Excellent physical performance of soccer players is inevitable for the success of a team. Despite of this, a large-scale, quantitative analysis of the maximal speed of the players is missing due to the sensitive nature of trajectory datasets. We propose a novel method to derive the in-game speed pro le of soccer players from event-based datasets, which are widely accessible. We show that eight games are enough to derive an accurate speed pro le. We also reveal team level discrepancies: to estimate the maximal speed of the players of some teams 50% more games may be necessary. The speed characteristics of the players provide valuable insights for domains such as player scouting.
Quantitative performance analysis in sports has become mainstream in the last decade. The focus of the analyses is shifting towards more sport-speci c metrics due to novel technologies. These systems measure the movements of the players and the events happening during trainings and games. This allows for a more detailed evaluation of the professional athletes with implications on areas such as opponent scouting, planning of training sessions, or player scouting.
Previous works that analyze soccer-related logs focus on the game-related
performance of the players and teams. Vast majority of these methodologies
concentrate on descriptive statistics that capture some part of the strategy of
the players. For example, in case of soccer, the average number of shots, goals,
fouls, passes are derived both for the teams and the players [
It is a challenging task to get access to metrics related to the physical performance of soccer players. The teams consider such information highly con dential, especially if it covers in-game performance. Despite the fact that numerous teams deployed player tracking systems in their stadiums, datasets of this nature are not available for the research or public domain. It is nearly impossible to have quantitative information on the physical performance of all the teams in a competition. Hence, most of the analysis and evaluation of the players' performance do not contain too much information on the physical aspect of the game.
We address this issue by proposing a methodology that is able to derive the in-game speed pro le of soccer players, i.e., how much time a player needs to cover a certain distance in the best case scenario. In other words, we determine the relation between the maximal speed of a player for a given range. In addition, we are able to do this on scale: our method is able to analyze the physical performance of the players across multiple seasons and competitions without any major investment. It is not required to have an expensive, dedicated player tracking system deployed in the stadium. Instead, if the game is broadcasted, our methodology can be used. As a consequence, our technique does not require the consent of the involved teams yet it provides insights on the physical performance of the players of both teams. Soccer data companies are covering 50+ leagues providing the potential to analyze the speed pro le of tens of thousands of players. The main contribution of our work is threefold: 1. we propose a methodology to extract the maximal speed characteristics of the players, 2. we determine the minimal number of games necessary to determine the physical capabilities of a player, 3. and we show that the playing style of a team has a signi cant impact on the accuracy of the speed estimation. 2
In this section we introduce our methodology used to extract the movements of the players and then to estimate their maximal speed. Our nal goal is to derive a regression model between the distance of the movement and the minimal time necessary for it. We use an event-based dataset throughout our analyses that we describe next.
Dataset. We use an event-based dataset generated by Opta [
60 40 y _ ttr a s 20 0 0 25 50 75 100 Fig. 1. Movement vectors of a playerstdarte_xrived from an event-based dataset. Not only the location of the end points are present in the data but the speed of the movement too.
Handling passes. It is straightforward to determine the timestamp and the position of the players in case of single-player events (i.e., all the events except passes). In terms of passes, we have a complete datapoint for the initiator of the pass (i.e., timestamp and location), however, at the receiving end, the dataset does not contain a timestamp. To overcome this issues, and to increase the wealth of the extracted time-series, we apply four methods to estimate the time when a pass was received. The four options are: { 0. Neglect. The event of receiving a pass is neglected, i.e., we do not use this partial information. { 1. Previous event. The timestamp of the previous event is used, i.e., the initiation of the pass. This is a lower-bound estimation of the time of reception. { 2. Next event. The timestamp of the next event is applied. This timestamp is an upper-bound on the reception of the pass. { 3. Regression. Two passes may follow each other immediately in soccer, i.e., when a player receives a pass, handles the ball, and passes the ball forward with a single touch. We can select these consecutive passes from the dataset, i.e., in this case the (x; y) coordinates and the identity of the player are the same (the receiver of the rst pass and the initiator of the next one). Therefore, in case of the rst passes we know the timestamp of both the initiation and the reception. Therefore, based on these accurate ball movements, we build a linear regression model between the range and the elapsed time of the passes. We apply a 10-fold cross validation of the model; the accuracy score is 33.26%, while 73.2% of the times we are able to estimate the time duration of the pass with an error of at most one second. Using this regression model, we estimate the speed of the passes and as such the time of the pass reception to increase the instances where the position of the players are known.
At the end of the data extraction step, for each game and each player we have a
list movements done during the game. Such a tuple contains the start and end
(x; y) coordinates of the player along with the appropriate timestamps.
Diverse eld sizes. An interesting property of the rules of soccer is that the
sizes of the eld are not xed, there is some room to design a soccer pitch even in
case of international matches. According to the rst law of the game, the length
of the pitch shall be between 100 and 110 meters, while the width between 64
and 75 meters [
Filtering. Before building the regression model of the maximal speed, we apply
a data cleaning step. As we mentioned above, the derived movement dataset
contains a lot of noise. On the one hand, it is owed to the methodology we use
to derive the movement vectors, while on the other hand the time is annotated
in seconds. As a sanity check, we apply two lters to remove the obvious aws
from the dataset. We lter out all the movement vectors that span more than
20 seconds. Our choice of this constraint is based on the fact that professional
sprinters are able to run 100 meters in less than 10 seconds. Thus, it is
reasonable to assume that the maximal speed of soccer players is above 50% of the
sprinters. The second lter is based on the speed of the movement: we remove
those movements where the speed of the player is larger than 15m/s.
