00.

Team | Season
---|---
| 2015-18 | 2016-19 | 2017-20 | 2018-21 | 2019-22 | 2020-23
Adelaide | 0.73 | 0.36 | -0.02 | -0.43 | -0.69 | -0.75
Brisbane Lions | -1.58 | -0.95 | -0.15 | 0.33 | 0.86 | 0.95
Carlton | -1.41 | -1.33 | -1.13 | -0.94 | -0.35 | -0.04
Collingwood | 0.02 | 0.14 | 0.43 | 0.29 | 0.28 | 0.43
Essendon | -0.57 | -0.43 | 0.00 | 0.01 | -0.25 | -0.37
Fremantle | -0.26 | -0.87 | -0.50 | -0.35 | 0.02 | 0.00
Gold Coast | -1.39 | -1.59 | -1.40 | -1.24 | -0.86 | -0.62
Geelong | 0.71 | 0.66 | 0.65 | 0.72 | 1.04 | 0.80
Greater Western Sydney | 0.64 | 0.60 | 0.47 | 0.33 | 0.00 | -0.09
Hawthorn | 0.75 | 0.28 | -0.05 | -0.12 | -0.49 | -0.82
Melbourne | 0.02 | -0.23 | -0.07 | 0.34 | 0.40 | 0.81
North Melbourne | 0.00 | -0.37 | -0.60 | -0.60 | -1.20 | -1.90
Port Adelaide | 0.24 | 0.00 | 0.43 | 0.62 | 0.56 | 0.75
Richmond | 0.65 | 0.63 | 1.16 | 0.88 | 0.69 | 0.28
Saint Kilda | -0.45 | -0.53 | -0.38 | -0.36 | -0.01 | 0.08
Sydney | 0.82 | 0.32 | -0.06 | 0.00 | 0.15 | 0.29
Western Bulldogs | 0.36 | 0.07 | -0.09 | 0.21 | 0.41 | 0.38
West Coast | 0.91 | 0.63 | 0.68 | 0.62 | -0.13 | -0.88
Feature (AT_HOME) | 0.32 | 0.36 | 0.33 | 0.24 | 0.30 | 0.31

Table 20: AIC and classification accuracy for the Contest-Specific Bradley-
Terry model, fitted to windows of two to four seasons (2015-2023) and all
available data.

Window: 2 seasons
---
Train Seasons | Test Season | Train AIC | Train Accuracy | Test Accuracy
2015-16 | 2017 | 393.84 | 72.33% | 59.89%
2016-17 | 2018 | 403.27 | 68.66% | 64.32%
2017-18 | 2019 | 416.55 | 69.86% | 60.54%
2018-19 | 2020 | 411.12 | 69.57% | 60.84%
2019-20 | 2021 | 390.83 | 67.68% | 56.35%
2020-21 | 2022 | 386.91 | 68.52% | 61.88%
2021-22 | 2023 | 408.92 | 68.85% | 65.26%
2022-23 |  | 407.56 | 74.33% |
Window: 3 seasons
Train Seasons | Test Season | Train AIC | Train Accuracy | Test Accuracy
2015-17 | 2018 | 527.27 | 68.26% | 65.76%
2016-18 | 2019 | 519.56 | 68.73% | 62.16%
2017-19 | 2020 | 550.78 | 68.18% | 55.24%
2018-20 | 2021 | 514.49 | 65.62% | 55.80%
2019-21 | 2022 | 530.17 | 66.14% | 61.96%
2020-22 | 2023 | 513.40 | 67.26% | 67.37%
2021-23 |  | 537.55 | 70.50% |
Window: 4 seasons
Train Seasons | Test Season | Train AIC | Train Accuracy | Test Accuracy
2015-18 | 2019 | 618.02 | 68.59% | 61.92%
2016-19 | 2020 | 632.80 | 67.58% | 56.74%
2017-20 | 2021 | 629.43 | 65.51% | 56.35%
2018-21 | 2022 | 626.85 | 65.61% | 61.33%
2019-22 | 2023 | 628.95 | 65.17% | 64.36%
2020-23 |  | 620.77 | 65.95% |
Window: All Available Data
Train Seasons | Test Season | Train AIC | Train Accuracy | Test Accuracy
2015-23 |  | 945.57 | 61.92% |

