An important task in sports analytics is to devise playerperformance metrics that allow managers to take better-informed decisions. While several such metrics have been proposed for baseball, basketball, and ice hockey, this task has virtually remained unexplored to date for soccer. This paper presents an approach for automatically rating the actions performed by soccer players based on historical match data. The approach considers all player actions that contribute to a team's o ensive output and accounts for the context of the actions.
possession-based teams should not be favored over players in counter-attacking teams. Second, the metric should account for the spatial context at the time of each action. For example, a key pass in the nal third of the pitch should be valued higher than a pass in mid eld.
In this paper, we present STARSS (Spatio-Temporal Action Rating System for Soccer), which leverages historical match data to assign a rating to the actions (e.g., a pass or a shot) performed by the players in a match. For a given match, the presented approach proceeds in three steps. First, the approach splits the match into phases, which are uninterrupted sequences of actions where one team is in possession of the ball. Second, it assigns a phase rating to each phase based on historical match data. The higher the assigned rating, the more likely that the phase will end in a goal. Hence, our approach focuses on the actions that contribute to the o ensive output of the team. Third, the approach distributes the phase rating across the individual actions that constitute the phase.
We use STARSS to rate players and teams in individual matches as well as throughout the course of a season. We present the top-15 players for the 2015/2016 season in the English Premier League, the German Bundesliga, and the Spanish La Liga. We nd that wingers and attacking mid elders tend to contribute more to a team's STARSS rating than strikers, that ve of the top-15 players in the German Bundesliga play for FC Bayern Munich, and that Lionel Messi is the best player in the world. 2
Our dataset consists of play-by-play data for the English Premier League, German Bundesliga, and Spanish La Liga for the 2012/2013 through 2015/2016 seasons. Our dataset comprises 4253 matches, 7,569,802 game events, 110,290 shots, and 11,842 goals.
The data for each match consist of a stream of events. For each event, the following information is available: the type (e.g., a foul or cross), a timestamp, the player involved, the team involved, and the location on the pitch (i.e., the x- and y-coordinate of the ball). Depending on the type of the event, additional information is available. For example, the end location for a pass or the outcome (e.g., o target, on target, or goal) for a shot.
The presented approach rates players by assessing the \actions" they perform on the pitch. We de ne an \action" as an event performed by a player who either is in possession of the ball or attempts to gain possession of the ball. The set of considered actions includes, among others, passes, dribbles, crosses, shots, interceptions, and tackles. 3
This section introduces STARSS, which is an approach for automatically rating the actions performed by soccer players. Unlike traditional approaches,5 which 5 For instance, the approaches used by WhoScored.com and Squawka.com. simply compute a weighted sum of the frequencies of a hand-picked set of actions, our approach accounts for the spatio-temporal context in which the actions were performed. More speci cally, our approach leverages the outcomes of similar actions that were performed in similar circumstances in the past to assess the value of a particular action to the team.
To rate the player actions in a given match, our approach performs the following three steps. First, it splits the match into phases of related actions. Second, it assigns phase ratings to the resulting phases based on historical match data. Third, it assigns action ratings to the individual actions that constitute the phases. 3.1
We view a match as a sequence M = (a1; : : : ; an) = (ai)in=1, where each ai is an action performed by a player and n is the total number of actions. We start a new phase each time possession switches from one team to the other or too much time (i.e., 10 seconds) has passed between consecutive actions (Figure 1). For example, when the ball goes out of play for a throw-in or corner kick, when a goal is scored, or when a free kick is awarded.
This way, a match M is split into subsequences (Pj )jm=1, where each Pj is a
phase and m is the total number of phases. Each phase Pj is a subsequence of
consecutive actions (ak)jk2=j1 appearing in the sequence M .
We assign a rating to a given phase P in two steps as follows. In the rst step,
we search the k most-similar phases in terms of their spatial location on the
pitch in historical match data. This historical match data is split up in phases
using the same procedure as in Section 3.1. To measure the similarity between
two phases P and P 0, we employ dynamic time warping (DTW) [
DT Wi(P; P 0)2
where DT Wi is the DTW-based similarity of P and P 0 in the ith dimension.