Quantile regression. We use the ltered movement vectors to build a
regression model that estimates the maximal speed of the players depending on the
distance they cover. Our goal is to determine the minimal time a player needs to
cover a certain distance. For this purpose, we apply the techniques of quantile
regression where the regression model estimates a speci c quantile of the dataset
(instead of the mean in case of the linear regression) [
We evaluate the accuracy of the derived regression models based on their consistency, i.e., how stable the parameters of the regression model are. If the parameters of the regression model|namely, the intercept and the slope|are similar irrespective to which subset of the dataset we use, the model can be considered sound. 3
The evaluation of the proposed methodology is twofold. First we focus on the overall performance of the speed estimators and then we analyze the scalability of the methods. To investigate the accuracy of the regression models (i.e., the four 1.00 variants how we handle the passes), we derive the quantile regression model of all the players in the dataset using all the movements the players had throughout the season. In case of each player, we divide the movement vectors into two and then compute the parameters of the quantile regression line. Afterwards, we determine the standard deviation of the parameters in case of all the players separately. In Figure 3 we show the cumulative distribution function of the parameters in case of the four methods. In case of both parameters, the previous event (#1) provides the best accuracy, i.e., it has the lowest deviation in the parameters given the random subsets of the sample. Not only the precision of speed estimation is the highest in case of the previous event method but it enables us to investigate the maximal speed of more players compared to the neglect version (539 vs. 529 players). The next event method (#2) does not enhance the accuracy of the speed estimation as the results reveal.
We next focus on the following question: how many games do we need to accurately estimate the maximal speed of the players? We answer this question by analyzing the standard deviation of the parameters of the quantile regression models given di erent subset of the games a player was involved. Speci cally, 0.0 ●●● ●● ●●●●●●●●● ●●●●●●●●●●●● ●●●●●●●●●●●● ●●●●●●●●●●●● ●●●●●●●●● ●●●●●●●●● ●●●●●●● ●●●●●● ●●●●●●● ●●●●●● ●●●●●● ●●●●● ●●●●● ●●●●●●● 0.3 ●●●● ●●●● l.t.svsddeope00..12 ●●●●●●●●●●●●●● ●●●●●●●●●●●●●●●● ●●●●●●●●●● ●●●●●●●●●●●● ●●●●●●●●●● ●●●●●●●●●● ●●●●●●● ●●●●●●●● ●●●●●●● ●●●●●●●●●● ●●●●●●●● ●●●●●● ●●●●●● ●●●●● 0.0 we randomly select n = 1; 2; : : : games from the ones the player participated in and derive the regression model; we repeat this ten times for each n and for each player. We show the deviation of the parameters in Figure 4, where we focus on the best estimator we have seen above. As the results reveal, the accuracy of the previous event method is stable if we have data from at least 8 games. This is a fascinating result that implies we are able to characterize the in-game maximal speed of a player based on one quarter of a season|which has 38 games.
We analyze the accuracy and the information need of the di erent methods in Figure 5. Here we apply thresholds for the deviation of the parameters. For each player we determine the minimal number of games that enable us to estimate the maximal speed of the players with the given accuracy. Speci cally, the thresholds are 0.25 and 0.025 in case of the intercept and the slope, respectively. In case of 50 percent of the players, it is enough to have data for ve games to have an accurate enough estimation of their maximal speed (in case of the previous event method). There are large discrepancies among the methods, e.g., the neglect and next event methods need twice as much games to provide accurate speed estimation for 80 percent of the players compared to the previous event method. Based on the results we can draw the following conclusion: one should use the previous event or the regression methods.
There are team speci c discrepancies in case of the information need of the methods. Table 1 presents the mean number of games required to estimate the speed of the players of a given team accurately. In general, we need the fewest number of games in case of the players of FC Barcelona. This is inline with the fact that FC Barcelona dominates the ball possession in its games and such its players have numerous ball related events, and as such, movement vectors. However, in case of the previous event method,we need only 2.6 games to estimate the speed of the players of Celta de Vigo too. In some cases, the discrepancy of the required number of games is signi cant, e.g., we need 50% more games in case of Espanyol and Valencia using the neglect methodology compared to FC Barcelona. These di erences have a crucial impact on one of the application domain of the methodology: player scouting (i.e., one has to analyze more games if the player is part of a speci c team). ● ● 0 ● ● ●● ● ●●● ● ● ● ●●● ●●●●● ●● ● ●● ● ●●●●●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● ●●●●●●● ● ●● ●●●●● ● ● ●● ● ● ●
● intercept ● ● ● 10 ●
The proposed methodology indeed can be used for player scouting. As Figure 6 shows, the maximal in-game speed characteristics of the players are diverse, hence, it provides an additional facet for performance evaluation. One can identify suitable candidate to sign who has the physical capabilities necessary for the playing style of a given team. 4
We proposed a new technique to estimate the maximal speed of soccer players. Using event-based datasets of eight games we are able to accurately determine the speed pro le of the players. The investigations revealed that teams require diverse size of datasets for a precise speed estimations. As a future work, we plan to analyze the discrepancies of the estimations across players and leagues. Our method provides a new way to evaluate the performance of soccer players,
Team intercept #0 #1 #2 #3 particularly, from a physical performance point of view. Such insights can be used as competitive advantage for opponent and player scouting.