Table 21: Estimated coefficients for the time-variant Bradley-Terry fitted to
windows of one season and all available data with PIs encoded as cumulatives
over the season (2015-2023). Significant coefficients are in bold and
underlined. Significant coefficients at the individual level only are in
italics.

| Season
---|---
FEATURE | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2015-23
| MATCH DIFFICULTY
AT_HOME |  | 0.599 | 0.392 |  | 0.303 |  |  | 0.521 | 0.551 | 0.182
HOMEGROUND | 0.381 | 0.316 |  |  | 0.653 |  |  | 0.746 | 0.408 | 0.363
INTERSTATE | -0.459 | -0.443 | -0.506 |  | -0.530 | -0.645 |  | -0.515 | -0.437 | -0.268
| FORM
CONSECUTIVE_LOSSES |  |  |  |  |  |  | 0.344 |  | -0.164 | -0.139
CONSECUTIVE_WINS |  |  |  |  |  |  |  |  |  | 0.106
LADDER_POSITION_DIFF | 0.039 | 0.061 | 0.038 | 0.030 |  | 0.029 |  | 0.050 |  | 0.044
LADDERLY_POSITION_DIFF | 0.056 | 0.043 | 0.034 | 0.077 | 0.037 | 0.043 | 0.036 |  | 0.027 | 0.025
LG_WON |  |  |  |  |  |  |  |  | 0.787 | 0.278
PERCENTAGE_DIFF |  |  | 0.009 | 0.007 |  |  | 0.010 | 0.012 |  | 0.009
POINTSAGAINST_DIFF |  |  |  |  |  |  | 0.002 | 0.002 | 0.001 | 0.001
POINTSFOR_DIFF | 0.001 |  | 0.003 | 0.003 | 0.003 | 0.003 |  | -0.005 | 0.001 | 0.001
WINS_CUMULATIVE_DIFF |  |  | -0.268 | -0.148 |  | 0.130 |  | 0.133 |  | 0.100
| PIs
BOUNCES_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.002
CLANGERS_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
CLEARANCES_CENTRE_CSUM_DIFF | 0.012 |  |  |  |  |  |  |  |  | 0.006
CLEARANCES_CSUM_DIFF |  | 0.006 |  |  | -0.004 |  |  |  |  | 0.003
CLEARANCES_STOPPAGE_CSUM_DIFF |  |  |  |  | -0.005 |  |  |  |  | 0.002
CONTEST_DEFENSIVE_LOSS_CSUM_DIFF |  |  |  |  | 0.022 |  |  |  |  | 0.009
CONTEST_DEFENSIVE_LOSS_RATE_CSUM_DIFF |  |  |  |  | -0.031 |  |  |  |  | -0.014
CONTEST_OFFENSIVE_WIN_CSUM_DIFF |  |  | 0.013 |  |  |  |  |  |  | 0.006
CONTEST_OFFENSIVE_WIN_RATE_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
DISPOSALS_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.001
DISPOSALS_EFFECTIVE_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.000
DISPOSALS_EFFICIENCY_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
FREES_AGAINST_CSUM_DIFF |  |  | -0.011 |  |  |  |  |  |  |
GETS_GROUNDBALL_CSUM_DIFF |  |  |  |  | -0.002 |  | 0.003 |  |  | -0.001
GETS_GROUNDBALL50_CSUM_DIFF |  |  | 0.006 |  |  |  | 0.008 |  |  | 0.004
GOALS_ACCURACY_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.009
GOALS_SHOTS_CSUM_DIFF |  |  | -0.029 | 0.010 | 0.011 | 0.027 |  | 0.009 |  | 0.008
HANDBALLS_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
HITOUTS_ADVANTAGE_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.002
HITOUTS_ADVANTAGE_RATE_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.010
HITOUTS_WIN_RATE_CSUM_DIFF |  |  | -0.003 |  |  |  |  |  |  |
INSIDE50_CSUM_DIFF |  | 0.005 | 0.003 | 0.004 |  | 0.014 |  | 0.006 | 0.005 | 0.005
INTERCEPTS_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.002
KICK2HANDBALL_CSUM_DIFF | -1.535 |  |  |  |  |  |  |  |  | 0.371
KICKS_CSUM_DIFF |  |  |  |  |  |  |  |  |  | -0.001
KICKS_EFFECTIVE_CSUM_DIFF |  |  |  |  |  | 0.002 |  |  |  | 0.001
KICKS_EFFICIENCY_CSUM_DIFF |  |  |  |  | 0.060 |  |  |  |  |
MARKS_CONTESTED_CSUM_DIFF |  | 0.011 |  | 0.013 |  |  |  |  |  | 0.008
MARKS_CSUM_DIFF |  |  |  |  |  | 0.003 |  |  |  | 0.001
MARKS_INSIDE50_CSUM_DIFF |  |  | 0.008 |  |  | 0.021 |  | 0.014 |  | 0.008
MARKS_INTERCEPT_CSUM_DIFF |  |  |  | 0.009 |  |  |  |  |  | 0.005
MARKS_ONLEAD_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.003
METRES_GAINED_L4_CSUM_DIFF |  |  |  | 0.000 |  |  |  |  |  | 0.000
ONE_PERCENTERS_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.001
POSSESSIONS_CONTESTED_CSUM_DIFF |  |  |  |  | -0.002 |  | 0.003 |  |  | 0.002
POSSESSIONS_CONTESTED_RATE_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
POSSESSIONS_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.000
POSSESSIONS_UNCONTESTED_CSUM_DIFF |  |  |  |  |  |  |  |  |  | 0.000
PRESSURE_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
PRESSURE_DEFENSEHALF_CSUM_DIFF |  | -0.002 |  | -0.002 |  |  |  |  |  | -0.001
REBOUND_INSIDE50S_CSUM_DIFF | -0.008 |  |  |  |  | -0.008 |  | -0.010 |  | -0.004
SCORE_LAUNCHES_CSUM_DIFF |  |  | 0.039 | 0.009 | 0.009 | -0.037 |  | 0.030 | 0.005 | 0.008
SPOILS_CSUM_DIFF |  |  |  |  |  |  |  |  |  |
TACKLES_CSUM_DIFF |  |  |  |  |  |  | 0.003 |  |  |
TACKLES_INSIDE50_L4_CSUM_DIFF |  |  |  |  |  |  | 0.009 |  |  | 0.006
TURNOVERS_L4_CSUM_DIFF |  |  |  |  |  | 0.009 |  |  |  |

