Fig 1.
(a) Example of events observed for a player in our dataset. Events are shown at the position where they have occurred. This plain “geo-referenced” visualization of events allow understanding how to reconstruct the player’s behavior during the match. (b) Distribution of the number of events per match. On average, a football match in our dataset has 1600 events.
Table 1.
Example of event corresponding to an accurate pass.
eventName indicates the name of the event’s type: there are seven types of events (pass, foul, shot, duel, free kick, offside and touch). eventSec is the time when the event occurs (in seconds since the beginning of the current half of the match); playerId is the identifier of the player who generated the event. matchId is the match’s identifier. teamId is team’s identifier. subEventName indicates the name of the sub-event’s type. positions is the event’s origin and destination positions. Each position is a pair of coordinates (x, y) in the range [0, 100], indicating the percentage of the field from the perspective of the attacking team. tags is a list of event tags, each describing additional information about the event (e.g., accurate). A thorough description of this data format and its collection procedure can be found in [10].
Table 2.
Statistical difference of technical features between male and female teams.
The summary data for both women and men are report as mean±standard deviation per matches. Grey rows indicates features for which the difference between men and women is statistically significant. The highest values are highlighted in bold.
Fig 2.
Heatmaps describing the pitch zones from where free-kick shots and shots in motion are more likely to be made by male and female players, computed as the kernel estimate of the first grade intensity function, where the event points are the free-kick shots and the shots in motion, and the football field is the region of interest.
The darker is the green, and the higher is the number of free-kick shots and shots in motion in that field zone. The pitch length (x) and width (y) are in the range [0, 100], which indicates the percentage of the field starting from the left corner of the attacking team.
Fig 3.
Pitch zones from where free-kicks and shots in motion are more likely to be made by male players (a) and female players (b).
We split the attacking midfield into three equal zones: Z1 is the area closest to the opponents’ goal, Z3 the furthest, and Z2 the zone in the middle. In each zone, we show the percentage of free kicks and shots in motion made in that zone and depict the kernel estimate of the First Grade Intensity function, where the event points are the free-kicks and the shots in motion, and the football field is the region of interest. The darker the color, the higher is the number of events in a specific field position. Female zones are 1.1 meters closer to the opponents’ goal than male zones.
Fig 4.
PlayeRank score by role fro male and female players.
Asterisks indicate significant statistical difference between male and female for that role.
Table 3.
Average H indicator, FC, and PR score for each team in the two competitions.
Fig 5.
ROC curves for the implemented classifiers.
They trace the true positive rate and the false positive rate as the probability threshold changes, i.e., the threshold beyond which an observation is assigned to class 1 (male team). When the true positive rate and the false positive rate are 0, the threshold is 1 (all the observations are classified as class 0) [29]. In this case, the true positive rate is the percentage of male teams correctly classified, and the false positive rate is the percentage of female teams mistaken as male, using a given threshold. The actual thresholds are not shown. The AUC represents the area under the curve; the larger the AUC, the better the classifier [29]. Random Forest and Adaboost M1 show the best predictive performance.
Table 4.
Table of the leave-one-team out cross-validation results (i.e., accuracy, precision, recall and F1-score) computed on the training dataset of each machine learning classifiers used to predict a football team in a game as male (class 0) or female (class 1).
The baseline classifier always predicts by respecting the training set’s class distribution, which is balanced. The percentages in the table refer to the improvement of machine learning model compared to the baseline results.
Fig 6.
Ranking of features importance (mean Shap value) extracted from the team gender classifier.
Fig 7.
Distribution of the impact of each feature on the team gender classifier.
The color represents the feature value (red high, blue low); and position of the point indicates the Shap value.
Fig 8.
Local Shap explanations for two examples in our dataset: France in France vs Croatia and USA in match USA vs Spain.
Feature values that increase the probability of a team to be male are shown in red, those decreasing the probability are in blue.
Fig 9.
(a, b) Scatter plots displaying AccP versus RecT for a test set of teams in male matches (a) and female matches (b). Circles indicate a team correctly classified by the team gender classifier; crosses indicate a mistake by the classifier. The dashed lines are at the median values for the two variables over the entire data set. In plots (c) and (d), we report the local Shap explanations of two misclassified examples.