A Generalized Valuation Method for Team Defense

by Estimating Probabilities in Football Games

Rikuhei Umemoto

, Kazushi Tsutsui

and Keisuke Fujii

1 a

Graduate School of Informatics, Nagoya University, Japan

Graduate School of Arts and Sciences, The University of Tokyo, Japan

Keywords:

Machine Learning, Soccer, Spatiotemporal Data, Prediction.

Abstract:

Analyzing team defense in soccer is challenging due to limited labeled data. Some previous methods for

evaluating soccer defenses were based on the prediction of defensive events using the locations of all players

and the ball. However, they did not consider the importance of multiple events and assumed perfect observation

of all 22 players, which is not open-source, with a larger amount for learning the classiﬁer. In this paper, we

propose a generalized valuation method for defensive teams by score-scaling the predicted probabilities of

events, including gaining possession of the ball and being attacked. Our method can be applied to the open-

source location data of all players in frames from broadcast video of events, such as football games from Euro

2020, by investigating the effect of the number of players on event prediction performance. Our validation

results using Euro 2020 data show that event prediction accuracy can be maintained with a limited number

of player features for scoring, conceding, gaining the ball, and effective attacks. Additionally, our defensive

metric effectively explains the defensive characteristics and strengths of the top four teams in the tournament,

while also highlighting the reasons why some teams received poor defensive evaluations. Our approach offers

a practical way to analyze and evaluate team defenses even with self-recorded or broadcast videos.

1 INTRODUCTION

With advancements in measurement and information

processing technologies, the soccer community has

enabled data-driven evaluations and analyses of team

performances. For instance, xG, which represents

the probability that a shot will result in a future

goal, has become widely recognized not only among

researchers (Pollard and Reep, 1997; StatsPerform,

2012) but also in popular media, where it is used to

assess team performance (SkySports, 2024). How-

ever, it presents signiﬁcant challenges due to the con-

tinuous movement of players and the ball throughout

the game, as well as the infrequency of critical events

such as goals (for a comprehensive review, see (Fujii,

2021; Fujii, 2025)).

Data plays a crucial role in conducting practical

analysis and evaluation of game performance analyt-

ics. Two primary types of data are commonly used in

this ﬁeld. The ﬁrst is tracking data, which records the

positions of all players throughout the entire match.

This data enables the creation of performance metrics

that consider the movements of off-ball players (Fer-

https://orcid.org/0000-0001-5487-4297

nandez and Bornn, 2018; Llana et al., 2020; Nakahara

et al., 2023; Spearman, 2018; Teranishi et al., 2022)

and the relationships between players with some deep

neural network methods (Anzer et al., 2022; Mehrasa

et al., 2018; Rahimian et al., 2023; St

ockl et al., 2021;

Wang et al., 2024). However, tracking data is of-

ten private or requires purchase, making it inacces-

sible for amateur teams and individuals with limited

ﬁnancial resources. The second type is event data,

which records information about speciﬁc events, such

as passes or shots, and typically includes details about

the player in possession of the ball at the time. Since

much of this data is publicly available, many stud-

ies have used event data to develop evaluation metrics

(Decroos et al., 2019; Liu et al., 2020; Pappalardo

et al., 2019; Rudd, 2011; Simpson et al., 2022; Yeung

et al., 2025). However, since the actions of the ball

carrier depend on their relationships with both team-

mates and opponents without the ball, it is challeng-

ing to accurately evaluate the team solely based on

information about the ball carrier.

In 2021, StatsBomb Inc. introduced StatsBomb

360 data, which includes event and ball handler infor-

mation, as well as the coordinates of players visible in

Umemoto, R., Tsutsui, K. and Fujii, K.

A Generalized Valuation Method for Team Defense by Estimating Probabilities in Football Games.