Table 22: Estimated coefficients for the time-variant Bradley-Terry fitted to
windows of two seasons with PIs encoded as cumulatives over the previous four
games (2015-2023). Significant coefficients are in bold and underlined.
Significant coefficients at the individual level only are in italics.

| Season |
---|---|---
FEATURE | 2015-16 | 2016-17 | 2017-18 | 2018-19 | 2019-20 | 2020-21 | 2021-22 | 2022-23 |
| MATCH DIFFICULTY |
AT_HOME | 0.005 | 0.465 | 0.324 | 0.268 | 0.312 |  | 0.279 | 0.431 |
HOMEGROUND | 0.003 | 0.316 | 0.257 | 0.464 | 0.610 |  | 0.406 | 0.563 |
INTERSTATE | -0.497 | -0.463 | -0.348 | -0.359 | -0.583 | -0.351 | -0.358 | -0.488 |
| FORM |
CONSECUTIVE_LOSSES |  | -0.092 |  |  | -0.124 |  |  |  |
CONSECUTIVE_WINS |  |  |  |  |  |  |  | 0.111 |
L4G_WINS |  | 0.161 |  |  |  |  |  |  |
LADDER_POSITION_DIFF | 0.038 | 0.035 | 0.023 | 0.019 |  |  | 0.032 | 0.022 |
LADDERLY_POSITION_DIFF | 0.039 |  | 0.030 | 0.033 | 0.029 |  |  |  |
LG_WON |  |  |  |  |  |  |  |  |
PERCENTAGE_DIFF | 0.005 | 0.005 | 0.007 | 0.005 |  |  | 0.009 | 0.005 |
POINTSAGAINST_DIFF | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 0.002 | 0.001 |
POINTSFOR_DIFF | 0.001 | 0.001 | 0.001 | 0.002 | 0.002 |  | 0.001 | 0.001 |
| PIs |
BOUNCES_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
CLANGERS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
CLEARANCES_CENTRE_L4_CSUM_DIFF | 0.012 | 0.012 |  |  |  |  |  |  |
CLEARANCES_L4_CSUM_DIFF |  |  |  |  |  | 0.010 |  |  |
CLEARANCES_STOPPAGE_L4_CSUM_DIFF |  |  |  |  |  | 0.011 |  |  |
CONTEST_DEFENSIVE_LOSS_L4_CSUM_DIFF |  |  |  |  | 0.024 |  |  |  |
CONTEST_DEFENSIVE_LOSS_RATE_L4_CSUM_DIFF |  |  |  | -0.014 | -0.014 |  |  |  |
CONTEST_OFFENSIVE_WIN_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
CONTEST_OFFENSIVE_WIN_RATE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
DISPOSALS_EFFECTIVE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
DISPOSALS_EFFICIENCY_L4_CSUM_DIFF |  |  |  |  |  |  | -0.043 |  |
DISPOSALS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
FREES_AGAINST_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
GETS_GROUNDBALL_L4_CSUM_DIFF |  |  |  |  |  | 0.005 | 0.005 |  |
GETS_GROUNDBALL50_L4_CSUM_DIFF |  |  |  |  |  | 0.014 | 0.014 | 0.009 |
GOALS_ACCURACY_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
GOALS_SHOTS_L4_CSUM_DIFF |  |  | 0.008 | 0.009 | 0.011 |  |  | 0.008 |
HANDBALLS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
HITOUTS_ADVANTAGE_L4_CSUM_DIFF |  |  | 0.008 | 0.009 |  |  |  |  |
HITOUTS_ADVANTAGE_RATE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
HITOUTS_WIN_RATE_L4_CSUM_DIFF | 0.004 |  | 0.003 |  |  |  |  |  |
INSIDE50_L4_CSUM_DIFF | 0.007 | 0.006 | 0.006 | 0.008 |  | 0.006 | 0.005 | 0.007 |
INTERCEPTS_L4_CSUM_DIFF |  |  |  | 0.004 |  |  | 0.005 | 0.004 |
KICK2HANDBALL_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
KICKS_EFFECTIVE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
KICKS_EFFICIENCY_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
KICKS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
MARKS_CONTESTED_L4_CSUM_DIFF |  |  | 0.011 |  |  |  |  |  |
MARKS_INSIDE50_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
MARKS_INTERCEPT_L4_CSUM_DIFF |  |  | 0.009 |  |  |  |  |  |
MARKS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
MARKS_ONLEAD_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
METRES_GAINED_L4_CSUM_DIFF |  | 0.000 | 0.000 | 0.000 |  |  |  |  |
ONE_PERCENTERS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
POSSESSIONS_CONTESTED_L4_CSUM_DIFF |  |  |  | 0.002 |  | 0.005 | 0.001 |  |
POSSESSIONS_CONTESTED_RATE_L4_CSUM_DIFF |  |  |  |  |  |  | 0.030 |  |
POSSESSIONS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
POSSESSIONS_UNCONTESTED_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
PRESSURE_DEFENSEHALF_L4_CSUM_DIFF | -0.002 |  |  |  |  |  |  |  |
PRESSURE_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
REBOUND_INSIDE50S_L4_CSUM_DIFF | -0.009 |  |  |  |  |  |  |  |
SCORE_LAUNCHES_L4_CSUM_DIFF |  |  | 0.008 | 0.147 | 0.012 |  | 0.007 | 0.012 |
SPOILS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
TACKLES_INSIDE50_L4_CSUM_DIFF |  |  |  |  | 0.009 |  | 0.010 |  |
TACKLES_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |
TURNOVERS_L4_CSUM_DIFF |  |  |  |  |  |  |  |  |

Table 23: Estimated coefficients for the time-variant Bradley-Terry fitted to
windows of two seasons with PIs encoded as cumulatives over the season
(2015-2023). Significant coefficients are in bold and underlined. Significant
coefficients at the individual level only are in italics.

