RESEARCH ARTICLE

Effective injury forecasting in soccer with GPS

training data and machine learning
Alessio Rossi1*, Luca Pappalardo1,2, Paolo Cintia2, F. Marcello Iaia3, Javier Fernàndez4,
Daniel Medina5
1 Department of Computer Science, University of Pisa, Pisa, Italy, 2 ISTI, National Research Council, Pisa,
Italy, 3 Department of Biomedical Science for Health, University of Milan, Milan, Italy, 4 Sports Science and
Health Department, FC Barcelona, Barcelona Spain, 5 Athletic Care Department, Philadelphia 76ers,
Philadelphia, Pennsylvania, United States of America
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* alessio.rossi2@gmail.com
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a1111111111 Abstract
Injuries have a great impact on professional soccer, due to their large influence on team per-
formance and the considerable costs of rehabilitation for players. Existing studies in the liter-
ature provide just a preliminary understanding of which factors mostly affect injury risk, while
OPEN ACCESS
an evaluation of the potential of statistical models in forecasting injuries is still missing. In
Citation: Rossi A, Pappalardo L, Cintia P, Iaia FM, this paper, we propose a multi-dimensional approach to injury forecasting in professional
Fernàndez J, Medina D (2018) Effective injury
forecasting in soccer with GPS training data and
soccer that is based on GPS measurements and machine learning. By using GPS tracking
machine learning. PLoS ONE 13(7): e0201264. technology, we collect data describing the training workload of players in a professional soc-
https://doi.org/10.1371/journal.pone.0201264 cer club during a season. We then construct an injury forecaster and show that it is both
Editor: Jaime Sampaio, Universidade de Tras-os- accurate and interpretable by providing a set of case studies of interest to soccer practition-
Montes e Alto Douro, PORTUGAL ers. Our approach opens a novel perspective on injury prevention, providing a set of simple
Received: February 8, 2018 and practical rules for evaluating and interpreting the complex relations between injury risk
Accepted: July 10, 2018
and training performance in professional soccer.

Published: July 25, 2018

Copyright: © 2018 Rossi et al. This is an open

access article distributed under the terms of the
Creative Commons Attribution License, which
Introduction
permits unrestricted use, distribution, and Injuries of professional athletes have a great impact on the sports industry, due to their influ-
reproduction in any medium, provided the original ence on the mental state of the individuals and the performance of a team [1, 2]. Furthermore,
author and source are credited.
the cost associated with a player’s recovery and rehabilitation is often considerable, both in
Data Availability Statement: The owner of the terms of medical care and missed earnings deriving from the popularity of the player himself
data is an elite soccer club in Italy which wants to [3]. Recent research demonstrates that injuries in Spain cause about 16% of season absence by
remain anonymous and did not give the
permission to make the original data publicly
professional soccer players, corresponding to a cost of around 188 million euros per season
available. The club has the right to choose which [4]. It is not surprising, hence, that injury forecasting is attracting a growing interest from
information, results and data can be made public researchers, managers, and coaches, who are interested in intervening with appropriate actions
and has granted the access to these data to the to reduce the likelihood of injuries of their players.
authors only for research aims. In accordance with Historically, academic work on injury forecasting has been deterred by the limited availabil-
SoBigData Ethical Committee, we can provide upon
ity of data describing the physical activity of players. Nowadays, the Internet of Things have
request transformed data that are processed in
such a way that it is not possible to re-identify the
the potential to change rapidly this scenario thanks to Electronic Performance and Tracking
subjects involved in the study. The transformed Systems (EPTS), new tracking technologies that provide high-fidelity data streams extracted
data reflect the same data distribution of real data from every training and game session [5, 6]. These data depict in detail the movements of

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 Injury forecasting in soccer

