# Beyond Rankings: Exploring the Impact of SERP Features on Organic Click-
through Rates††thanks: *Note: these authors contributed equally to this work
and shared first authorship

Erik Fubel1, Niclas Michael Groll1, Patrick Gundlach1, Qiwei Han1, Maximilian
Kaiser2  1Nova School of Business and Economics, Carcavelos, Portugal
{49155, 48699, 49594<EMAIL_ADDRESS>2Universität Hamburg, Hamburg,
Germany
<EMAIL_ADDRESS>
###### Abstract

Search Engine Result Pages (SERPs) serve as the digital gateways to the vast
expanse of the internet. Past decades have witnessed a surge in research
primarily centered on the influence of website ranking on these pages, to
determine the click-through rate (CTR). However, during this period, the
landscape of SERPs has undergone a dramatic evolution: SERP features,
encompassing elements such as knowledge panels, media galleries, FAQs, and
more, have emerged as an increasingly prominent facet of these result pages.
Our study examines the crucial role of these features, revealing them to be
not merely aesthetic components, but strongly influence CTR and the associated
behavior of internet users. We demonstrate how these features can
significantly modulate web traffic, either amplifying or attenuating it. We
dissect these intricate interaction effects leveraging a unique dataset of
67,000 keywords and their respective Google SERPs, spanning over 40 distinct
US-based e-commerce domains, generating over 6 million clicks from 24 million
views. This cross-website dataset, unprecedented in its scope, enables us to
assess the impact of 24 different SERP features on organic CTR. Through an
ablation study modeling CTR, we illustrate the incremental predictive power
these features hold.

###### Index Terms:

SERP features, Click-through rates prediction, Organic search

##  I Introduction

Search Engine Optimization (SEO) is a strategic process used in online
marketing with the aim of enhancing a website’s visibility in search engine
results pages (SERPs). The objective is to attract the highest possible volume
of organic traffic to a website, which is a cornerstone strategy for long-
standing online marketing [1]. In the realm of e-commerce, it’s estimated that
33% of total web traffic originates from organic search results [2]. Organic
traffic encompasses those instances where a user inputs a keyword in a search
engine and lands on a website by clicking on one of the non-ad results. Given
the high relevance of organic traffic, it is crucial for website providers to
optimize their strategies to maximize the likelihood of generating clicks
through search engines. Generally, the clicks to a website on a search result
page for a specific keyword can be formulated as follows:

$Clicks=Impressions*CTR$ (1)

where CTR refers to the click-through rate of a result [3]. To enhance the
CTR, SEO efforts usually center on a website’s rank on a result page, as top-
ranked websites command more user attention and consequently receive more
clicks [4]. To secure a high rank on a result page, a website needs to
demonstrate relevance for the particular keyword. Achieving this typically
involves aligning a website’s content and metadata with the keyword, a focus
for many SEO practitioners [5, 6, 7, 8, 9, 10].

Although introduced in the early 2000s, SERP features — a visually prominent
component of search results—have been heavily utilized by Google since the
mid-2010s [11]. These SERP features are elements that encapsulate information
from organic search results with the intent of making Google’s result pages
more engaging [12]. They can take various forms, such as providing an instant
answer to a user’s question, displaying a knowledge panel on the right of the
result page, or including an image alongside a result [13]. Figure 1 provides
an illustration of SERP features.

Figure 1: Exemplification of SERP features on a Google result page adapted
from [14], between organic results (1) and (3), such as answer box (2), video
results (4), knowledge panel (5), among others.

Introducing these visual elements can significantly influence users’ clicking
decisions, thus impacting CTR and the revenue funneling into e-commerce
websites. Some argue that by integrating additional features into its result
pages and leveraging information originally published on third-party websites,
Google reduces users’ need to leave its ecosystem [15]. This could potentially
disadvantage the publishers of the original information who rely on website
traffic. In contrast, Google asserts that inclusion in SERP features can
significantly boost CTR, visits, and time spent on a website [12]. Despite the
increasing prevalence of SERP features, their precise impact on CTR remains
poorly understood. This gap in our knowledge raises an important research
question: To what extent do SERP features influence CTR, and how does their
presence affect the importance of a website’s ranking position?

In this study, we broaden the existing analysis of the influence of a
website’s ranking position, which has been identified as the main direct
influence on CTR, to include the characteristics of SERP features. This
inclusion of SERP feature characteristics presents a novel aspect of CTR
research. Furthermore, we compare the relative importance of SERP features
with other result page characteristics.

This paper is structured as follows: Section II offers a comprehensive review
of related works on the influences on CTR, including research on SERP features
and CTR prediction models. Section III and IV provide detailed descriptions of
the dataset used in this study and the methodology applied, respectively.
Section V presents an exploratory data analysis of the interactions between
SERP features, CTR, and other features. In Section VI, we investigate the
importance of SERP features by examining their predictive power. Finally,
Section VIII provides a discussion of the findings and concludes the paper.

##  II Related Works

###  II-A Determinants of CTR

Search engine optimization (SEO) is one of the most widely adopted online
advertising strategies in the present day, and it plays a crucial role in
driving organic website traffic [10, 16]. A significant body of research in
the field of SEO marketing has identified the ranking position of a website on
a search engine results page (SERP) as the primary determinant of click-
through rates (CTR), making it a central focus of SEO efforts [5, 6, 7, 8, 9,
10]. SEO strategies aim to elevate the rank of a website by meticulously
tailoring its content to align with specific keywords. This might involve
adding new, high-quality blog posts to improve the relevance of the website to
search engines [9]. Other factors such as keyword characteristics or result
characteristics have been studied predominantly for their impact on the
position of a website in search results, and less so for their direct
influence on CTR [17]. For instance, much of the literature on keywords aims
to identify strong keywords and trends and recommends optimal keyword
characteristics, content adaptation, linkage optimization, or structure
adjustment to achieve higher rankings on search engine result pages [18, 19,
20, 21]. While the position of a website has been widely recognized as the
primary driver of CTR, it is equally important to consider additional
characteristics such as result, keyword, and SERP features that directly
influence CTR.

###  II-B SERP Features

Although Google introduced the first SERP feature as early as 2002, it was not
until the mid-2010s that their usage intensified [13]. Today, SERP features
are among the most conspicuous and widely used elements on search engine
result pages. Oliveira and Texeira Lopes provide a comprehensive overview of
the evolution of SERP features on Google Search and Microsoft Bing, noting
that these features have become more common and diverse, aggregating content
from different verticals and providing more features that give direct answers
[13]. However, critics argue that Google’s addition of more SERP features and
use of information originally published on third-party websites has reduced
the need for users to leave Google’s ecosystem, thereby disadvantaging the
publishers of the original information who depend on traffic to their
websites. According to a Semrush study, zero-click searches, where a user does
not leave Google’s ecosystem, account for 25.6% of all searches [15].

Despite the long-standing existence of SERP features and their visual
dominance on search engine result pages, their influence on user behavior has
only been sporadically studied. For instance, one study analyzes the positive
effect on CTR when a website appears in the featured snippet, but this
analysis relies on information found on blogs from influential SEO companies
[22]. Numerous influential marketing blogs tout the benefits of appearing in
SERP features, with many suggesting that SERP features can enhance the
visibility of websites featured in them and reduce the CTR of websites that
appear alongside SERP features without being featured [23, 14, 24]. Google
advertises significant improvements in click-through rate, visits, and time
spent on websites when websites are chosen to be shown in SERP features [12].
Despite these claims, the actual effect of SERP features on CTR remains
largely unexplored and under-theorized. This gap in the literature indicates
that there is significant potential for this work to illuminate the opaque
role of SERP features in Google’s search engine ecosystem and provide the
first empirical research on the SERP features’ impact on website performance
[24].

