Estimating the Maximal Speed of Soccer Players
on Scale
Laszlo Gyarmati and Mohamed Hefeeda
Qatar Computing Research Institute, HBKU
{lgyarmati,mhefeeda}@qf.org.qa
Abstract. 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 profile of soccer players from event-based datasets, which
are widely accessible. We show that eight games are enough to derive
an accurate speed profile. 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.
1 Introduction
Quantitative performance analysis in sports has become mainstream in the last
decade. The focus of the analyses is shifting towards more sport-specific 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 [1, 2]. Other works
identify and analyze the outcome of the strategies that teams apply [10, 8, 6,
4]. However, the physical performance of the players has not received detailed
attention from the research community.
It is a challenging task to get access to metrics related to the physical perfor-
mance of soccer players. The teams consider such information highly confidential,
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 com-
petition. 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 profile of soccer players, i.e., how much time a player needs to
2 L. Gyarmati, M. Hefeeda
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 addi-
tion, 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 per-
formance of the players of both teams. Soccer data companies are covering 50+
leagues providing the potential to analyze the speed profile 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 phys-
ical capabilities of a player,
3. and we show that the playing style of a team has a significant impact on the
accuracy of the speed estimation.
2 Methodology
In this section we introduce our methodology used to extract the movements of
the players and then to estimate their maximal speed. Our final 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 [9] covering the
2012/13 season of La Liga (i.e., the first division soccer league of Spain). The
dataset contains all the major events of a soccer game including passes, shots,
dribbles, tackles, etc.. For example, the dataset has more than 300,000 passes
and nearly 10,000 shots. The feature of the dataset we explore is that it contains
the time and the location of these events as well along with the identity of the
involved players. Hence, it is possible to derive a coarse grain time-series of the
movements of the players. We note that the precision of the time annotation is
one second. The procedure uses all the (x, y) positions a player has during a game
and creates a movement vector using a consecutive pair of (x, y) coordinates and
timestamps to create a movement vector. We illustrate the derived movements of
a player in Figure 1 given a single game. This is the first step of our methodology:
extracting the movement vectors of the players. The event-based dataset we use
is sparse in terms of the position of the players, i.e., the physical location of a
player is only recorded when the player was involved in some ball-related event1 .
As such, the elapsed time between two events of a player can be as low as couple
of seconds but it can reach several minutes too. This introduces significant noise
to the data that we have to handle in the regression model.
1
This is a consequence of the data acquisition process: the games are annotated based
on the television broadcast that focuses on the ball all the time.
Estimating the Maximal Speed of Soccer Players on Scale 3
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Fig. 1. Movement vectors of a player derived 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 ini-
tiation 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 first pass and the initiator of the
next one). Therefore, in case of the first 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.
4 L. Gyarmati, M. Hefeeda
Diverse field sizes. An interesting property of the rules of soccer is that the
sizes of the field are not fixed, there is some room to design a soccer pitch even in
case of international matches. According to the first law of the game, the length
of the pitch shall be between 100 and 110 meters, while the width between 64
and 75 meters [3]. There is an ongoing standardization effort, most of the newly
constructed stadiums have a pitch with a size of 105x68m[11]. Spain is not an
exception to this extent, where the dimension of Elche’s stadium is 108x70m
while the same is 100x65m in case of Rayo Vallecano [7]. The dataset we apply
uses relative coordinates, i.e., both sides of the pitch are measured between 0
and 100 unit. We transform these relative units into the metric system using the
sizes of the stadiums. At the end of this transformation, the end points of the
movement vectors are measured in 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 filters to remove the obvious flaws
from the dataset. We filter 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 reason-
able to assume that the maximal speed of soccer players is above 50% of the
sprinters. The second filter 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 filtered movement vectors to build a regres-
sion 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 specific quantile of the dataset
(instead of the mean in case of the linear regression) [5]. We show the speed of all
the movement vectors of a player throughout a whole season in Figure 2 along
with the 0.05, 0.1, 0.2, 0.3, 0.4, and 0.5 quantile regression lines. We note that
the 0.5 quantile regression model equals the regular linear model. Due to the lack
of accessibility of ground truth, it is challenging to evaluate quantitatively which
quantile is the best estimator of the players’ maximal speed. Based on extensive
qualitative analysis we decided to use the 0.05 quantile regression model for the
speed estimation (annotated by red solid line in the figure).
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 Evaluation
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
Estimating the Maximal Speed of Soccer Players on Scale 5
20
15
Time (sec)
10
5
0
0 20 40 60
Distance (meters)
Fig. 2. The speed of the movement vectors of a player throughout a season. The solid
lines show the 0.05, 0.1, 0.2, 0.3, 0.4, and 0.5 quantile regression models. The red line
is the 0.05 quantile we decided to use as the estimator of the players’ maximal speed.