to guarantee that the experiments performed on players on the playing field [5, 6] and have been used for many purposes, from identifying
the transformed data produce the same results as training patterns [7] to automatic tactical analysis [5, 8, 9]. Despite this wealth of data, little
the ones shown in the paper. We specify that the
effort has been put on investigating injury forecasting in professional soccer so far [10, 11, 12].
researchers from FC Barcelona participated to the
study only as collaborators, and that FC Barcelona State-of-the-art approaches provide just a preliminary understanding of which variables affect
is not the owner of the data. For data requests the injury risk, while an evaluation of the potential of statistical models to forecast injuries is
please contact us at the following email addresses: still poor. A major limit of existing studies is that they are mono-dimensional, i.e., they use just
alessio.rossi2@gmail.com or info@sobigdata.eu. one variable at a time to estimate injury risk, without fully exploiting the complex patterns
Funding: This work is partially supported by the underlying the available data.
European Community’s H2020 Program under the Professional soccer clubs are interested in practical, usable and interpretable models as a
funding scheme “INFRAIA-1-2014-2015: Research decision making support for coaches and athletic trainers [13]. In this perspective the creation
Infrastructures” grant agreement 654024, www.
of injury forecasting models poses many challenges. On one hand, injury forecasters must be
sobigdata.eu, “SoBigData”. The funders had no
role in study design, data collection and analysis,
highly accurate, as models which frequently produce “false alarms” are useless. On the other
decision to publish, or preparation of the hand, a “black box” approach (e.g., a deep neural network) is not desirable for practical use
manuscript. There was no additional external since it does not provide any insights about the reason behind the injuries. It goes hence with-
funding received for this study. out saying that injury forecasting models must achieve a good tradeoff between accuracy and
Competing interests: The authors have declared interpretability.
that no competing interests exist. In this paper, we consider injury prediction as the problem of forecasting that a player will
get injured in the next training session or official game, given his recent training workload.
We observe that existing mono-dimensional approaches are not effective in practice due to
their low precision (< 5%), and we propose a multi-dimensional, easy-to-interpret and fully
data-driven approach which forecasts injuries with a better precision (50%); we validate this
result by simulating the usage of our forecaster over a season, with new training data available
as the season goes by. Our approach is entirely based on automatic data collection through
standard GPS sensing technologies and can be a valid supporting tool to the decision making
of a soccer club’s staff. This is crucial since the decisions of managers and coaches, and hence
the success of soccer clubs, also depend on what they measure, how good their measurements
are, the quality of predictions and how well these predictions are understood.

Related work
The relationship between training workload and injury risk has been widely studied in the
sports science literature [14, 15, 16, 17, 18]. For example Gabbett et al. [14, 15, 17, 19] investi-
gate the case of rugby and find that a player has a high injury risk when his workloads are
increased above certain thresholds. To assess injury risk in cricket, Hulin et al. [20] propose
the Acute Chronic Workload Ratio (ACWR), i.e., the ratio between a player’s acute workload
and his chronic workload. When the acute workload is lower than the chronic workload,
cricket players are associated with a low injury risk. In contrast, when the acute/chronic ratio
is higher than 2, players have an injury risk from 2 to 4 times higher than the other group of
players. Hulin et al. [20] and Ehrmann et al. [11] find that injured players, in both rugby and
soccer, show significantly higher physical activity in the week preceding the injury with respect
to their seasonal averages.
In skating, Foster et al. [21] measure training workload by the session load, i.e., the product
of the perceived exertion and the duration of the training session. When the session load out-
weighs a skater’s ability to fully recover before the next session, the skater suffers from the so-
called “overtraining syndrome”, a condition that can cause injury [21]. In basketball, Anderson
et al. [18] find a strong correlation between injury risk and the so-called monotony, i.e., the
ratio between the mean and the standard deviation of the session load recorded in the past 7
days. Moreover, Brink et al. [8] observe that injured young soccer players (age < 18) recorded
higher values of monotony in the week preceding the injury than non-injured players.

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 Injury forecasting in soccer

Venturelli et al. [12] perform several periodic physical tests on young soccer players
(age < 18) and find that jump height, body size and the presence of previous injuries are signif-
icantly correlated with the probability of thigh strain injury. Talukder et al. [22] create a classi-
fier to predict 19% of the injuries that occurred in NBA. They also show that the most
important features for predicting injuries are the average speed, the number of past competi-
tions played, the average distance covered, the number of minutes played to date and the aver-
age field goals attempted. An attempt to injury forecasting in soccer has been made by
Kampakis [23], although it considers a reduced set of features obtaining an accuracy that is, in
the best scenario, not significantly better than random classifiers.