###  II-C CTR Prediction Models

Generally, CTR prediction research has largely been concerned with binary
classification problems, asking questions such as ”Will user X click on item
Y?” The items under consideration are typically ads on a search engine result
page, but they can also be articles in an online shop [25]. This approach
differs fundamentally from the problem formulation in this work, which treats
CTR prediction as a regression problem, predicting a continuous value based on
aggregated data, as opposed to making a classification for a single
observation. This difference is also reflected in the nature of the datasets
and models used for classification. Datasets consisting of individual users
and items are often highly sparse and high-dimensional after one-hot encoding
[25, 26]. As a result, the research and the resulting models have been
developed to handle this high dimensionality and sparsity [26].

The field of CTR prediction has seen the development of a range of models,
including multivariate statistical models [27, 28], factorization machines and
field-aware factorization machines [29, 30, 31], and combinations of deep
learning models and factorization machines [32, 33, 34, 35, 36, 37]. Yang
provides a detailed overview of CTR prediction in the context of user-item
interactions [25]. However, these models, which were developed for
classification on sparse ad-click datasets, are not suitable candidates for
predicting aggregated organic CTR (see section IV-A). While recent research
has focused on predicting user-item interactions, to our knowledge, only one
work has proposed a model for predicting aggregated CTR [38]. However, this
work is concerned with the prediction of ad CTR rather than organic results.

To summarize, although a substantial body of literature exists on CTR
prediction, these works differ from the problem at hand in terms of the nature
of prediction (individual vs. aggregated) and the type of clicks (organic
results vs. ads). This suggests that the models proposed in these works may
not be directly well-suited to the prediction problem in our study, especially
in light of understanding the importance of SERP features.

##  III Dataset Description

###  III-A Data Acquisition and Preprocessing

The primary dataset employed for this study was provided by Grips, a German
startup that endeavors to generate a comprehensive map of online commerce for
retailers and brands [39]. The dataset is an aggregation of historical Google
search data, specifically gathered from US-based desktop searches during the
period spanning May 31st, 2022, to August 18th, 2022. With more than 24
million views and over 6 million user clicks on search engine result pages,
the dataset presents an extensive source of information. The data has been
collected across approximately 67,000 distinct search terms, commonly referred
to as keywords, and 43 different e-commerce stores representing a broad array
of industries.

Each data point in the dataset provides insight about a specific URL and
keyword, encapsulating metrics related to the performance of the URL for the
corresponding keyword. To illustrate, the data could reflect metrics pertinent
to the performance of the URL ’www.amazon.coom/’ for the searched keyword
’amazon’. Thus, the data is presented in a tabular, heterogeneous format.

The primary dataset was further enhanced with additional features derived from
a leading search engine marketing company and Google’s Keyword Planner. These
features encompass a diverse range of aspects, from the searched keyword and
metadata about the result page to information specific to the result and the
displayed SERP features. The dataset also includes the click-through rate for
each result. In its raw form, the dataset comprises 70 features, among which
is information about the presence of 24 distinct SERP features (see the source
of each feature in appendix -A). The dataset also provides granular data about
which specific result was included in which SERP feature. As such, given its
extensive set of result page features, which encompass real-world, non-
publicly accessible data for numerous e-commerce stores, this dataset
represents a unique and innovative resource for research.

In order to prepare the data for subsequent analysis and modeling, the
guidelines for data preprocessing as outlined by Google adhered to [40, 41].
To reduce the potential for noise in the data due to the observations of
result pages that received minimal user exposure, an impression threshold of
20 impressions per result was imposed. As a result, 58,898 data entries remain
for analysis.

###  III-B Feature Categorization and Engineering

To facilitate a comprehensive comparison of the impact of SERP features on
CTR, in relation to other characteristics of the result page, the variables
within the dataset were divided into three distinct categories or subsets:
Position, Keyword, and SERP features. Moreover, self-generated features were
incorporated, where relevant, to augment these subsets. These engineered
feature subsets are employed in both the overall data analysis and the
modeling process. A brief overview of these subsets is provided below. For a
comprehensive list of features within each subset, please see appendix -B, and
for a detailed description of all features, please refer to the data
dictionary in appendix -A.

  * •

Position: This subset includes features that are explicitly related to the
ranked position of the result. These features encompass the current result
position at the time of measurement, the monthly average position, and the
positional difference from the previous measurement. While the position subset
is treated as a distinct subset in the subsequent analysis, it is crucial to
acknowledge that the position feature plays a pivotal role in addressing the
problem at hand. As emphasized by the literature review and the findings of
this study, the position is the most significant predictor of CTR. Therefore,
the analysis will be conducted using an ablation study approach, using the
position subset as a baseline and incorporating the additional subsets as
components to assess their relative importance beyond that of position.

  * •

Keywords: This subset comprises the keyword itself and all directly resulting
elements from the keyword a user inputs into the search engine. This includes
details about the keyword, such as the length of the keyword, information
indirectly related to that keyword like the level of competition or the search
volume, and finally, the search intent. To provide a numerical representation
of the complexity of each keyword, the Flesch reading ease score was computed
[42]. Although more recent readability measures have been developed, Flesch’s
reading ease score was chosen for its widespread acceptance and
straightforward interpretability. This score is calculated based on the
average number of words per sentence and the average number of syllables per
word. A high score signifies good readability, typically characterized by
short sentences and words.

  * •

SERP features: The SERP features in the dataset are binary features that
denote for each entry whether a specific SERP feature is present (1) or absent
(0). These features can be further divided into page SERP features and
positional SERP features. Page SERP features indicate whether a certain
feature is present anywhere on the page. In contrast, positional SERP features
specify whether a result is included in a particular SERP feature. This can
manifest in various forms. For instance, a Review could be displayed beneath a
URL, or a Snippet from the URL could be featured in the Knowledge Panel.
Consequently, if a positional SERP feature is present, the corresponding page
SERP feature must also be present, although the converse is not necessarily
true. Page SERP features also include details about the type of ads displayed
on a result page. We have consolidated this information into a binary feature
that describes whether ads are shown. To enhance the interpretability of the
dataset, it was further enriched with the total count of SERP features for
both page and positional features.

##  IV Methodology

###  IV-A Examined Models

This research treats the task of predicting Click-Through Rates (CTR) as a
regression problem. Based on a review of relevant literature and the
characteristics of the dataset at hand, three primary categories of off-the-
shelf regression models were chosen for examination: linear regression models
and tree-based models, and neural network models.

Linear regression models are favored for their computational efficiency and
interpretability. Ordinary least squares regression (OLS) was chosen as a
baseline model, given its statistical robustness and popularity in the field.
To account for potential feature interactions, an adapted version of the OLS
model was utilized, incorporating interactions between two features as the
product of their values (Poly2). However, to control the exponential growth in
the number of features, only interactions between two features with a Pearson
correlation coefficient greater than 0.05 in the training dataset were
included in the model. A Ridge regression model was introduced as a third
variant to address potential overfitting. The Ridge model employs L2-Norm for
implicit feature selection.

Tree-based models were the second category selected, specifically, ensemble
models based on decision trees. These models are advantageous as they do not
require specific data distributions and perform swiftly without preprocessing
while being capable of modeling feature interactions. The top three performing
tree-based models for tabular data from a recent comparative benchmark—Random
Forest, Gradient Boosting Decision Trees (GBDT), and XGBoost—were tested,
along with CatBoost, another tree-based model that has shown strong
performance in recent studies.

The third category included neural network regression models. While Deep
Neural Networks (DNN) have shown outstanding performance with homogeneous data
types like images, audio, and text, they have been less successful with
heterogeneous, tabular data [43] in comparison to tree-based models. However,
other study reports that DNNs can match or even surpass the performance of
traditional machine learning models on tabular data with over 10 million
samples[44]. Given that some of the best-performing models in recent CTR
prediction research incorporate neural networks, this study also tests
TabNet[45], a neural network structure specifically designed for tabular data,
as well as Wide&Deep[33] and DeepFM[34], which are recommended by recent CTR
prediction research.

###  IV-B Subset Combinations

To assess the predictive power of each subset, combinations of subsets were
tested using the selected models. Drawing from both the literature review in
section II, the position subset, highlighted in the literature review and our
analysis as the most significant feature, serves as the baseline for an
ablation study. When testing a model on a subset combination, all features
from the combined subsets are utilized for prediction. The position subset is
consistently included, with the other subsets added incrementally.