Here, we only consider the x and y coordinates of the individual actions that
make up the phases P and P 0. The core idea behind this approach is to reward
teams and players for phases that get the ball into dangerous places, even if the
phases do not lead to a shot. Furthermore, we are less interested in which action
is used to get the ball into the location, as we do not want to favor one style
of play over another. Most existing approaches to rate phases in soccer (e.g.,
[
In the second step, we compute the phase rating as the proportion of similar phases that end in a goal: X
1goal(P 0) phase rating(P ) = P 02NNk(P )
k wi = ) wi+1 if k if i = l; i < l (1) (2) (3) where 1goal(P ) is an indicator function that is 1 if P ends in a goal and 0 if it does not and N Nk(P ) is the set of the k most similar phases to P (i.e., the Nearest Neighbors) according to distance function d(P; P 0) in Equation 1. For example, if we want to rate a phase P using k = 100 similar phases and 13 out of the 100 most similar phases end in a goal, then the rating of P amounts to 0.13. 3.3
Assume we are given a phase P = (ai)i=k with ak the rst action of the phase and al the last action of the phase. We then assign a rating to each action ai in P in two steps. We rst compute an action weight wi that indicates the relevance of the action ai to the phase P , and then compute the action rating by multiplying the rating for the phase P with the normalized action weight w0. i
We use an exponential-decay-based approach to compute the action weights. We consider actions that happen at the end of a phase more important than actions that happen at the start of a phase. Hence, we assign low weights to actions that happen at the start and high weights to actions that happen at the end. Intuitively, this makes sense as the last few actions in a phase have the highest in uence on its outcome. We compute the action weights in reverse order, starting with the last action al and working our way down to the rst action ak, using the following formula: (4) (5) where is a user-speci ed parameter.
We normalize the weights such that they sum to one, which means that the phase rating is completely distributed across the individual actions. Finally, the rating for an action ai 2 P is computed by multiplying the phase rating with the normalized action weight.
action rating(ai) = phase rating(P ) w0 i 4
This section explains how we leverage the proposed STARSS approach to address the case studies presented in the next section.
We use STARSS to rate players in individual matches as well as throughout the course of an entire season as follows. For a given player, we rst sum the ratings for the actions performed by the player during a match or season, then divide this sum by the total number of minutes that the player played, and nally multiply by 90 to obtain a rating normalized per 90 minutes. Similarly, we also rate teams in individual matches and over the course of a season.
We respect the chronological order of the matches when rating player actions. To rate a player or team in a particular match, we only leverage matches from the same league that had already been played at the time of that match to discover similar phases. For example, to rate the Leicester City players in their 1-3 win over Manchester City on 6 February 2015, we only consider the Premier League matches in our dataset that were played before that date.
For each of the case studies, we set the parameters k = 100 and for computing the action weights to 0:25 based on domain knowledge and an empirical analysis of the available data. 5
This section presents case studies that illustrate the utility of the presented STARSS approach. Concretely, we address the following two questions: 1. Can STARSS identify the top-performing players in a league? 2. Can STARSS identify the top-performing players in a match? 5.1
To answer this question, we compute the player ratings for all players that played
at least 10 hours in the 2015/2016 season of the English Premier League, German
Bundesliga, and Spanish La Liga. We present the top-15 players for each league
in tables 1, 2, and 3, respectively. Note that these rankings di er from simply
ranking players based on a combination of goals and assists per 90 minutes,
and hence they provide insight beyond using these traditional metrics. Alexis
Sanchez was a key player for championship contenders Arsenal and tops the
Premier League ranking. Zlatko Junuzovic, whose assists were instrumental for
Werder Bremen in their battle against relegation, is the top-ranked player in
the Bundesliga. Lionel Messi, who helped Barcelona claim the league title, tops
the La Liga ranking. Unsurprisingly, the ve-time FIFA Ballon d'Or winner is
also the top-ranked player across the three leagues. Unlike the Premier League
and Bundesliga, the La Liga ranking exhibits a clear gap between Lionel Messi
and the rest, indicating that the Argentine forward is a class apart as was also
suggested by earlier work [
The Premier League ranking suggests that Arsenal's o ensive compartment excelled in the 2015/2016 season. The Gunners, who eventually nished second, have four players in the top 15 with Santi Cazorla, Mesut O zil, and Olivier Giroud alongside top-ranked Alexis Sanchez. In contrast, surprise champions Leicester City have not a single player in the top 15, despite the fact that Riyad Mahrez won the Player's Player of the Year award and Jamie Vardy won the Premier League Player of the Season Award. These players were ranked rst and second in the league according to summing total goals and assists. Traditional metrics like expected-goals indicated that Leicester were hugely over-performing last season, that is, the results were much better than the underlying numbers. Additionally, Leicester were also awarded a remarkably high number of penalties (13 in total, while the league average was 4.5 league average).
The Bundesliga ranking clearly shows FC Bayern Munich's superiority in the 2015/2016 season. Although Werder Bremen's free-kick specialist Zlatko Junuzovic tops the ranking, the eventual champions have ve players in the top 15. The La Liga ranking sees most of the usual suspects near the top of the ranking with Lionel Messi (Barcelona), Neymar (Barcelona), Cristiano Ronaldo (Real Madrid), and Gareth Bale (Real Madrid) occupying the rst four positions.