Material and method

Data collection and feature extraction
We set up a study on twenty-six Italian professional male players (age = 26±4 years;
height = 179±5 cm; body mass = 78±8 kg) during season 2013/2014. Six central backs, three
fullbacks, seven midfielders, eight wingers and two forwards were recruited. Participants gave
their written informed consent to participate in the study.
We monitored the physical activity of players during 23 weeks–from January 1st to May
31st, 2014 –using portable 10 Hz GPS devices integrated with a 100Hz 3-D accelerometer, a
3D gyroscope, a 3D digital compass (STATSports Viper). The devices were placed between the
players’ scapulae through a tight vest. We recorded a total of 931 individual training sessions
during the 23 weeks. From the data collected by the devices, we extracted a set of training
workload indicators through the software package Viper Version 2.1 provided by STATSports
2014.
The club’s medical staff recorded 23 non-contact injuries during the study. According to
the UEFA regulations [24], a non-contact injury is defined as any tissue damage sustained by a
player that causes absence in physical activities for at least the day after the day of the onset.
We observed that 19 out of 23 injuries are associated with players who got injured at least once
in the past. In particular, half of the players never get injured during the study, while the others
get injured once (seven players), twice (five players) or four times (one player). For every
player, we collected information about age, body mass index, height and role on the field.
Moreover, for every single training session of a player, we collected information about the play
time in the official game before the training session and the number of official games played
before the training session.
From the players’ GPS data we extract 12 features describing different aspects of the work-
load in a training session [25]. Two features–Total Distance (dTOT) and High Speed Running
Distance (dHSR)–are kinematic, i.e., they quantify a player’s overall movement during a train-
ing session. Three features–Metabolic Distance (dMET), High Metabolic Load Distance (dHML)
and High Metabolic Load Distance per minute (dHML/m)–are metabolic, i.e., they quantify the
energy expenditure of a player’s overall movement during a training session. The remaining
seven features–Explosive Distance (dEXP), number of accelerations above 2m/s2 (Acc2), num-
ber of accelerations above 3m/s2 (Acc3), number of decelerations above 2m/s2 (Dec2), number
of decelerations above 3m/s2 (Dec3), Dynamic Stress Load (DSL) and Fatigue Index (FI)–are
mechanical features describing a player’s overall muscular-scheletrical load during a training
session. In addition, we associated a player’s training session with feature PI, indicating the
number of the player’s previous injuries up to that session. Table 1 and S1 Appendix provides
the description and some statistics of the workload features extracted from the GPS data,
respectively.

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 Injury forecasting in soccer

Table 1. Training workload features used in our study. Description of the training workload features extracted from
GPS data and the players’ personal features collected during the study. We defined four categories of features: kine-
matic features (blue), metabolic features (red), mechanical features (green) and personal features (white).
dTOT Distance in meters covered during the training session
dHSR Distance in meters covered above 5.5m/s
dMET Distance in meters covered at metabolic power
dHML Distance in meters covered by a player with a Metabolic Power is above 25.5W/Kg
dHML/m Distance in meters covered by a player with a Metabolic Power is above 25.5W/Kg per minute
dEXP Distance in meters covered above 25.5W/Kg and below 19.8Km/h
Acc2 Number of accelerations above 2m/s2
Acc3 Number of accelerations above 3m/s2
Dec2 Number of decelerations above 2m/s2
Dec3 Number of decelerations above 3m/s2
DSL Total of the weighted impacts of magnitude above 2g. Impacts are collisions and step impacts during
running
FI Ratio between DSL and speed intensity
Age age of players
BMI Body Mass Index: ratio between weight (in kg) and the square of height (in meters)
Role Role of the player
PI Number of injuries of the players before each training session
Play Minutes of play in previous games
time
Games Number of games played before each training session
https://doi.org/10.1371/journal.pone.0201264.t001

Multi-dimensional and data-driven injury forecaster

We construct a multi-dimensional model to forecast whether or not a player will get injured
based on his recent training workload. The construction of the injury forecaster consists of
two phases. In the first phase (training dataset construction), given a set of features S, a training
dataset T is created where each example refers to a single player’s training session and consists
of: (i) a vector of features describing both the player’s personal features and his recent work-
load, including the current training session; (ii) an injury label, indicating whether (1) or not
(0) the player gets injured in the next game or training session. In the second phase (model
construction and validation), a decision tree learner is used to train an injury classifier on the
training dataset T.
Phase 1: Training dataset construction. From the features extracted from GPS data,
which are described in Table 1, we construct a training dataset T consisting of 55 features and
952 examples (i.e., individual training sessions). S4 Appendix provides an example of the con-
struction of T. These 55 features are:
• 18 daily features: the 12 workload features extracted from the GPS data and the 6 personal
features described in Table 1.
• 12 EWMA features: 12 features computed as the Exponential Weighted Moving Average
(EWMA) of the 12 workload features in Table 1. The EWMA decreases exponentially the
weights of the values according to their recency, i.e., the more recent a value, the more it is
weighted in an exponential function according to a decay α = 2/(span+1). In our experi-
ments we consider a span equal to six (see S5 Appendix).
• 12 ACWR features: 12 features consisting of the ACWR of the 12 workload features in
Table 1. Given a feature, the ACWR of a player is the ratio between (i) the player’s acute