Initially, the position subset is individually combined with each of the other
subsets to evaluate the additional predictive power contributed by each
subset. Subsequently, the predictive power of all three subsets
combined—position, keyword, and SERP features—is examined to understand their
collective impact. Consequently, four subset combinations are tested on each
model presented in IV-A. To maximize the potential of each model,
hyperparameter tuning was conducted where reasonable. Please find the full
documentation on tested parameter ranges in appendix -C and the resulting
parameters in appendix -D.

###  IV-C Evaluation Metric

A common evaluation metric, the Root Mean Squared Error (RMSE), is employed
for a comparative analysis of the different feature subsets across models, as
defined in the equation:

$RMSE=\sqrt{\frac{1}{N}\Sigma_{i=1}^{N}{({y_{i}-\hat{y}_{i}})^{2}}}$ (2)

This metric effectively penalizes larger errors, which aligns with the
objectives of the present business case where substantial errors can lead to
significant misallocations of SEO resources. Moreover, the RMSE serves as a
convenient optimization metric across all model categories, offering
advantages over alternative metrics like Mean Absolute Error (MAE).

###  IV-D Feature Importance Evaluation

To evaluate the significance of SERP features in predicting CTR and to compare
them with position and keyword characteristics, this research employs model
interpretation techniques. These techniques assign importance values to
features in a machine learning model. A high importance value indicates a
greater impact on the overall prediction compared to a feature with a lower
importance value. By grouping features into subsets as described earlier, we
can examine the collective importance of SERP features in relation to position
and keyword features. The XGBoost model is utilized for assessing the feature
importance, as it has shown superior performance.

Three techniques were employed: SHAP, permutation importance, and average gain
in XGBoost splits. These were chosen for two reasons: their ability to compare
the global relevance of features for the prediction and their effectiveness in
providing a more holistic conclusion when used together. They also serve as a
way to cross-check the results.

SHAP importances are based on Shapley explanations, a game-theoretic approach
that assigns individual features a share of an aggregated outcome [46]. It
measures the average contribution of a feature to the prediction across all
observations [47, 48]. Permutation importance is calculated by randomly
shuffling each feature and measuring the decrease in a model’s performance
caused by the permutation [49]. Features that cause a large decrease in
performance when shuffled are ones that the model heavily relies on to make
predictions [48]. The average gain in XGBoost’s tree splits is calculated
based on the intrinsic structure of the XGBoost model by averaging the
improvement of the loss function in all splits in a feature is used [50].
According to the gain metric, features with a larger average contribution to
reducing the loss function are more relevant for the overall prediction.

##  V Exploratory Data Analysis (EDA)

###  V-A The Broad Impact of SERP Features

The first stage of this study’s exploration involves a high-level analysis of
the influence of SERP features on CTR. A notable trend is observed when the
count of positional SERP features, those attached to a single result,
increases. This trend shows a positive correlation with CTR ($\rho=0.22$).
However, an increase in the number of page SERP features appearing on the
entire results page doesn’t exhibit a similarly clear trend ($\rho=-0.11$),
suggesting a potential negative influence on CTR. This overall negative trend,
albeit slight, can be better understood by differentiating the unique SERP
features, thereby illuminating the individual drivers of this influence
illustrated in Figure 2).

Figure 2: Correlation of SERP features with CTR when they are generally
present on a result page. The color represents the strength of the effect:
dark red refers to a strong negative correlation while dark green refers to a
strong positive correlation.

The data suggest that the presence of most SERP features correlates negatively
with CTR. This implies that businesses aiming to optimize their search engine
performance should potentially focus on keywords associated with fewer SERP
features. However, the dataset indicates that SERP features are almost
ubiquitous, with 99.8% of the result pages showcasing at least one SERP
feature and the majority displaying between four and six features. Given this
prevalence, it becomes essential for website providers to comprehend the
specific effects and dynamics of individual SERP features, especially those
that could enhance their CTR. The impact of appearing in certain SERP features
will be further examined in section V-C.

###  V-B Variations in Effects Across Positions

The general analysis in section V-A revealed a negative overall influence of
the presence of SERP features on CTR. However, when incorporating the position
of a result as an additional variable, intriguing trends emerge. For some SERP
features, the average CTR per position remains relatively unaffected by the
presence of the SERP feature. For others, the presence significantly
influences the average CTR. Two primary patterns are observable: with the
presence of a SERP feature, either the average CTR declines across all
positions (pattern: ‘Lower’), or the average CTR decreases for the initial
three positions and then increases for subsequent positions (pattern: ‘Lower →
Higher’). Figure 3 exemplifies these patterns and lists the SERP features to
which they apply.

Figure 3: Mean CTR per position if a SERP feature is present (1) compared to
when it is not present (0). The left plot shows the pattern ‘Lower’ and the
right plot pattern ‘Lower → Higher’. SERP features without a clear pattern or
$n<1000$ are not listed.

The reasons for the emergence of these patterns for specific SERP features
aren’t immediately evident. Nonetheless, it’s worth noting that certain
features have a considerable correlation with user intents. For instance, the
presence of Image SERP features is strongly correlated with transactional
search intent ($\rho=0.29$). Therefore, while interpreting these results, it
is crucial to bear in mind that the observed effects might be influenced by
other feature categories, such as the search intents.

While it is a well-established notion that a high-ranking position is vital
for maximizing CTR, the detailed investigation into the impact of SERP
features prompts the question of whether the importance of top-ranking
positions varies in different scenarios. As discussed above, the effects of
individual SERP features have been isolated for analysis. However, in real-
world situations, SERP features often appear concurrently, which likely leads
to inter-feature influence. To account for this, we examine the importance of
positions for each combination of page SERP features. For a more comprehensive
comparison, the CTR is normalized to the average value at the first position
for each combination that appears more than 200 times. Subsequently, the rate
of decay for each subsequent position is calculated. The analysis reveals that
patterns identified for individual SERP features persist across combinations
of them. Among the top three combinations by count, two show a faster decay in
CTR, while the other decays much slower compared to the entire dataset. For
instance, the presence of three different SERP features can double the CTR at
the third position, as demonstrated by the contrast between the green and blue
combinations in Figure 4.

Figure 4: Loss in CTR per position. Values are the average CTR loss for each
position in the percentage of average CTR on position 1. Only combinations
with more than 200 occurrences are considered (n=59). Dashed lines represent
the top three most frequent SERP feature combinations. Shaded areas represent
the range in which 50% and 90% of all values fall.

###  V-C Differential Impact of SERP Features on Included and Excluded Results

Sections V-A and V-B established that SERP features significantly affect
consumer click behavior on search result pages. Initially, the investigation
of SERP features was conducted at the page level, evaluating their overarching
impact on all results on a page. However, it is critical to acknowledge that
SERP features are not merely passive elements on a page; they actively link to
some of the websites listed on the results page, thereby directly contributing
to the CTR of those specific results.

To gain a comprehensive understanding of SERP features’ impact, it becomes
imperative to differentiate between their influence on results they link and
those they do not. An illustrative example can be derived from analyzing
images shown next to a result. We need to differentiate between (i) the effect
the image has on the result it is linked with and (ii) the effect on a result
that does not have an accompanying image, while others do. This
differentiation warrants the introduction of a new set of feature categories,
encapsulating whether a result is displayed within a SERP feature (termed as
”Result in feature”) or not included within the SERP feature (”Result not in
feature”). For example, the general trend observed in Figure 2, which
indicates a negative correlation, encapsulates the effect of SERP features
without considering whether the results are included within them or not. A
more nuanced understanding can be obtained by differentiating these two
possibilities.

Figure 5: Correlation of SERP features with CTR differentiating between
”Result in feature” and ”Result not in feature”. For some features, not enough
results were included, which is why there are more features in the ”Result not
in feature” category than ”Result in feature”.