| Season
---|---
FEATURE | 2015-16 | 2016-17 | 2017-18 | 2018-19 | 2019-20 | 2020-21 | 2021-22 | 2022-23
| MATCH DIFFICULTY
AT_HOME | 0.316 | 0.475 | 0.324 | 0.268 | 0.312 |  | 0.279 | 0.007
HOMEGROUND | 0.458 | 0.316 | 0.257 | 0.469 | 0.688 |  | 0.438 | 0.616
INTERSTATE | -0.457 | -0.463 | -0.348 | -0.359 | -0.583 | -0.337 | -0.358 | -0.488
| FORM
CONSECUTIVE_LOSSES |  | -0.092 |  |  | -0.124 |  |  |
CONSECUTIVE_WINS |  |  |  |  |  |  |  | 0.133
LADDER_POSITION_DIFF | 0.038 | 0.029 | 0.023 | 0.019 |  |  | 0.032 | 0.022
LADDERLY_POSITION_DIFF | 0.047 |  | 0.030 | 0.038 | 0.026 |  |  |
LG_WON |  |  |  |  |  |  |  |
PERCENTAGE_DIFF | 0.005 | 0.007 | 0.007 | 0.005 |  |  | 0.006 | 0.005
POINTSAGAINST_DIFF | 0.001 | 0.002 | 0.001 | 0.001 | 0.001 | 0.001 | 0.002 | 0.002
POINTSFOR_DIFF | 0.001 | 0.001 | 0.001 | 0.002 | 0.002 |  | 0.001 | 0.001
WINS_CUMULATIVE_DIFF | 0.058 | 0.067 | 0.052 | 0.060 | -0.161 |  | 0.070 | -0.104
| PIs
BOUNCES_CSUM_DIFF |  |  |  |  |  |  |  |
CLANGERS_CSUM_DIFF |  |  |  |  |  |  | -0.004 |
CLEARANCES_CENTRE_CSUM_DIFF | 0.009 | 0.007 |  |  |  |  |  |
CLEARANCES_CSUM_DIFF | 0.004 |  |  |  | -0.005 |  |  |
CLEARANCES_STOPPAGE_CSUM_DIFF |  |  |  |  | -0.006 |  |  |
CONTEST_DEFENSIVE_LOSS_CSUM_DIFF |  |  | 0.013 |  | 0.031 |  |  |
CONTEST_DEFENSIVE_LOSS_RATE_CSUM_DIFF |  |  |  | -0.018 | -0.021 | -0.022 |  |
CONTEST_OFFENSIVE_WIN_CSUM_DIFF |  |  |  |  |  |  |  |
CONTEST_OFFENSIVE_WIN_RATE_CSUM_DIFF |  |  |  |  |  |  |  |
DISPOSALS_CSUM_DIFF | 0.000 |  |  |  |  | 0.001 |  |
DISPOSALS_EFFECTIVE_CSUM_DIFF |  |  |  |  | 0.001 |  |  |
DISPOSALS_EFFICIENCY_CSUM_DIFF |  |  |  |  |  |  |  |
FREES_AGAINST_CSUM_DIFF |  |  |  |  |  |  |  |
GETS_GROUNDBALL_CSUM_DIFF |  |  |  |  |  | 0.002 |  |
GETS_GROUNDBALL50_CSUM_DIFF |  | 0.005 | 0.004 | 0.004 |  | 0.007 | 0.005 |