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 Injury forecasting in soccer

workload, computed as the average of the values of the feature in the last 6 days; (ii) the play-
er’s chronic workload, computed as the average of the values of the feature in the last 27 days
[26].
• 12 MSWR features: 12 features consisting of the monotony of the 12 workload features in
Table 1. Given a feature, the monotony of a player is the ratio between the mean and the
standard deviation of the values of the feature in the last week [3, 10, 18].
• 1 previous injury feature: to take into account both the number of a player’s previous inju-
ries and their distance to the current training session we compute feature PI(WF), the EWMA
of feature PI computed with a span equal to six. PI(WF) reflects the distance between the cur-
rent training session and the training session when the player returned to regular training
after an injury. PI(WF) = 0 indicates that the player never got injured in the past; PI(WF) > 0
indicates that he got injured at least once in the past; PI(EWMA) > 1 indicate that he got
injured more than once in the past (see S6 Appendix).
We select 30% of T and obtain TTRAIN (step 1 and 2 in Fig 1) to perform a feature selection
process to determine the most relevant features for classification using Recursive Feature Elim-
ination with Cross-Validation (RFECV; we use the publicly available Python package scikit-
learn to perform RFECV and to train and validate the decision tree– http://scikit-learn.org/)
[27]. In RFECV, the subset of features producing the maximum score on the validation data is
considered to be the best feature subset [27]. The feature selection process is aimed at reducing
the dimensionality of the feature space and hence the risk of overfitting, and allowing for an
easier interpretation of the resulting machine learning model, due to the lower number of fea-
tures [28].
The class distribution in training dataset TTRAIN is highly unbalanced since we have 279
non-injury examples and just 7 injury examples. To adjust this imbalance we oversample the
minority class in TTRAIN by using the adaptive synthetic sampling approach (ADASYN; We
use the ADASYN function provided by the publicly available Python package imblearn–
http://scikit-learn.org/imbalanced-learn) [29]. The ADASYN algorithm generates examples of
the minority class to equalize the distribution of classes, hence reducing the learning bias (See
S7 Appendix). Finally, we use TTRAIN to detect the best hyper parameters of a decision tree
classifier DT (Step 2 in Fig 1).
Phase 2: Model construction and validation. We then split TTEST into two folds, f1 and
f2, in order to perform a stratified cross validation (step 3 in Fig 1; we use only two folds in
order to not excessively reduce the minority class size). In this step, we oversample fold f1 by
using ADASYN and test DT on the other fold f2 (which is not oversampled). For cross valida-
tion purposes, we perform again step 3 inverting f1 and f2. The goodness of the forecasting
model is evaluated by four metrics (i.e., precision, recall, F1-score and AUC) described in S8
Appendix. Note that, for injury forecasting purposes, we are interested in achieving high values
of precision and recall on class 1 (injury). Let us assume that a coach makes a decision about
whether or not to “stop” a player based on the suggestion of the injury forecaster, i.e., the
player skips next training session or game every time the forecaster’s prediction associated
with the player’s current training session is 1 (injury). In this scenario, the forecaster’s preci-
sion indicates how much we can trust the predictions: the higher the precision, the more a clas-
sifier’s predictions are reliable, i.e., the probability that the player will actually get injured is
high. Trusting an injury forecaster with low precision is risky as it means producing many
false positives (i.e., false alarms) and frequently stopping players unnecessarily, a condition
clubs want to avoid especially for the key players. The recall indicates the fraction of injuries
the forecaster detects over the total number of injuries: the higher the recall the more injuries

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 Injury forecasting in soccer

Fig 1. Construction of the training dataset and the forecasting model. In step 1 we split the dataset into two parts: TTRAIN (30% of T) and TTEST (70% of T). We
then oversample the minority class in TTRAIN by using ADASYN, select the most important features and fit the hyper parameters (Step 2). We then split TTEST into
two folds in order to perform a stratified cross validation (step 3).
https://doi.org/10.1371/journal.pone.0201264.g001

the forecaster can detect. An injury forecaster with low recall detects just a small fraction of the
injuries, meaning that many players will attend next training session or game and actually get
injured. Trusting a forecaster with a low recall is risky as it would misclassify many actual inju-
ries as non-injuries.
We repeated the entire injury prediction approach (i.e., all the three steps in Fig 1) 10,000
times in order to assess its stability with respect to the choice of the injury examples in the two
folds. For the sake of comparison, we implemented other injury forecasters based on the
ACWR and the monotony (or MSWR) techniques, which are among the two most used tech-
niques for injury risk estimation and prediction in professional soccer (see S2 Appendix and
S3 Appendix for details). Moreover, we compare our injury forecaster with four baselines.
Baseline B1 randomly assigns a class to an example by respecting the distribution of classes.
Baseline B2 always assigns the non-injury class, while baseline B3 always assigns the injury
class. Baseline B4 is a classifier which assigns class 1 (injury) if PI(EWMA) > 0, and 0 (no injury)
otherwise. We also compare DT with a Random Forest classifier (RF) and a Logit classifier
(LR).