Figure 5 underscore the divergent effects between the two categories. Not
being included in most SERP features negatively affects the CTR, while being
included within a feature generally increases the CTR. This dichotomy prompts
an investigation into what makes clicking on links within SERP features
attractive to users, and how website providers can leverage this to their
advantage. One noteworthy pattern emerges from the analysis of the Image Pack
feature. This feature, representing a collection of images on the results
page, exhibits a negative correlation ($\rho=-0.3$) with CTR when a result is
not included. Conversely, when a result is part of the Image Pack, the
correlation with CTR is positive ($\rho=0.25$). The SERP feature, ”People Also
Ask”, exhibits a similar pattern, albeit with a less pronounced magnitude.

Further analysis reveals that the presence of SERP features tends to
negatively influence the CTR of the first position, regardless of whether the
result is included within the SERP feature. The positive effect of ”Result in
feature”, as seen in Figure 5, only becomes evident from the second position
onward. In contrast, the effect of ”Result not in feature” remains negative
across all positions.

In conclusion, SERP features can have varying impacts on the CTR depending on
the position of a result, regardless of whether the result is included within
them. Results in the first position are particularly susceptible to decreased
CTR due to increased SERP features. For results in lower positions, being
featured within SERP features tends to be beneficial, while not being included
in SERP features can adversely affect a result’s CTR.

##  VI Evaluation and Interpretation of Model Results

###  VI-A Comparative Analysis of Models

Table I presents a comprehensive performance breakdown of each model and
subset combination, forming the basis of our analysis in this section. In the
evaluation of the model performance, a conspicuous trend surfaces. Tree-based
models consistently outperform linear models and neural networks. In
particular, GBDT and its variants, such as CatBoost and XGBoost, produce the
most impressive results. To better understand the reduction in RMSE and the
importance of the features, we decided to concentrate on a single model best
suited to address the problem in question. This approach ensures that our
interpretations are not skewed by outliers from models that perform poorly or
are unsuitable. Because both CatBoost and XGBoost perform equally well, we use
XGBoost for further analysis due to its widespread recognition and familiarity
in the field.

| RMSE of subset combinations
---|---
Model | Position | Position + Keyword | Position + SERP Feat | Position + Keyword + SERP Feat
OLS | 0.153 | 0.145 | 0.145 | 0.137
Poly2 | 0.143 | 0.129 | 0.131 | 0.122
Ridge | 0.152 | 0.144 | 0.144 | 0.137
Random Forest | 0.137 | 0.108 | 0.120 | 0.100
GBDT | 0.134 | 0.109 | 0.122 | 0.108
XGBoost | 0.133 | 0.104 | 0.120 | 0.098
CatBoost | 0.134 | 0.103 | 0.120 | 0.099
TabNet | 0.137 | 0.121 | 0.130 | 0.118
Wide&Deep | 0.137 | 0.123 | 0.152 | 0.128
DeepFM | 0.136 | 0.135 | 0.137 | 0.133
TABLE I: Benchmark results on different feature subsets. The top results for
each feature subset are bold. We also underline the second-best results.

###  VI-B Assessing the Explanatory Power of Feature Subsets

By running the models on various combinations of feature subsets, we can
assess the explanatory power of each subset and infer their overall relevance
for CTR prediction. When evaluating the improvement in RMSE resulting from the
inclusion of additional feature subsets, we focus primarily on the results
from XGBoost. To further validate these comparisons, we also conduct paired
t-tests on the results of the top five models on average. This allows us to
determine if the observed differences in RMSE across feature subsets are
statistically significant. We observe that RMSE scores improve upon the
addition of other subsets to the position subset. Notably, the inclusion of
the keyword subset results in a significant reduction in RMSE ($-22.6\%$).
This subset demonstrates a greater explanatory power than the SERP features
subset, which further improves the RMSE ($-9.8\%$). When SERP features are
added to the position + keyword combination, which was previously the best,
there is an additional improvement in prediction ($-4.9\%$). All these
differences are statistically significant according to the paired t-test.

Collectively, these findings suggest that all feature subsets are valuable, as
they decrease error when added and enhance the baseline model that solely
relies on the position feature. Consequently, we can deduce that the
additional SERP features do have an impact on CTR and, by extension, user
behavior. The larger reduction in RMSE for the keyword subset compared to the
SERP feature subset indicates that they have a more pronounced effect on CTRs.
However, this observation is merely indicative, as the importances of the
features are not quantified from the perspective of the model. The next
section provides a quantification of feature importances.

###  VI-C Assessing the Importances of Features

To evaluate the relevance of the feature subsets defined in section IV-B, we
applied three different metrics: gain, permutation importance, and SHAP
importance. Table II presents the comparison of feature subset importance as
per different measures, and corroborates our previous findings. The position
subset consistently demonstrates the highest importance score across all
metrics, followed by the keyword and SERP feature subsets. Regarding
attributing feature importances, SHAP importance offers the most balanced
perspective, with all subsets having an importance value between 28.9% and
36.7%. In contrast, permutation importance presents the most variance, with
the ’position’ subset receiving 55.9% and ’SERP features’ only 16.2%.

| Importance Measure
---|---
Feature Subset | Gain |  | Permutation
---
Importance
SHAP Importance
Position | 44.7% | 55.9% | 36.7%
Keyword | 35.9% | 27.9% | 34.4%
SERP Features | 19.3% | 16.2% | 28.9%
TABLE II: Comparison of feature subset importance as per different measures

This difference can be explained by the methodology underlying each
calculation. Both permutation importance and average gain rely heavily on RMSE
as an evaluation metric, which tends to penalize large deviations
disproportionately. For instance, the ’position’ feature, which has a major
impact and sets a range of plausible CTR values, will be greatly affected by
permutations. To illustrate, a permutation of the ’position’ feature from 1 to
10 would yield a significantly different range of expectable CTRs compared to
permuting the presence of a single SERP feature, which would have a much
smaller impact on RMSE.

Nonetheless, the interpretation of SHAP values indicates that, on average,
SERP features contribute to 28.9% of the difference between a given prediction
and the average prediction, suggesting that SERP features may have a greater
significance for CTR than previously assumed. These findings, which are both
data and model-driven, highlight the need for further research that could
delve into the behavior of individual users and explore the significance of
SERP features for non-e-commerce searches.

##  VII Discussion

###  VII-A Theoretical Implications

This study contributes to the knowledge of search engine optimization (SEO)
practices by comparing the influence exerted by ranked positions, keyword-
related characteristics, and SERP features on CTR. Our findings not only
confirm the widely accepted view that the ranking position of a search engine
page result greatly influences its click-through rate (CTR) but also reveal
that other SERP characteristics — such as the presence of specific SERP
features, the nature of the searched keyword — can considerably affect CTR.

Our analysis, which encompasses a vast array of relevant SERP characteristics,
is facilitated by an extensive and novel dataset that surpasses previous
studies in its scope and comprehensiveness. This study also marks the first
attempt to incorporate many diverse SERP features into a single analytical
framework, thereby expanding upon existing research that typically only
assesses the impact of individual SERP features. Furthermore, this research
provides valuable insights into the effectiveness of various off-the-shelf
machine learning models for predicting aggregated CTR. Notably, we demonstrate
that easily applicable tree-based models can outperform state-of-the-art CTR
prediction models.

###  VII-B Implications for Practitioners

The findings from this study hold significant implications for SEO
practitioners. While securing a high ranking remains a crucial optimization
goal, our analysis also emphasizes the considerable potential of other SERP
characteristics, particularly SERP features, in enhancing CTR.

The implications of SERP features can be distilled into three key insights.
Firstly, SERP features typically reduce the click-through rate of results,
leading to an increase in zero-click searches. Consequently, website providers
should anticipate that the continual introduction of higher quality and a
greater quantity of SERP features may lead to increased searches where users
do not leave the SERP, thereby negatively impacting providers’ revenues.
Secondly, the presence of certain SERP features, especially in specific
combinations, can significantly affect the importance of a high ranking on a
results page. Some SERP features can either divert CTR away from or
concentrate it towards the top positions. Therefore, efforts to secure a high
ranking should be strategically directed towards keywords that, in conjunction
with the present SERP features, yield high CTR. Lastly, appearing within SERP
features emerges as a new potential focus for SEO efforts. Similar to securing
a high ranking, having a website linked within a SERP feature can
significantly enhance CTR, irrespective of the position of the actual result.