DOI: 10.5220/0013706900003988

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 13th International Conference on Sport Sciences Research and Technology Support (icSPORTS 2025), pages 79-89

ISBN: 978-989-758-771-9; ISSN: 2184-3201

Figure 1: Overview of our approach. Spatial features describing attackers, defenders, and ball movements feed a classiﬁer,

which outputs the probabilities of scoring, conceding, gaining possession, and being attacked. We validated these classiﬁers

by examining the impact of the number of player-related features. We also evaluated defensive team evaluations by the

GVDEP formulation. GVDEP generalizes the defensive evaluation method (Toda et al., 2022) by weighting its values with

the VAEP, focusing on the probabilities of scoring and conceding goals (Decroos et al., 2019).

broadcast footage at the time of the event. Available

as open data for speciﬁc competitions, this dataset

bridges some gaps: it is more accessible than track-

ing data and richer in player information than event

data, potentially leading to increased research lever-

aging this resource. However, since this dataset was

only recently made available, studies utilizing it have

been still limited (Rahimian et al., 2022; Robberechts

et al., 2023; Umemoto and Fujii, 2023; Yeung and Fu-

jii, 2024). Moreover, compared to complete tracking

data, StatsBomb 360 provides fewer details on player

coordinates, making it necessary to examine how this

difference in data volume impacts tasks such as ma-

chine learning-based predictions.

Additionally, most analysis and evaluation meth-

ods in soccer focus on attackers, with few address-

ing defense, as defensive statistics (e.g., tackles) are

often limited, making it challenging to deﬁne eval-

uation targets. Previous studies have evaluated de-

fensive actions, such as pressing effectiveness based

on expected goal-scoring opportunities (Robberechts,

2019), using event data. (Toda et al., 2022) developed

Valuing Defense by Estimating Probabilities (VDEP)

to assess team defense using tracking data, focusing

on the predicted probabilities of gaining possession

and preventing effective attacks. However, VDEP has

two main limitations: (1) it weights ball recovery and

effective attacks by event frequency rather than event

importance; and (2) it assumes access to complete

player location data, leaving the impact of missing

player data unclear.

To address these limitations, we examine how the

number of player features affects the performance of

a classiﬁcation model, using UEFA EURO 2020 data

publicly provided by StatsBomb Inc. (UK). We also

introduce Generalized Valuing Defense by Estimating

Probabilities (GVDEP). This method offers a compre-

hensive evaluation of team defense by weighting the

predicted probabilities of ball recovery and effective

attacks with those of goals scored and conceded (De-

croos et al., 2019). Using this evaluation method, we

analyze the defenses of teams that advanced to Round

16 in the tournament.

The main contributions of this study are as fol-

lows: (i) We generalize the previous method of valu-

ating team defenses (Toda et al., 2022) by incorporat-

ing a weighting system based on the predicted proba-

bilities of goals scored and conceded (Decroos et al.,

2019). We adjust the evaluation of defensive pro-

cesses by considering the impact of their actions on

the action evaluation metric, using the probabilities of

goals and concedes. (ii) We veriﬁed the classiﬁcation

performance of the machine learning model under

varying levels of available player data, applying our

method to open-source, partially observed tracking

data. The models’ classiﬁcation accuracy remained

robust even when using information from only a sub-

set of players near the ball. (iii) Our method success-

fully evaluated the defensive characteristics of the top

four teams at UEFA EURO 2020, providing insight

into why speciﬁc teams performed well or poorly in

defense. Our approach will enhance our understand-

ing of team defenses, even for the public data.

2 METHODS

In this section, we provide an overview of our ap-

proach, as illustrated in Figure 1. First, we describe

the dataset we used. Second, we deﬁne the input fea-

icSPORTS 2025 - 13th International Conference on Sport Sciences Research and Technology Support

tures and objective variables for classiﬁers. Third, we

describe the training of a classiﬁer for event predic-

tion. Fourth, we validate our method by examining its

impact on the number of player features. Lastly, we

propose our method, GVDEP, for valuing team de-

fenses.

2.1 Datasets

In this study, we utilized an open-access dataset pro-

vided by StatsBomb Inc. (UK), which contains data

from all 51 matches of UEFA EURO 2020. It is avail-

able at: https://github.com/statsbomb/open-data.