GOALS_ACCURACY_CSUM_DIFF |  |  |  |  |  | -0.021 |  |
GOALS_SHOTS_CSUM_DIFF | 0.004 | 0.004 | 0.005 | 0.012 | 0.024 | 0.005 | 0.006 | 0.006
HANDBALLS_CSUM_DIFF |  |  |  |  |  |  |  |
HITOUTS_ADVANTAGE_CSUM_DIFF |  |  |  |  |  |  |  |
HITOUTS_ADVANTAGE_RATE_CSUM_DIFF |  |  |  |  |  |  |  |
HITOUTS_WIN_RATE_CSUM_DIFF |  |  |  |  |  |  |  |
INSIDE50_CSUM_DIFF | 0.004 | 0.003 | 0.003 | 0.003 |  | 0.005 | 0.005 | 0.004
INTERCEPTS_CSUM_DIFF |  | 0.002 | 0.002 |  |  |  | 0.003 |
KICK2HANDBALL_CSUM_DIFF | -0.941 |  |  |  |  |  |  |
KICKS_CSUM_DIFF |  |  |  |  |  |  |  |
KICKS_EFFECTIVE_CSUM_DIFF |  |  |  | 0.001 | 0.001 |  |  |
KICKS_EFFICIENCY_CSUM_DIFF |  |  |  |  |  |  |  |
MARKS_CONTESTED_CSUM_DIFF |  | 0.005 | 0.006 |  |  |  |  |
MARKS_CSUM_DIFF |  |  |  |  | 0.001 |  |  |
MARKS_INSIDE50_CSUM_DIFF |  |  | 0.005 | -0.008 | -0.015 |  |  | 0.008
MARKS_INTERCEPT_CSUM_DIFF |  |  |  |  |  |  |  |
MARKS_ONLEAD_CSUM_DIFF |  |  |  |  |  |  |  |
METRES_GAINED_L4_CSUM_DIFF | 0.000 | 0.000 | 0.000 | 0.000 |  |  |  |
ONE_PERCENTERS_CSUM_DIFF |  |  |  |  |  |  | 0.002 |
POSSESSIONS_CONTESTED_CSUM_DIFF |  | 0.001 |  |  |  | 0.002 | 0.002 |
POSSESSIONS_CONTESTED_RATE_CSUM_DIFF | 0.001 |  |  |  |  |  |  |
POSSESSIONS_CSUM_DIFF | 0.000 |  |  |  |  | 0.001 |  |
POSSESSIONS_UNCONTESTED_CSUM_DIFF |  |  |  |  | 0.001 |  |  |
PRESSURE_CSUM_DIFF |  |  |  |  |  |  |  |
PRESSURE_DEFENSEHALF_CSUM_DIFF | -0.001 | -0.001 | -0.001 |  |  |  |  |
REBOUND_INSIDE50S_CSUM_DIFF | -0.004 |  | -0.004 | -0.003 | -0.005 |  | -0.007 |
SCORE_LAUNCHES_CSUM_DIFF |  | 0.004 | 0.006 | 0.009 | 0.009 | 0.004 | 0.007 | 0.009
SPOILS_CSUM_DIFF |  |  |  |  |  |  |  |
TACKLES_CSUM_DIFF | -0.002 |  |  |  |  | 0.003 | 0.002 |
TACKLES_INSIDE50_L4_CSUM_DIFF |  | 0.005 |  |  |  | 0.007 | 0.006 |
TURNOVERS_L4_CSUM_DIFF |  |  |  |  | 0.003 |  |  |