However, optimizing for SERP feature appearances presents a unique challenge.
Although website developers can increase the likelihood of their content being
selected by Google’s crawlers through the appropriate use of metadata
descriptions, there are no guarantees. This process is largely dependent on
Google’s discretion, and the algorithmic process determining feature selection
remains largely opaque.

Looking forward, one potential game-changer in the SERP landscape is the
integration of Large Language Models (LLM) like ChatGPT. These AI models have
demonstrated their ability to surpass traditional search engines in terms of
user experience and problem resolution. If Google were to incorporate its own
LLM as a SERP feature or in another capacity within its search engine, this
could have an even more profound impact than the findings of this study
suggest. Therefore, it is imperative for practitioners to stay abreast of
changes in SERP features.

###  VII-C Limitations

Despite our findings, some limitations inherent to the dataset warrant
mention. The data only includes US-based desktop searches. As such, we cannot
conclusively state whether these findings are applicable to mobile searches or
searches conducted in other countries. Although the structure of Google’s
search result page is largely uniform globally, user behaviors may differ
across countries, and even more so across devices. Furthermore, our dataset
was of medium size and did not allow for the analysis of rare combinations of
result page characteristics due to a limited sample size. Lastly, our findings
are based on data collected between May and August 2022. However, Google’s
search result pages are subject to frequent changes, including the
introduction and adjustment of SERP features. As a result, our findings may
have limited applicability to result pages that have undergone substantial
changes post-dataset collection.

###  VII-D Future Research

Future research could address the limitations of the current study by
extending the scope of the dataset to include searches from other countries,
mobile devices, and a larger time horizon. This would enable a more
comprehensive time series analysis. In addition, future studies could delve
deeper into the analysis of result page characteristics other than position
and SERP features, such as keyword or result characteristics, which this study
has revealed to be significant. Finally, given the importance of appearing in
SERP features highlighted in our study, future work could explore the factors
that determine the likelihood of a result appearing in these features.

##  VIII Conclusion

This paper aims to provide an in-depth analysis of the influence that Search
Engine Results Page (SERP) features exert on the Click Through Rates (CTR) of
organic search engine results. The results of our study confirm that SERP
features, on average, exert a negative influence on CTR. Nevertheless, it has
been emphasized that the specific circumstances surrounding a result - such as
its position, the specific SERP features shown, and whether a website is
included in particular SERP features - can significantly modulate this
influence. As such, it has been demonstrated that websites that are featured
in specific SERP features, or those that are ranked lower in the results, can
actually derive benefits from the presence of SERP features. This paper also
provides a comparative analysis of the influence of SERP features against
other result page characteristics. The findings underscore that SERP features
have a tangible impact on CTR, thereby holding their own against other result
page characteristics. Despite this, it remains clear that the most dominant
determinant of CTR is the result’s position.

Our work offers several major contributions. Primarily, we conducted a
comprehensive, wide-reaching analysis using a dataset that is novel in its
scope and detail. With this dataset, we have examined the impact of more than
20 different SERP features, thereby offering a holistic view of the landscape
of SERP features. Additionally, we have compared the importance of SERP
features to virtually all other relevant result page characteristics, thereby
offering a well-rounded perspective on the factors that influence CTR.

Our findings also have strong practical applications. The insights derived
from this work can be highly valuable to SEO practitioners, shedding light on
the relevance of SERP features as a new dimension to consider in website
optimization. The study elucidates the SERP features it is most beneficial to
be featured in, and also provides insights into the specific combinations of
SERP features that can either increase or decrease the importance of high
ranking on a results page.