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 Injury forecasting in soccer

Table 2. Performance of DT compared to RF, LR, the four baselines and the ACWR- and MSWR-based forecasters. For each forecaster we report precision, recall
and F1 on the two classes and the overall AUC.
precision recall F1 AUC
DT NI 0.96±0.05 0.87±0.09 0.91±0.04 0.76±0.12
I 0.50±0.11 0.80±0.07 0.64±0.10
RF NI 0.94±0.06 0.90±0.08 0.93±0.07 0.78±0.15
I 0.41±0.08 0.87±0.05 0.65±0.08
LR NI 0.69±0.11 0.61±0.15 0.65±0.13 0.60±0.03
I 0.18±0.03 0.60±0.08 0.31±0.06
B4 NI 0.98 0.77 0.86 0.60
I 0.04 0.43 0.07
B1 NI 0.98 0.98 0.98 0.51
I 0.06 0.05 0.05
B2 NI 0.98 1.00 0.99 0.50
I 0.00 0.00 0.00
B3 NI 0.00 0.00 0.00 0.50
I 0.02 1.00 0.04
C(ACWR)DEC NI 1.00 0.43 0.60 0.67
I 0.04 0.91 0.07
C(MSWR)HML NI 0.98 0.80 0.88 0.57
I 0.04 0.33 0.07
https://doi.org/10.1371/journal.pone.0201264.t002

Results
Table 2 compares the performance of DT with the performance of RF, LR, the ACWR and
MSWR forecasters, and the four baselines. The results in Table 2 refer to the mean and the stan-
dard deviation of the evaluation metrics over 10,000 cross validation tasks. We find that DT has
recall = 0.80±0.07 and precision = 0.50±0.11 on the injury class, meaning that the decision tree
can predict almost all the injuries (80%) and that it correctly labels a training session as an injury
in 50% of the cases. This is a significant improvement with respect to both the baselines B1, . . .,
B4, for which the maximum precision is about 6%, and the ACWR- and MSWR-based injury
forecasters, for which the maximum precision is lower than 4%. RF has better recall but worse
precision (recall = 0.87±0.05, precision = 0.41±0.08) that DT, while LR has much lower perfor-
mance than the decision tree (Table 2). These results show that, typically, DT drastically reduces
false alarms and hence scenarios where players are “stopped” unnecessarily before next game or
training session. On the one hand, the distributions of the forecasters’ performances over the
10,000 tests indicate that the quality of the injury forecasting strongly depends on the type of
injuries in the training set, which in turn depends on the different training and test split made
in each trial (Fig 2). On the other hand, the higher performance detected by DT, compared to
several baselines and the ACWR- and MSWR-based injury forecasters, shows that our approach
outperforms state-of-the-art approaches and achieve good results in forecasting injuries. The
results for DT without ADASYN and the oversampling process are presented in S9 Appendix.
As a further test of the forecasting potential of our approach we investigate the benefit of
using our multi-dimensional injury forecaster in a real-world injury prevention scenario,
where we assume that a club equips with appropriate GPS sensor technologies and starts
recording training workload data since the first training session of the season (in other words,
no data are available to the club before the beginning of the season). Assuming that we train
the injury forecaster with new data every week, how many injuries the club can actually pre-
vent throughout the season?

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 Injury forecasting in soccer

Fig 2. Classifiers performances. Distributions of the classifiers—DT, LR and RF—performances obtained testing the algorithms 10,000 times. This figure shows the
performance of the baselines and the ACWR- and MSWR-based injury forecasters as well.
https://doi.org/10.1371/journal.pone.0201264.g002

To answer this question we group the training sessions by week and proceed from the least
recent to the most recent week. At training week wi we first construct the dataset Ti consisting
of all the training examples collected up to week i, oversampling the injury examples through
ADASYN and reducing the feature space through RFECV. Then, we use Ti to train DTi, RFi,
LRi, B1,i, . . .,B4,i, the ACWR- and MSWR-based forecasters and try to predict the injuries in
week wi+1. At week i, we evaluate the accuracy of our approach by the cumulative F1-score,
i.e., the F1-score computed by considering all the predictions made up to week i by the models
DT6,. . ., DTi. Due to the initial scarcity of data, we start the forecasting task from week w6.
Fig 3 and S7 Table show the evolution of the cumulative F1-score and the feature extracted
by RFECV as the season goes by, respectively. We find that in the first weeks DT has a poor
predictive performance and misses many injuries (the black crosses in Fig 3). The predictive
ability of DT improves significantly throughout the season: as more and more training and
injury examples are collected, the forecasting model predicts most of the injuries in the second
half of the season (the red crosses in Fig 3). We find that DT is the one performing the best,
outperforming all the other models from week w14. In particular, DT detects 9 injuries out of
14 from w6 to the end of the season, resulting in F1-score = 0.60 and precision = 0.56. After an
initial period of data collection, the injury forecaster becomes a useful tool to prevent the inju-
ries of players and, by extracting the rules from the decision tree as we show in the next section,
to understand the reasons behind the forecasted injuries as well as the injuries that are not
detected by the model.