Table 24: Classification accuracy for the Bradley-Terry team-specific, time-
variant expansion, fitted to windows of two seasons and all available data
(2015-2023) with both encodings of PIs.

Window: 2 seasons
---
|  | Last 4 games cumulative | Season cumulative
Train Season | Test Season | Train Accuracy | Test Accuracy | Train Accuracy | Test Accuracy
2015-16 | 2017 | 69.83% | 61.27% | 70.32% | 60.29%
2016-17 | 2018 | 67.64% | 65.05% | 67.64% | 65.05%
2017-18 | 2019 | 66.59% | 63.29% | 65.61% | 63.77%
2018-19 | 2020 | 68.28% | 68.12% | 68.28% | 66.88%
2019-20 | 2021 | 68.39% | 58.82% | 70.84% | 54.90%
2020-21 | 2022 | 65.93% | 67.48% | 64.84% | 67.96%
2021-22 | 2023 | 68.29% | 63.55% | 68.54% | 64.02%
2022-23 |  | 70.00% |  | 69.05% |
All available data
|  | Last 4 games cumulative | Season cumulative
Train Season | Test Season | Train Accuracy | Test Accuracy | Train Accuracy | Test Accuracy
2015-23 |  | 68.54% |  | 68.54% |

Table 25: Number of correctly predicted games in the Finals Series for the
Bradley-Terry team-specific, time-variant (TS-TV) expansion, fitted to windows
of one season (2015-2023) with both encodings of PIs. The Finals Series has 9
games in total.

|  |  | Last 4 games cumulative
---|---|---|---
Train Season | Test Season | Contest-Specific | TS-TV | Addition | Substitution | Incremental | Majority Voting
2015 | 2016 | 4 | 3 | 3 | 3 | 3 | 3
2016 | 2017 | 6 | 5 | 5 | 5 | 5 | 5
2017 | 2018 | 4 | 4 | 6 | 5 | 6 | 5
2018 | 2019 | 7 | 6 | 6 | 6 | 6 | 6
2019 | 2020 | 4 | 5 | 5 | 3 | 5 | 5
2020 | 2021 | 5 | 3 | 4 | 5 | 5 | 5
2021 | 2022 | 5 | 4 | 6 | 6 | 6 | 6
2022 | 2023 | 5 | 5 | 7 | 6 | 3 | 5
|  |  | Season cumulative