The dataset for this tournament consists of two main

types of data. The ﬁrst is event data, which includes

labels for speciﬁc events (e.g., passes, shots), along

with the xy-coordinates of the ball at the start and

end of each event. This kind of event data is widely

used in academic research for performance analy-

sis in soccer (Decroos et al., 2019; Gregory et al.,

2022). The second type is 360 data, which provides

the xy-coordinates of all visible players in the broad-

cast video frame at the time each event occurred. Note

that the 360 data may not capture the position of all

22 players at all times, as the broadcast camera does

not always cover the entire ﬁeld during live soccer

matches.

We constructed a data frame from the dataset for

validation and evaluation purposes. Following the

format of SPADL (Soccer Player Action Description

Language), which offers a standardized format for de-

scribing soccer events on an event-by-event basis (De-

croos et al., 2019), we documented the position of the

ball, the player involved, the type of action, and the

outcome of each event. Since the StatsBomb dataset

includes the xy-coordinates of the ball and some play-

ers, we incorporated additional SPADL columns to

capture player positional information. To enable a

more detailed analysis of team defense, we classiﬁed

players as attackers or defenders based on their ac-

tions and ordered them by proximity to the ball. Ad-

ditionally, we reﬁned the ‘foul‘ action type in SPADL

format by categorizing it into ‘offensive foul‘ (com-

mitted by attackers) and ‘defensive foul‘ (committed

by defenders) to provide a more nuanced defensive

evaluation. The remaining action types were deﬁned

according to the format. Ultimately, we identiﬁed 21

action types, including pass, tackle, and clearance,

among others. As a result of these processes, a to-

tal of 113,080 events were used in this study, creating

a data frame where each event included a median of 4,

mode of 4, and mean of 4.58 players for attackers and

a median of 3, mode of 1, and mean of 4.21 players

for defenders in each event.

2.2 Deﬁnition of Features and Objective

Variables

Here, we deﬁne the explanatory and objective vari-

ables used in our machine-learning model and defen-

sive evaluation for the classiﬁcation task. Table 1 and

2 provide speciﬁc deﬁnitions for each variable.

First, we deﬁne the explanatory variables based

on previous studies (Decroos et al., 2019; Toda et al.,

2022). In the data frame created in the last subsection,

let s

represent the state at the ith event. From s

, we

derive the following features: a

for the action type,

for the body part involved in the action, b

for

the ball positions and movements, and pl

for player-

related information. Additionally, we exclude penalty

shootout events from the feature creation process.

Next, we deﬁne the objective variables, which

indicate whether certain key events, such as a goal

scored, a goal conceded, a ball gain, and an effective

attack, occurred within a speciﬁed number of subse-

quent events. These labels represent scores, concedes,

gains, and effective attacks, respectively. The ﬁrst

two variables are labeled based on their occurrence

within ten events after an event occurred, and are used

to calculate the probabilities of these variables (De-

croos et al., 2019). In contrast, the last two are labeled

based on their occurrence within ﬁve events after an

event occurred, and are used to calculate the probabil-

ities of these (Toda et al., 2022). As a result, out of

113,080 events in the dataset, 1,209 were labeled as

scores, 211 as concedes, 4,601 as gains, and 16,116

as effective attacks.

2.3 Training of Classiﬁers for Event

Prediction

Our approach is based on the classiﬁers for multiple

event prediction. Here we outline the setup for train-

ing the models.

First, we employed XGBoost (Chen and Guestrin,

2016) as the machine learning classiﬁcation model.

XGBoost is a gradient boosting decision tree model

(Friedman, 2001) that emphasizes scalability and

computational efﬁciency. It includes regularization

to reduce overﬁtting and can handle missing values,

making it suitable for large datasets with sparse fea-

tures. In this study, most missing values were related

to player coordinates, which vary over time. To avoid

assigning a default direction for missing values in the

decision tree, we replaced these missing values with

predeﬁned values, as described in Table 1.