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###  -A Data Dictionary

[ label = III, entry = none, ] width = colspec = Q[130]Q[500]Q[150]Q[130],
hline2-67 = -, Variable & Description Data Source Example
Ads Any type of ad on the page. This can include ads on top of the search, at
bottom, or shopping ads. Describes whether the SERP feature appears at least
once on the page. Self-engineered 1
AdWords Bottom A series of ads (up to 4) that appear at the bottom of the
first search results page. Describes whether the SERP feature appears at least
once on the page. SEO data provider 1
AdWords Top A series of ads (up to 4) that appear at the top of the first
search results page. Describes whether the SERP feature appears at least once
on the page. SEO data provider 1
AMP AMP pages (i.e., results marked with the word ”AMP” and a gray lightning
bolt) shown in search results on mobile devices. SEO data provider 1
Avg. Monthly Volume Search volume averaged over months Keywordplanner 1312.65
Branded If the keyword includes a brand name. Grips 1
Carousel A row of horizontally scrollable images displayed at the top of
search results. Describes whether the SERP feature appears at least once on
the page. SEO data provider 1
Clicks Number of clicks on targeted search result Grips 25
Competition Measure of competition on search term with 0.0 being the lowest
and 1.0 being the highest. Keywordplanner 0.22
Count Page SERP Feat. Count of positive (=1) page SERP features for search
result page. Self-engineered 2
Count Positional SERP Feat. Count of positive (=1) positional SERP features
for search result. Self-engineered 5
CPC Cost per click of ad entry. Keywordplanner 2.34
CTR Click-through rate (clicks divided by impressions). Grips 0.25
Domain Domain of the URL of each search result. SEO data provider
‘jomashop.com’
FAQ A list of questions related to a particular search that shows up for a
particular organic search result. When clicked on, each of the questions
reveals the answer. Describes whether the SERP feature appears at least once
on the page. SEO data provider 1
FAQ (Positional) A list of questions related to a particular search that shows
up for a particular organic search result. When clicked on, each of the
questions reveals the answer. Describes whether the result is featured in the
SERP feature. SEO data provider 1
Featured Images A collection of images is usually displayed at the top of the
SERP if Google considers visual results to be more relevant than text results.
Only for mobile devices. Describes whether the SERP feature appears at least
once on the page. SEO data provider 1
Featured Snippet A short answer to a user’s search query with a link to the
third-party website it is taken from that appears at the top of all organic
search results. Describes whether the SERP feature appears at least once on
the page. SEO data provider 1
Featured Snippet (Positional) A short answer to a user’s search query with a
link to the third-party website it is taken from that appears at the top of
all organic search results. Describes whether the result is featured in the
SERP feature. SEO data provider 1
Featured Video A video result to a search query that is displayed at the top
of all organic search results. Describes whether the SERP feature appears at
least once on the page. SEO data provider 1
Flights A block that displays flights related to a search query. Flight
results include information on flight dates, duration, the number of transfers
and prices. Data is taken from Google Flights. Describes whether the SERP
feature appears at least once on the page. SEO data provider 1
Hotels Pack A block that displays hotels related to a search query. Hotel
results include information on prices and rating, and allows users to check
availability for certain dates. Describes whether the SERP feature appears at
least once on the page. SEO data provider 1
Image An image result with a thumbnail displayed along with other organic
search results. Describes whether the SERP feature appears at least once on
the page. SEO data provider 1
Image (Positional) An image result with a thumbnail displayed along with other
organic search results. Describes whether the result is featured in the SERP
feature. SEO data provider 1
Image Pack A collection of images related to a search query that is usually
displayed between organic search results. Describes whether the SERP feature
appears at least once on the page. SEO data provider 1
Image Pack (Positional) A collection of images related to a search query that
is usually displayed between organic search results. Describes whether the
result is featured in the SERP feature. SEO data provider 1
Impressions Impressions of the result, including estimates for results on the
second search page.. Grips 100
Instant Answer A direct answer to a user’s search query that is usually
displayed at the top of organic search results in the form of a gray-bordered
box. Describes whether the SERP feature appears at least once on the page. SEO
data provider 1
Intent: Commercial Trying to learn more before making a purchase decision
(e.g. “Subaru vs. Nissan”) SEO data provider 1
Intent: Informational Trying to learn more about something (e.g., “What’s a
good car?”) SEO data provider 1
Intent: Navigational Trying to find something (e.g., “Subaru website”) SEO
data provider 1
Intent: Transactional Trying to complete a specific action (e.g., “buy Subaru
Forester”) SEO data provider 1
Jobs Search A number of job listings related to a search query that appear at
the top of the search results page. Job listings include the job title, the
company offering the job, a site where the listing was posted, etc. Describes
whether SERP feature appears at least once on the page. SEO data provider 1
Keyword The searched keyword. SEO data provider ‘jomashop burberry scarf’
Keyword Complexity Score Flesch reading ease score (Flesch 1948) of the
keyword, with higher values indicating easier-to-read keywords. Self-
engineered 112
Keyword Count Number of words the search query (keyword) consists of. Grips 3
Keyword Difficulty Difficulty to rank for given keyword expressed from 0 to
100 SEO data provider 87
Keyword Included in Domain Keyword Included in Domain. Self-engineered 0
Keyword Included in URL Keyword Included in URL. Self-engineered 1
Keyword Length Number of characters in keyword Grips 23
Knowledge Panel Panel on right side of results that often includes images,
facts, social media links, and other relevant information to the search query.
Describes whether SERP feature appears at least once on the page. SEO data
provider 1
Knowledge Panel (Positional) Panel on right side of results that often
includes images, facts, social media links, and other relevant information to
the search query. Describes whether the result is featured in the SERP
feature. SEO data provider 1
Local Pack Embedded Google Maps frame on top of search results. Describes
whether SERP feature appears at least once on the page. SEO data provider 1
Local Pack (Positional) Embedded Google Maps frame on top of search results.
Describes whether the result is featured in the SERP feature. SEO data
provider 1
Number of Results Total number of results for search of keyword SEO data
provider 456789
People Also Ask A series of questions that may relate to a search query that
appears in an expandable grid box labeled ”People also ask” between search
results. Describes whether SERP feature appears at least once on the page. SEO
data provider 1
People Also Ask (Positional) A series of questions that may relate to a search
query that appears in an expandable grid box labeled ”People also ask” between
search results. Describes whether the result is featured in the SERP feature.
SEO data provider 1
Position Position of the result among other search results SEO data provider 3
Position (monthly) Average position in the last month. Grips 2.45
Position Difference Position subtracted from previous position, i.e. positive
values mean a decrease in position SEO data provider -1
Previous Position Position last month SEO data provider 2
Reviews Organic search results marked with star ratings and including the
number of reviews the star rating is based on. Describes whether SERP feature
appears at least once on the page. SEO data provider 1
Reviews (Positional) Organic search results marked with star ratings and
including the number of reviews the star rating is based on. Describes whether
the result is featured in the SERP feature. SEO data provider 1
Search Volume The search volume of a keyword, cleaned from the original
(inflated) value. Grips 75643
SERP Features by Keyword SERP features listed by ID, before one-hot-encoded.
SEO data provider 1
Shopping Ads A row of horizontally scrollable paid shopping results that
appear at the top of a search results page for a brand or product search
query, and include the website’s name, pricing, and product image. Describes
whether SERP feature appears at least once on the page. SEO data provider 1
Site Links A set of links to other pages of a website that is displayed under
the main organic search result and for brand-related search queries. Describes
whether SERP feature appears at least once on the page. SEO data provider 1
Site Links (Positional) A set of links to other pages of a website that is
displayed under the main organic search result and for brand-related search
queries. Describes whether the result is featured in the SERP feature. SEO
data provider 1
Top Stories A card-style snippet presenting up to three news-related results
relevant to user’s search query, which is usually displayed between organic
search results. Describes whether SERP feature appears at least once on the
page. SEO data provider 1
Top Stories (Positional) A card-style snippet presenting up to three news-
related results relevant to user’s search query, which is usually displayed
between organic search results. Describes whether the result is featured in
the SERP feature. SEO data provider 1
Trends How much interest web searchers have shown in a given keyword in the
last 12 months. SEO data provider 1
Tweet A card-style snippet displaying the most recent tweets related to a
search query. Describes whether SERP feature appears at least once on the
page. SEO data provider 1
URL The url of a google search result SEO data provider
‘https://www.jomashop.com/ burberry-4031051.html’
Video Video results with a thumbnail displayed along with other organic search
results. Describes whether SERP feature appears at least once on the page. SEO
data provider 1
Video (Positional) Video results with a thumbnail displayed along with other
organic search results. Describes whether the result is featured in the SERP
feature. SEO data provider 1
Video Carousel A row of horizontally scrollable videos displayed among search
results. Describes whether SERP feature appears at least once on the page. SEO
data provider 1
Video Carousel (Positional) A row of horizontally scrollable videos displayed
among search results. Describes whether the result is featured in the SERP
feature. SEO data provider 1

###  -B Feature Subsets

[ label = none, entry = none, ] width = colspec = Q[129] — Q[207]Q[301]Q[299],
hline2-5 = -, cell12 = c=3c Subset Features
Position Position Position Difference Position (monthly)
Keyword Number of Results
Keyword Difficulty
Intent: Commercial
Intent: Informational
Intent: Navigational Intent: Transactional
Competition
CPC
Search Volume
Avg. Monthly Search Vol. Keyword Length
Keyword Count
Branded
Complexity Score
SERP Feat. Instant Answer
Knowledge Panel
Carousel
Local Pack
Top Stories
Image Pack
Site Links
Reviews
Tweet
Video
Featured Video Featured Snippet
Image
Jobs Search
Video Carousel
People Also Ask
FAQ
Flights
Knowledge Panel (Positional)
Local Pack (Positional)
Top Stories (Positional)
Image Pack (Positional) Site Links (Positional)
Reviews (Positional)
Video (Positional)
Featured Snippet (Positional)
Image (Positional)
Video Carousel (Positional)
People Also Ask (Positional)
FAQ (Positional)
Ads
Count Page SERP Feat.
Count Positional SERP Feat.
Result Keyword in Domain Keyword in URL Domain (One-Hot-Encoded)

###  -C Tested Hyperparameters

[ label = IV, entry = none, ] width = colspec = Q[131]Q[207]Q[574]Q[25],
hline2,10,20,30,35,38,43 = 1-3, Model Parameter Values considered for
hyperparameter tuning
Random Forest Max depth Categorical: [None, 2, 3, 4], p=[0.7, 0.1, 0.1, 0.1]
Number of estimators Integer Log Uniform: 10 → 3000
Criterion Categorical: [‘squared_error’, ‘absolute_error’]
Max features Categorical: [’sqrt’, ’log2’, None, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6,
0.7, 0.8, 0.9]
Min samples split Categorical: [2, 3], p=[0.95, 0.05]
Min samples leaf Integer Log Uniform: 1 → 50
Bootstrap Categorical: [True, False]
Min impurity decrease Categorical: [0.0, 0.01, 0.02, 0.05], p=[0.85, 0.05,
0.05, 0.05]
GBDT Loss Categorical: [‘squared_error’, ‘absolute_error’, ‘huber’]
Learning rate Real Log Uniform: 0.01 → 10.0
Subsample Real Uniform: 0.5 → 1.0
Number of estimators Integer Log Uniform: 10 → 1000
Criterion Categorical: [‘friedman_mse’, ‘squared_error’]
Max depth Categorical: [None, 2, 3, 4, 5], p=[0.1, 0.1, 0.6, 0.1, 0.1]
Min samples split Categorical: [2, 3], p=[0.95, 0.05]
Min samples leaf Integer Log Uniform: 1 → 50
Min impurity decrease Categorical: [0.0, 0.01, 0.02, 0.05], p=[0.85, 0.05,
0.05, 0.05]
Max leaf nodes Categorical: [None, 5, 10, 15], p=[0.85, 0.05, 0.05, 0.05]
XGBoost Max depth Integer Uniform: 1 → 11
Number of estimators Integer Uniform: 100 → 1000
Min child weight Integer Log Uniform: 1 → 100
Subsample Real Uniform: 0.5 → 1.0
Learning rate Real Log Uniform: 1e-5 → 0.7
Col sample by level Real Uniform: 0.5 → 1.0
Col sample by tree Real Uniform: 0.5 → 1.0
Gamma Real Log Uniform: 1e-8 → 7.0
Lambda Real Log Uniform: 1.0 → 4.0
Alpha Real Log Uniform: 1e-8 → 100.0
CatBoost Max depth Integer Uniform: 3 → 10
Learning rate Real Log Uniform: 1e-5 → 1.0
Bagging temperature Real Uniform: 0.0 → 1.0
L2 leaf regression Real Log Uniform: 1.0 → 10.0
Leaf estimation iterations Integer Uniform: 1 → 10
TabNet Number decision steps Categorical: [3, 5, 10]
Layer size Categorical: [8, 16, 64]
Learning rate Categorical: [0.01, 0.02]
WideDeep Layer 1 size Categorical: [64, 128, 256]
Layer 2 size Categorical: [64, 128, 256]
Layer 3 size Categorical: [None, 64, 128, 256]
Dropout ratio Categorical: [0.0, 0.01, 0.05]
Embedding dimension Categorical: [4, 16, 32]
DeepFM Layer 1 size Categorical: [64, 128, 256]
Layer 2 size Categorical: [64, 128, 256]
Layer 3 size Categorical: [None, 64, 128, 256]
Use batch normalization Categorical: [True, False]
Dropout ratio Categorical: [0.0, 0.01, 0.05]
Embedding dimension Categorical: [4, 16, 32]