Interpretation of the injury forecaster

A set of simple rules can be extracted from DT build on w21, allowing for the investigation of
the reasons behind the observed injuries. These rules can be seen as a short handbook for
coaches and athletic trainers, which can consult it to modify the training schedule and improve
the players’ fitness.
Fig 4B visualizes DT highlighting two types of node: decision nodes (black boxes) and leaf
nodes (green or red boxes). Each decision node has two branches each indicating the next
node to select depending on the range of values of the feature associated with the decision
node. A leaf node represents the final prediction based on a player’s individual training ses-
sion. There are two possible final decisions: Injury (red boxes) indicates that the player will get
injured in next game or training session; or No-Injury (green boxes) otherwise. Given a feature

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 Injury forecasting in soccer

Fig 3. Performance of forecasters in the evolutive scenario. As the season goes by, we plot week by week the cumulative F1-score of the forecasters DT, RF, LR, B1, . . .,
B4 trained on the data collected up to that week. Black crosses indicate injuries that not detect by DT, red crosses indicate injures correctly predicted by DT. For every
week i we highlight in red the number of injuries detected by DT up to week i.
https://doi.org/10.1371/journal.pone.0201264.g003

vector describing a player’s training session, the prediction associated with it is obtained by fol-
lowing the path from the root of the tree down to a leaf node, through the decision nodes. Fig
4 shows the rules and the tree extracted from the DT built until w21. At the end of the season,
the RFECV process selects just 3 features out of 55: PI(EWMA), dHSR(EWMA) and dTOT(MSWR).
The importances of these features in DT, computed as the mean decrease in Gini coefficient,
are 0.71, 0.23 and 0.06, respectively [30].
As a practical example of application of these rules, let us consider a player’s training session
with PI(EWMA) = 0.28, dHSR(EWMA) = 126.58 and dTOT(MSWR) = 1.66, associated with an injury.
This example is associated with rule 2 (Fig 4A), corresponding to the following decision path:

dHSR ðEWMAÞ > 112:35 ! dTOT ðMSWRÞ  1:78 ! PIðEWMAÞ > 0:03 ! PIðEWMAÞ  0:68
! INJURY

From the rules in Fig 4A we summarize three main injury scenarios in DT:
1. a previous injury can lead to a new injury when a player has a HSR(EWMA) (high speed run-
ning distance) lower than 112.35 (rule 1 in Fig 4A). This rule describes 42% of the injuries
in the dataset and it is correct in 100% of the cases.
2. a previous injury can lead to a new injury when a player has a HSR(EWMA) higher than
112.35 and a Dtot(MSWR) (total distance Monotony) three times lower than 1.78 (rule 2 in
Fig 4A). This rule describes 30% of the injuries and has an accuracy of 100%.

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 Injury forecasting in soccer

Fig 4. Interpretation of the multi-dimensional injury forecaster. (a) The six injury rules extracted from DT. For each rule we show the range of values of every
feature, its frequency (Freq) and accuracy (Acc). (b) A schematic visualization of decision tree. Black boxes are decision nodes, green boxes are leaf nodes for class No-
Injury, red boxes are leaf nodes for class Injury.
https://doi.org/10.1371/journal.pone.0201264.g004

3. a previous injury can lead a new injury when a player has a HSR(EWMA) higher than 112.35
and a Dtot(MSWR) two and half times higher than the player’s average (rules 3 and 4 in Fig
4A). These rules have a cumulative frequency of 28% and a mean accuracy of 75±5%.
These scenarios suggest that coaches and athletic trainers must take care of the total dis-
tance and the distance at high speed running performed by the players who recently returned
to play after an injury.