A Generalized Valuation Method for Team Defense by Estimating Probabilities in Football Games

Table 1: Deﬁnitions of explanatory variables.

Variable Description Examples of values

One-hot encoded type of action taken

at the i-th event.

pass, tackle, shot, cross, defensive foul.

One-hot encoded body part involved

at the i-th event.

foot, foot right, foot left, head, and other.

Ball position and movement characteristics

at the i-th event.

rectangular and polar coordinates (start

and end), distance traveled, and change

in xy-coordinates (11 dimensions).

Player position and relative distance

to the ball at the i-th event.

xy-coordinates, distance to the ball,

and angle to the ball (4 dimensions per player).

If data is missing, we set the x-coordinate

to -105, the y-coordinate to -68, the distance

to 0, and the angle to 0.

Table 2: Deﬁnitions of objective variables.

Variable Description Values

scores

An indicator of whether a goal was scored

within the next 10 events (Decroos et al., 2019).

Binary (1 if scores, 0 if not).

concedes

An indicator of whether a goal was conceded

within the next 10 events (Decroos et al., 2019).

Binary (1 if concedes, 0 if not).

gains

An indicator of whether a team gained the ball

within the next ﬁve events, such as tackle and

offside (Toda et al., 2022).

Binary (1 if gains, 0 if not).

effective attacks

An indicator of whether an effective attack,

deﬁned as entry into the opponent’s penalty area

or a shot taken, occurred within the next ﬁve

events (Toda et al., 2022).

Binary (1 if effective attacks, 0 if not).

2.4 Validation of the Classiﬁers

This subsection outlines the methodology used to val-

idate the impact of the number of player-related fea-

tures on the classiﬁcation models.

First, as a performance test, we conducted a 5-fold

cross-validation (Fujii et al., 2018; Toda et al., 2022)

because the total number of events in the dataset was

relatively small (113,080). To achieve this, we ran-

domly divided all 51 UEFA EURO 2020 matches

into ﬁve subsets, each containing a similar number of

matches (four subsets with ten games and one sub-

set with 11 games). For each iteration, one subset

was used as the test dataset, and the remaining sub-

sets were used as the training dataset; this process was

repeated across all ﬁve subsets. As a result, the fre-

quency of the objective variables—scores, concedes,

gains, and effective attacks—in a typical training and

test dataset split (example from the ﬁrst fold) is shown

in Table 3. As can be seen from this table, the data ob-

tained by this operation was extremely imbalanced,

with far fewer positive examples than negative exam-

ples. However, in this study, we did not employ over-

sampling or other measures to maintain the robust-

Table 3: The frequency of the objective variables in a typ-

ical training and test dataset split (example from the ﬁrst

fold).

Set Variable Positive Negative

Training scores 975 87,424

concedes 155 88,244

gains 3,572 84,827

effective attacks 12,897 75,502

Test scores 234 24,447

concedes 56 24,625

gains 1,029 23,652

effective attacks 3,219 21,462

ness of the XGBoost model to imbalanced data, en-

suring comparability with existing studies (Decroos

et al., 2019; Toda et al., 2022).

Next, to investigate the impact of player-related

features, we varied the number of pl

features by in-

cluding 0, 1, ..., and up to 11 players (attackers and

defenders) in order of proximity to the ball. We de-

ﬁned the number of attackers and defenders included

as n nearest. Speciﬁcally, when n nearest = 0, only a

, and b

were used as inputs, with no player-related

icSPORTS 2025 - 13th International Conference on Sport Sciences Research and Technology Support

features pl

. When n nearest = 1, we included the pl

features (4 × 2 dimensions) for the nearest attacker

and defender to the ball. For each value of n nearest,

we performed 5-fold cross-validation and calculated

summary statistics.