###  -D Used Hyperparameters

[ label = none, entry = none, ] width = colspec =
Q[69]Q[107]Q[65]Q[75]Q[90]Q[100]Q[81]Q[150]Q[190], hline2 = 4-9,
hline3,11,21,31,36,39,44 = -, cell14 = c=6c, Used for Subset
Model Parameter Default Position Position + Keyword Position + SERP Feat
Position + Result Position + Keyword + SERP Feat Position + Keyword + SERP
Feat + Result
Random Forest Max depth None None None None None None None
Number of estimators 100 897 823 3000 3000 175 516
Criterion squared _error squared _error squared _error squared _error squared
_error squared_error squared_error
Max features 1.0 0.1 sqrt 0.3 0.4 0.3 0.6
Min samples split 2 3 2 2 3 2 2
Min samples leaf 1 38 5 8 9 1 2
Bootstrap True True False False True False True
Min impurity decrease 0.0 0.0 0.0 0.0 0.0 0.0 0.0
GBDT Loss squared _error squared _error squared _error squared _error squared
_error squared_error huber
Learning rate 0.10 0.067 0.033 0.030 0.351 0.126 0.767
Subsample 1.0 0.517 1.0 0.711 0.833 0.634 0.819
Number of estimators 100 128 497 220 196 487 268
Criterion friedman _mse friedman _mse friedman _mse friedman _mse friedman
_mse friedman_mse friedman_mse
Max depth 3 2 None None 4 5 2
Min samples split 2 3 2 2 3 3 2
Min samples leaf 1 24 50 1 10 24 9
Min impurity decrease 0.0 0.010 0.050 0.050 0.010 0.010 0.010
Max leaf nodes None 15 None 15 5 5 15
XGBoost Max depth 6 11 11 8 11 11 11
Number of estimators 100 406 689 603 786 460 714
Min child weight 1 100 1 1 1 1 1
Subsample 1.0 1.0 0.993 1.0 1.0 1.0 0.668
Learning rate 0.30 0.015 0.030 0.035 0.016 0.039 0.031
Col sample by level 1.0 0.50 0.50 0.50 0.50 0.917 0.50
Col sample by tree 1.0 1.0 1.0 0.50 0.50 0.708 1.0
Gamma 0.0 1.0e-08 7.7e-05 0.009 1.0e-08 1.0e-08 0.001
Lambda 1.0 4.0 4.0 2.859 1.0 4.0 1.0
Alpha 0.0 1.0e-08 0.080 0.113 1.0e-08 0.014 1.0e-08
CatBoost Max depth 6 5 10 9 9 10 9
Learning rate 0.030 0.013 0.041 0.033 0.026 0.056 0.054
Bagging temperature 1.0 0.885 1.0 1.0 0.0 1.0 0.0
L2 leaf regression 3.0 6.601 10.0 10.0 10.0 10.0 10.0
Leaf estimation iterations Dynamic 10 10 1 6 10 10
TabNet Num decision steps 3 3 3 3 3 3 3
Layer size 8 8 8 8 8 8 64
Learning rate 0.02 0.02 0.02 0.02 0.02 0.02 0.025
WideDeep Layer 1 size 256 256 256 256 256 256 256
Layer 2 size 128 128 128 128 128 128 128
Layer 3 size 64 64 64 64 64 64 64
Dropout ratio 0.0 0.0 0.0 0.0 0.0 0.0 0.01
Embedding dimension 4 4 4 4 4 4 16
DeepFM Layer 1 size 256 256 256 256 256 256 256
Layer 2 size 128 128 128 128 128 128 128
Layer 3 size 64 64 64 64 64 64 64
Use batch normalization False False False False False False False
Dropout ratio 0.0 0.0 0.0 0.0 0.0 0.0 0.01
Embedding dimension 4 4 4 4 4 4 16

##  Appendix A Tables


# Totimorphic structures for space application

Amy Thomas, Jai Grover, Dario Izzo, Dominik Dold
Advanced Concepts Team
European Space Agency, European Space Research and Technology Centre
Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands

###### Abstract

We propose to use a recently introduced Totimorphic metamaterial for
constructing morphable space structures. As a first step to investigate the
feasibility of this concept, we present a method for morphing such structures
autonomously between different shapes using physically plausible actuations,
guaranteeing that the material traverses through valid configurations only
while morphing. With this work, we aim to lay a foundation for exploring a
promising and novel class of multi-functional, reconfigurable space
structures.

_K_ eywords morphing structure $\cdot$ deployable structure $\cdot$ multi-
functional metamaterial $\cdot$ totimorphic $\cdot$ programmable material

##  1 Introduction

The last decade has seen rapid expansion and interest in the field of advanced
materials and structures, especially in the development of programmable,
multi-functional, and morphable structures. Such structures are particularly
suited for space environments, where payload mass and volume are tightly
constrained, making light structures capable of performing multiple functions
highly desirable. For instance, Origami principles have already been used in
the development of deployable solar panels and antennae, and applications for
other advanced structures, such as NASA’s starshade [1], have been proposed
[2, 3]. However, most deployable space structures are currently limited
between strict configurations (typically stowed and deployed), often
prohibiting any reconfiguration thereafter.

Here, we explore a recently proposed metamaterial called a _Totimorphic
structure_ [4] whose characteristic properties might enable designs capable of
redeployment and reconfiguration into many different shapes after initial
deployment. This is especially intriguing for constructing adaptive
structures, as many recent papers [5, 6] have demonstrated the feasibility of
changing a structure’s mechanical properties through geometric alterations
alone. Such systems might enable mission designs capable of complex and
efficient post-launch reconfiguration, adjusting to changing mission goals or
conditions in situ and providing space missions with greater flexibility, thus
fundamentally changing the types of missions possible in the future.

In the following, we first explain the concept of totimorphic structures
before introducing a computational method for obtaining the actuations needed
to morph them into different shapes.