Discussion
Our experiments produce three remarkable results. First, DT can detect around 80% of the
injuries with about 50% precision, far better than the baselines and state-of-the-art injury risk
estimation techniques (see Table 2). The decision tree’s false positive rate is small, indicating
that it reduces the “false alarms”, i.e., situations where the classifier is wrong in predicting that
an injury will happen. In professional soccer, false alarms are deprecable because the scarcity

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 Injury forecasting in soccer

of players can negatively affect the performance of a team [2]. Our model also produces a mod-
erate false negative rate, meaning that situations where a player that will get injured is classified
as out of risk are infrequent.
Second remarkable results is that, in a real-world scenario of injury prevention where a
club starts collecting the data for the first time and re-train the injury forecaster as the season
goes by, the injury forecaster results in a cumulative F1-score = 0.60 on the injury class (Fig 3),
much better than the baselines, RF and LR (Table 2). Throughout the season, the usage of the
forecasting model allows for the prevention of more than half of the injuries. The forecasting
ability of DT is affected by the initial period where data are scarce. This suggests that an initial
period of data collection is needed in order to gather the adequate amount of data, and only
then a reliable forecasting model can be trained on the collected data. The length of the data
collection period depends on the club’s needs and strategy, including the frequency of training
sessions and games, the frequency of injuries, the number of available players and the tolerated
level of false alarms. Regarding this aspect, in our dataset, we observe that the performance of
the classifiers stabilizes after 14 weeks of data collection (see Fig 3).
Third, in the evolutive scenario the features selected change as the season goes by (see S7
Table). This is probably due to the initial scarcity of data and to the type of injuries that have
occurred up that a given moment. We observed that the just 3 out of 55 features are selected by
the feature selection (PI(EWMA), dHSR(EWMA) and dTOT(MSWR)) after 14 weeks of data collection,
and that these set of features remains stable for all subsequent weeks. Feature PI(EWMA), the
most important among the three and the only feature that is always selected as the season goes
by (see S7 Table), reflects the temporal distance between a player’s current training session and
his coming back to regular training after a previous injury. Less than half of the injuries
detected by DT in the evolutive scenario happened immediately after the coming back to regu-
lar training of injured player. Furthermore, 60% of the injuries detected by DT happened long
after a previous injury and are characterized by specific values of dHSR(EWMA) and dTOT(MSWR),
which indicate that the a player’s kinematic variability affects his injury risk. It is worth to
notice that the single feature PI(EWMA) alone does not provide a significant predictive power,
as the baseline B4, which is based on it, has a much lower accuracy than DT. It is hence the
combination of the three features which allows us to predict when a player will get injured.
Our results suggest that the club should take particular care of the first training sessions of
players who come back to regular training after a previous injury, as in this conditions they are
more likely to get injured again. In these first days and in the days long after the players return
to regular physical activity, the club should control kinematic workloads, which can lead to
injuries at specific values as well.
Injuries involve a great economic cost to the club, due to the expensive process of recovery
and rehabilitation for the players. Injury prevention can reduce these costs by avoiding the
injuries of players, which means improving the team’s performance and the player’s mental
state as well as reducing the seasonal costs of medical care. We estimate that 139 days of
absence during the seasons are due to injuries, corresponding to 6% of the working days. We
observe that a player returned to regular physical activity within 5 days (i.e., 15 times out of 23
injuries), while only 6 times a player needed more than 5 days to recover. We use a method
proposed in the literature [4] to estimate that the minimum total cost related to injuries that in
this soccer club is 11,583 euros (139x83 euros = days of absence x minimal legal salary per day)
corresponding to 3.81% of the salary cost of the club. If our model was used as the season goes
by to stop the players for which an injury is predicted, the club could had been able to prevent
9 injuries out of 14 and save 8,881 euros (107x83 euros = day of absence x minimal legal salary
per day), that represents a 77% decrease of injury costs.

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 Injury forecasting in soccer

Conclusion
In this paper we proposed a multi-dimensional approach to injury forecasting in soccer, fully
based on automatically collected GPS data and machine learning. As we showed, our injury
forecaster provides a good trade-off between accuracy and interpretability, reducing the num-
ber of false alarms with respect to state-of-the-art approaches and at the same time providing a
simple handbook of rules to understand the reasons behind the observed injuries. We showed
that the forecaster can be profitably used early in the season, and that it allows the club to save
a considerable part of the seasonal injury-related costs. Our approach opens a novel perspec-
tive on injury prevention, providing a methodology for evaluating and interpreting the com-
plex relations between injury risk and training performance in professional soccer.
Our work can be extended in many directions. First, we can include performance features
extracted from official games, where the player is exposed to the highest physical and psycho-
logical stress. Second, we can investigate the “transferability” of our approach from a club to
another, i.e., if a forecaster trained on a set of players can be successfully applied to a distinct
set of players, not used during the training process. In this case, it would be possible to exploit
collective information to train a more powerful forecaster which includes training examples
from different players, clubs, and leagues. Third, if data covering several seasons of a player’s
activity are available, a distinct forecaster can be trained for each player by combining GPS
data with other types of health data, such as heart rate, ventilation, and lactate.