These rankings also indicate several highly-ranked players who made moves to larger clubs following the season. These include Ilkay Gundogan and Nolito, who both transferred to Manchester City, and Henrikh Mkhitaryan, who moved to Manchester United. 5.2
To answer this question, we perform three steps. First, we compute the rating for each player in each match in the 2015/2016 season of the English Premier League, German Bundesliga, and Spanish La Liga. Second, we compute the team rating for each team in each match by summing the individual player ratings. Third, we compute each player's share of the team rating.
Figure 2 shows the shares of the player ratings in the team ratings for El Clasico, a match between erce rivals FC Barcelona and Real Madrid in La Liga, on 2 April 2016. Unsurprisingly, Lionel Messi, Luis Suarez, and Neymar occupy 1 Zlatko Junuzovic SV Werder Bremen 2 Ilkay Gundogan Borussia Dortmund 3 Alexandru Maxim VfB Stuttgart 4 Tobias Werner FC Augsburg 5 Sandro Wagner SV Darmstadt 98 6 Henrikh Mkhitaryan Borussia Dortmund 7 Thiago Alcantara FC Bayern Munchen 8 Franck Ribery FC Bayern Munchen 9 Robert Lewandowski FC Bayern Munchen 10 Thomas Muller FC Bayern Munchen 11 Arjen Robben FC Bayern Munchen 12 Dario Lezcano FC Ingolstadt 04 13 Hakan Calhanoglu Bayer 04 Leverkusen 14 Daniel Didavi VfB Stuttgart 15 Daniel Ginczek VfB Stuttgart
Player 0.147 0.420 0.000 0.196 0.225 0.209 0.561 0.084 0.109 0.404 0.398 0.223 0.178 0.340 0.550 0.383 0.135 0.430 0.129 0.145 0.524 0.165 0.396 0.068 0.192 0.082 0.072 0.199 0.111 0.143
Player 1 Lionel Messi Barcelona 2 Neymar Barcelona 3 Cristiano Ronaldo Real Madrid 4 Gareth Bale Real Madrid 5 Duda Malaga 6 Nolito Celta de Vigo 7 James Rodriguez Real Madrid 8 Yevhen Konoplyanka Sevilla 9 Ever Banega Sevilla 10 Isco Real Madrid 11 Luis Suarez Barcelona 12 Angel Correa Atletico de Madrid 13 Jese Real Madrid 14 Orellana Celta de Vigo 15 Saul Berjon Eibar the rst three spots for FC Barcelona, while Gareth Bale, Cristiano Ronaldo, and Karim Benzema occupy the rst three spots for Real Madrid. This section discusses related work in soccer as well as other sports.
Our approach is related to the work on expected-goals models, which have
been a hot topic in the soccer-analytics community for the past few years.
Expected-goals models aim to objectively quantify the quality of goal attempts
and several di erent models have been proposed in recent years [
There are a number of websites such as WhoScored.com and Squawka.com that provide player ratings for soccer on a match-by-match basis. These websites have hand-crafted formulas that simply compute a weighted sum of frequencies for a hand-picked set of actions (e.g., shots, tackles, etc.). The weights associated with each action are set by hand according to domain knowledge. The importance of some of the defensive statistics such as the number of tackles is debatable. A high percentage of successful tackles is often considered a good thing but can also be the result of poor positioning. Our method di ers from these approaches in that we avoid hand-crafting and use an automated data-driven approach to assign rankings. Furthermore, we consider the spatio-temporal context in which the actions were performed which the hand-crafted models ignore.
While virtually unexplored to date for soccer, the task of objectively
quantifying player actions has been investigated for other sports. [
This paper introduces STARSS, which is an approach for automatically rating the actions performed by soccer players. Viewing a soccer match as a sequence of actions performed by players, the approach proceeds in three steps to rate these actions. First, it splits the match into phases of related actions. Second, it assigns a rating to each phase, indicating how likely it is that the phase will end in a goal. Third, it distributes the assigned rating over the individual actions that constitute the phase.
Unlike most existing approaches for rating soccer players, our approach goes beyond shots and goals. It considers all the actions that contribute to a team's o ensive output and accounts for the spatio-temporal context in which these actions were performed. Several case studies show that our approach is able to identify top-performing players in individual matches as well as throughout the course of an entire season.
Tom Decroos is supported by the KU Leuven Research Fund (C22/15/015) and FWO-Vlaanderen (G.0356.12). Jan Van Haaren was supported by the Agency for Innovation by Science and Technology in Flanders (IWT). Vladimir Dzyuba was supported by FWO-Vlaanderen. Jesse Davis is partially supported by the KU Leuven Research Fund (C22/15/015) and FWO-Vlaanderen (G.0356.12, SBO150033).