##  2 Methodology

Totimorphic structures are composed of neutrally-stable unit cells (also
called Totimorphic Unit Cells, TUCs) [4] shown in Fig. 1a,b. A TUC consists of
a beam with a ball joint in its middle ($A-P-B$ in Fig. 1a), a lever
connecting to the joint ($P-C$) and two springs connecting the ends of the
beam with the end of the lever ($A-C$ and $B-C$). The neutrally stable
behaviour of TUCs arises from the lever-spring motive: if the two springs are
zero-length springs with identical spring stiffness, any position of the lever
results in zero moment acting on the lever. The result of this property is
propagated across larger structures built from TUCs (e.g. Fig. 1c), such that
in the absence of external forces (e.g. gravity), the totimorphic structure
will retain its shape while remaining completely compliant to any external
force or displacement. By selective locking and unlocking of the structure’s
joints, we predict that the totimorphic property will allow the structure to
be smoothly morphed between different shapes via beam/lever rotations alone –
which we exploit in our method presented in the next section. Once the desired
target shape is reached, the structure can be made rigid by locking all
joints.

Figure 1:  (a) Illustration of a TUC with lever rotation $\theta$. (b) The
TUCs beam rotation is given by $\varphi$, i.e., $A-P-B$ is seen from the side
here. (c) A simple auxetic structure built from four TUCs.

Before presenting our approach for morphing such structures, we first
introduce the used mathematical description. Each TUC is geometrically fully
defined by its position vector $P$, the beam vector $\overrightarrow{AB}$, the
lever length $r$, the angle between beam and lever $\theta$, and the roll
angle of the lever from the vertical $\varphi$ (Fig. 1b). TUCs may be
connected to each other at the $A$, $B$, $C$ nodes, however for this paper’s
analysis, only $A-B$ and $C-C$ connections were considered. Additionally, $r$
was set to be equal for all TUCs. If the coordinates of $A$, $B$ or $C$ are
already known (i.e. the unit cell is attached to another unit cell), the unit
cell can be described just by $\overrightarrow{AB}$, $\theta$, and $\varphi$ –
which is useful for implementing the morphing method.

##  3 Results

Our morphing method works as follows. We first define the initial and target
geometries, set a maximally allowed change in $\overrightarrow{AB}$, $\theta$,
and $\varphi$ per iteration (same for all TUCs), and a subset of nodes are set
as ‘pinned’ (i.e. their position is fixed, but they are allowed to rotate). We
also ‘activate’ the pinned cells, (i.e. allow them to morph). Then we run the
following iteration until the structure’s geometry is within some tolerance of
the desired target geometry: each activated TUC changes $\overrightarrow{AB}$,
$\theta$ and $\varphi$ as much as possible to reach its target configuration
while still maintaining structural cohesion (i.e. no beams
breaking/prolonging/squeezing or TUCs separating). Then they become ‘fixed’
(cannot be activated anymore in this iteration, so the TUCs are frozen in
place) and inform their neighbouring cells that they should move next (they
activate their neighbours). This process is repeated until all cells are
fixed. Consequently, all TUCs are unfixed and the next iteration begins.
Intuitively, a wave of ‘cell activation’ moves through the structure, where
activated cells are moved closer to their target and become immovable (fixed)
afterwards.

Figure 2: A totimorphic structure morphing continuously from a stowed plane to
a square plane (a) $\theta=30$ (b) $\theta=60$ (c) $\theta=90$, and then into
a semi-cylinder (d-f). Red lines indicate pinned nodes with fixed coordinates.

The morphing method is illustrated in Fig. 2 for continuously morphing a
structure to different target shapes: (a-c) turning a stowed geometry into a
large flat surface, and (d-f) turning the flat surface into a half-cylinder.
Although we halt at the shape in Fig. 2f here, in principle the structure can
be mapped to any developable surface of an equal or smaller surface area [4],
so long as there is a valid target geometry for the method.

In comparison with an Origami structure, which must necessarily unfold and
change its thickness during deployment, we can see in (a-c) that the stowed
totimorphic structure can continuously increase its surface area without any
increase in the stowing thickness, resulting in a large stowed-to-deployed
surface area ratio. Further, the stowing of the totimorphic structure does not
constrain its final structural geometry, since it is possible for the
structure to morph into intermediary states that enable better deployment
before morphing into the final configuration.

##  4 Discussion

For the presented method to work, one requires knowledge about the exact
initial and target configuration of the totimorphic structure (including
angles) instead of just the shapes. Moreover, the choice of pinned nodes is
crucial to ensure convergence to the target shape. Thus, we plan to develop an
improved non-rigid morphing methodology that is both more robust and general,
based on a model that predicts the whole structure’s response to small
perturbations. Such a model might further allow us to use inverse design
approaches from artificial intelligence [6] to autonomously find
configurations that possess desired effective mechanical properties.

Although totimorphic structures are more flexible in their morphing
capabilities than Origami-based structures, they come with the drawback of
having a high number of degrees of freedom as well as many movable mechanical
parts. We anticipate that this will lead to challenges in the production of a
physical prototype, which have to be overcome first for totimorphic structures
to compete with alternative approaches. For instance, the neutrally stable
behaviour will most likely not be perfectly realised in a physical system due
to effects such as bending of the beam in a TUC from radial forces applied
through the lever – an effect that has to be considered during the design and
testing stages of a real prototype.

We are confident that totimorphic structures are ideally suited for deployment
in extremely-low gravity environments such as orbits and deep space, where no
external loads due to gravity interfere with the morphing process and the
neutrally stable behaviour can be utilised to its fullest. As noted in [7],
the gravitational forces experienced on planetary bodies will impede the
morphing of totimorphic structures, the extent of which has to be investigated
in future work.

To lock and unlock the joints as well as induce beam/lever rotations, we
envision a thin and foldable support layer glued to the totimorphic structure
through which lock, unlock and rotation commands, e.g., from a
microcontroller, can be relayed electronically. For instance, since only a
small number of cells are unlocked at a time, electrical pulses could be used
with a shared bus to realise an efficient and economic solution.

##  5 Conclusion

Totimorphic structures offer unique structural characteristics that make them
ideal for space missions – providing a high degree of flexibility coupled with
a low mass and volume. They are suitable for a multitude of potential space
applications; such as deployable habitats and structures, tools (e.g. nets for
grabbing something), or for building moving structures by creating locomotion
from morphing. Hence, we believe that totimorphic structures are a promising
candidate in the search for technologies that enable morphable, multi-
functional space structures.

## Acknowledgments

We would like to thank Derek Aranguren van Egmond and Michael Mallon for
helpful discussions, and our colleagues at ESA’s Advanced Concepts Team for
their ongoing support. AT and DD acknowledge support through ESA’s young
graduate trainee and fellowship programs.

## References

  * [1] “Information on https://exoplanets.nasa.gov/exep/technology/starshade/. Accessed: 05/07/23.”
  * [2] Collin Ynchausti et al.  “Hexagonal Twist Origami Pattern for Deployable Space Arrays”  In _ASME Open Journal of Engineering_ 1 American Society of Mechanical Engineers Digital Collection, 2022  DOI: https://doi.org/10.1115/1.4055357
  * [3] Akash Biswas et al.  “An ultra-wideband origami microwave absorber”  In _Scientific Reports_ 12.1 Nature Publishing Group UK London, 2022, pp. 13449  DOI: https://doi.org/10.1038/s41598-022-17648-4
  * [4] Gaurav Chaudhary, S Ganga Prasath, Edward Soucy and L Mahadevan  “Totimorphic assemblies from neutrally stable units”  In _Proceedings of the National Academy of Sciences_ 118.42 National Acad Sciences, 2021, pp. e2107003118  DOI: https://doi.org/10.1073/pnas.2107003118
  * [5] Hamidreza Yazdani Sarvestani et al.  “Bioinspired stochastic design: tough and stiff ceramic systems”  In _Advanced Functional Materials_ 32.6 Wiley Online Library, 2022, pp. 2108492  DOI: https://doi.org/10.1002/adfm.202108492
  * [6] Dominik Dold and Derek Aranguren van Egmond  “Differentiable graph-structured models for inverse design of lattice materials”  In _arXiv preprint arXiv:2304.05422_ , 2023  DOI: https://doi.org/10.48550/arXiv.2304.05422
  * [7] Mark Schenk and Simon D Guest  “On zero stiffness”  In _Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science_ 228.10 SAGE Publications Sage UK: London, England, 2014, pp. 1701–1714  DOI: https://doi.org/10.1177/0954406213511903