1.00 1.00
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0 0
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2 2
3 3
0.25 0.25
0.00 0.00
0 1 2 3 0.0 0.1 0.2 0.3 0.4 0.5
std.dev. intercept std.dev. slope
Fig. 3. The accuracy of the methods estimating the maximal in-game speed of soccer
players. The cumulative distribution functions of the parameters of the quantile regres-
sion models reveal that the previous event method provides the best speed estimation.
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 different subset of the games a player was involved. Specifically,
6 L. Gyarmati, M. Hefeeda
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#games #games
Fig. 4. The accuracy of the previous event method given the number of games from
which we derive movement information. Having data from eight games provides a quite
accurate estimation of the speed of the players.
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 different 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. Specifically, 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 five 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 specific 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. How-
ever, 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 significant, e.g., we need 50% more games
in case of Espanyol and Valencia using the neglect methodology compared to
FC Barcelona. These differences 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 specific team).
Estimating the Maximal Speed of Soccer Players on Scale 7
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(a) Intercept (b) Slope
Fig. 5. The accuracy of the speed estimation methods given the used amount of data
(i.e., the number of games). The cumulative distribution functions show the minimal
number of games required for a good enough speed estimation. The previous event
method provides the best accuracy based on a given set of games.
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n e ep
F g 6 The speed profi e o p ayers n the Span sh first d v s on (the ntercept and
the s ope o the r quant e regress on mode ) P ayers have d verse n-game phys ca
act v t es that revea s a nove aspect o the r per ormance
The proposed methodo ogy ndeed can be used for p ayer scout ng As F g-
ure 6 shows the max ma n-game speed character st cs of the p ayers are d verse
hence t prov des an add t ona facet for performance eva uat on One can den-
t fy su tab e cand date to s gn who has the phys ca capab t es necessary for the
p ay ng sty e of a g ven team
4 Conclusions
We proposed a new techn que to est mate the max ma speed of soccer p ayers
Us ng event-based datasets of e ght games we are ab e to accurate y determ ne
the speed profi e of the p ayers The nvest gat ons revea ed that teams requ re
d verse s ze of datasets for a prec se speed est mat ons As a future work we
p an to ana yze the d screpanc es of the est mat ons across p ayers and eagues
Our method prov des a new way to eva uate the performance of soccer p ayers
8 L. Gyarmati, M. Hefeeda
intercept slope
Team #0 #1 #2 #3 #0 #1 #2 #3
Athletic Bilbao 8.1 3.1 7.6 4.0 7.9 5.7 7.2 5.5
Atletico Madrid 7.7 3.2 6.8 4.1 7.3 5.5 6.4 5.0
Barcelona 6.1 2.8 7.0 3.6 6.5 5.2 7.7 5.5
Celta de Vigo 7.4 2.6 7.9 4.2 7.0 6.0 6.8 6.2
Deportivo La Coruna 8.6 3.5 8.1 4.2 7.6 5.7 7.8 6.4
Espanyol 10.1 4.4 9.8 5.8 8.0 6.1 8.7 8.3
Getafe 8.0 4.6 8.4 5.8 7.3 8.0 8.5 7.9
Granada CF 9.3 3.7 9.2 5.5 8.3 6.5 8.3 7.0
Levante 8.8 4.4 8.3 6.3 8.2 5.6 7.8 6.9
Mallorca 9.2 4.1 7.9 6.1 9.2 6.4 8.2 7.5
Malaga 8.1 3.3 8.4 4.6 6.9 5.4 7.5 6.7
Osasuna 8.0 3.6 7.3 5.3 8.0 5.8 8.0 6.5
Rayo Vallecano 7.2 4.4 6.9 4.5 6.6 7.3 6.5 6.0
Real Betis 8.5 3.4 7.8 4.8 8.0 5.2 6.8 5.5
Real Madrid 7.3 3.2 7.3 4.2 6.8 5.3 7.1 6.1
Real Sociedad 9.2 2.5 8.4 4.1 7.7 5.6 7.1 6.3
Real Valladolid 9.0 3.6 8.4 5.3 7.4 6.2 7.5 7.6
Real Zaragoza 6.4 4.2 6.3 4.9 5.6 6.4 6.1 6.1
Sevilla 7.8 4.3 7.5 4.4 7.3 6.2 8.2 5.9
Valencia 8.8 3.6 8.0 5.7 9.0 5.7 8.3 7.3
Table 1. The mean number of games needed by the methods to estimate the speed of
the players of a given team. There are significant discrepancies among the teams, e.g.,
50% more games may be needed for an accurate estimation in case of Espanyol and
Valencia.
particularly, from a physical performance point of view. Such insights can be
used as competitive advantage for opponent and player scouting.
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