Supporting information
S1 Appendix. Descriptive statistics of the workload features.
(DOCX)
S2 Appendix. The ACWR method.
(DOCX)
S3 Appendix. The MSWR method.
(DOCX)
S4 Appendix. Example of the training dataset construction.
(DOCX)
S5 Appendix. Exponential Weighted Moving Average (EWMA).
(DOCX)
S6 Appendix. Computation of PI(WF).
(DOCX)
S7 Appendix. Adaptive synthetic sampling approach.
(DOCX)
S8 Appendix. Classifiers metrics assessment.
(DOCX)
S9 Appendix. Predictions results.
(DOCX)
S1 Table. Descriptive statistics of the 12 training workload features. We provide three cate-
gories of training workload features: kinematic features (blue), metabolic features (red) and
mechanical features (green).
(DOCX)

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 Injury forecasting in soccer

S2 Table. Performance of ACWR predictor. We report precision (prec), recall (rec), F1-score
(F1) and Area Under the Curve (AUC) for the injury class and the non- injury class for all the
predictors based on ACWR and MSWR. We also provide predictive performance of four base-
line predictors B1, B2, B3 and B4.
(DOCX)
S3 Table. Injury prediction report of ACWRq. We report precision (prec), recall (rec),
F1-score (F1) and Area Under the Curve (AUC) for the injury class and the non-injury class
for all the predictors defined on ACWR and monotony methodologies. We also provide pre-
dictive performance of four baseline predictors B1, B2, B3 and B4.
(DOCX)
S4 Table. Performance of MSWR predictor. We report precision (prec), recall (rec), F1-score
(F1) and Area Under the Curve (AUC) for the injury class and the non- injury class for all the
predictors based on ACWR and MSWR. We also provide predictive performance of four base-
line predictors B1, B2, B3 and B4.
(DOCX)
S5 Table. PI(WF) values after n training days (i.e., n = 1, . . ., 6) since the return of a player
to regular training. We report the values for different n of previous injuries (i.e., n = 1, . . ., 4).
PIi is the number of training days long after players return to regular physical activity. 6+ indi-
cates values for 6 and more than 6 days.
(DOCX)
S6 Table. Performance of the classifiers on T(ADA), T and T(REF). For each classifier, we
report the precision (prec), recall (rec) and F1-score (F1) on the two classes and the overall
AUC.
(DOCX)
S7 Table. Feature selection real-world scenario. Features extracted by RFECV in each Ti
built as the season went by.
(DOCX)
S1 Fig. Distribution of workload features. We provide three categories of training workload
features: kinematic features (blue), metabolic features (red) and mechanical features (green).
(TIF)
S2 Fig. Injury risk in ACWR groups. The plots show Injury Likelihood (IL) for pre- defined
ACWR groups [29], for every of the 12 training workload features considered in our study.
Bars are colored according to feature categorization defined in Table 1.
(TIF)
S3 Fig. Injury likelihood in ACWR groups. The plots show IL for the ACWR groups defined
the quantiles of the distribution, for every of the 12 training workload features considered in
our study. We provide three categories of training workload features: kinematic features
(blue), metabolic features (red) and mechanical features (green).
(TIF)
S4 Fig. Injury risk in MSWR groups. The plots show the Injury Likelihood (IL) for the
MSWR groups for every of the 12 training workload features considered in our study. Bars are
colored according to feature categorization defined in Table 1.
(TIF)

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 Injury forecasting in soccer

S5 Fig. We plot the AUC and F1-score of EWMA with span = 1, . . ., 10 in CALL. The red
line reflects the best span to injury prediction.
(TIF)

Acknowledgments
This work is partially supported by the European Community’s H2020 Program under the
funding scheme “INFRAIA-1-2014-2015: Research Infrastructures” grant agreement 654024,
www.sobigdata.eu, “SoBigData”.

Author Contributions
Conceptualization: Alessio Rossi, Luca Pappalardo, Paolo Cintia.
Data curation: F. Marcello Iaia.
Formal analysis: Alessio Rossi.
Investigation: Alessio Rossi.
Methodology: Alessio Rossi.
Validation: Alessio Rossi, Luca Pappalardo, Paolo Cintia.
Writing – original draft: Alessio Rossi, Luca Pappalardo, Paolo Cintia.
Writing – review & editing: Alessio Rossi, Luca Pappalardo, Paolo Cintia, Javier Fernàndez,
Daniel Medina.

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