Following previous studies (Decroos et al., 2019;

Robberechts, 2019; Toda et al., 2022), we used the

Brier score, ROC AUC, and F1 score as evaluation

metrics for the validation. The Brier score measures

the accuracy of predicted probabilities by comparing

them to the actual outcomes. The ROC AUC repre-

sents the area under the Receiver Operating Charac-

teristic curve, which plots the true positive rate against

the false positive rate for binary classiﬁcation. Fi-

nally, the F1 score, the harmonic mean of Precision

and Recall, was chosen to validate better classiﬁca-

tions of true positives, which were relatively few in

this study. Furthermore, as explained above, the data

used in this study were class-imbalanced, with a mini-

mal number of positive examples; therefore, this eval-

uation metric was employed to achieve a balanced

evaluation. For each value of n nearest, we performed

5-fold cross-validation, calculated these metrics for

the 5 test data.

2.5 GVDEP: Valuation of Team

Defenses

This subsection describes our proposed method:

GVDEP for valuing team defenses. The previous

study weighted the probabilities of gains and effec-

tive attacks based on the ratio of each event’s fre-

quency (Toda et al., 2022). In contrast, our proposed

method weighted these probabilities using each VAEP

value (Decroos et al., 2019), which is one of the of-

fensive evaluation metrics. This approach enabled a

more data-driven weighting system, aiming to eval-

uate whether defensive events effectively contributed

to subsequent offensive plays. Additionally, VDEP

evaluated the defensive process using the probabili-

ties at a single event point. However, in GVDEP, we

assessed the defensive process by calculating the dif-

ference between the probabilities at a given point and

the previous point, thereby emphasizing changes in

defensive dynamics more effectively.

We deﬁne key terms and derivation methods be-

fore explaining VDEP and GVDEP. For the state s

the ith event, we denoted the occurrence probabilities

of the four target events (scores, concedes, gains, and

effective attacks) as P

scores

), P

concedes

), P

gains

and P

attacked

). Here, we used ‘attacked’ instead

of ‘effective attacks’ to consider the probability from

a defensive perspective. Following these deﬁnitions,

the VDEP value (V

vdep

) at ith event was expressed us-

ing P

gains

) and P

attacked

) as follows (Toda et al.,

2022):

vdep

= P

gains

) −C ∗ P

attacked

), (1)

where C represented the frequency ratio between

gains and attacked. However, this formulation did not

account for the relative importance of these events,

making it challenging to evaluate changes in the de-

fensive process.

To address this, we propose GVDEP, a method

that weights VDEP using VAEP, an offensive evalua-

tion metric (Decroos et al., 2019). First, for P

gains

)

and P

attacked

), we calculate the change between the

ith event state s

and the (i − 1)th event state s

i−1

each probability as follows to track the defensive pro-

cess:

∆P

gains

) = P

gains

) − P

gains

i−1

), (2)

∆P

attacked

) = −(P

attacked

) − P

attacked

i−1

)).

(3)

In addition, we deﬁne the weights for P

gains

and

attacked

as w

gains

and w

attacked

, respectively, as fol-

lows:

gains

|Ev

gains

∑

j∈Ev

gains

vaep

), (4)

attacked

−1

|Ev

attacked

∑

j∈Ev

attacked

vaep

), (5)

where each of Ev

gains

and Ev

attacked

is the event

indices of gaining the ball and being effectively

attacked, respectively, in all games, and each of

|Ev

gains

| and |Ev

attacked

| is the total number of the

events in all games. Note that Ev

gains

and Ev

attacked

here refer to events that occurred and were differ-

ent from labels such as gains or attacked that said

they would happen in the future. Moreover, the

VAEP value at the ith event, V

vaep

, is expressed using

socres

) and P

concedes

) as follows (Decroos et al.,

2019):

∆P

scores

) = P

scores

) − P

scores

i−1

) (6)

∆P

concedes

) = P

concedes

) − P

concedes

i−1

) (7)

vaep

) = ∆P

scores

) − ∆P

concedes

) (8)

Using these, we deﬁne the GVDEP value, V

gvdep

as follows:

gvdep

) = w

gains

× ∆P

gains

)

− w

attacked

× ∆P

attacked

(9)

Next, we explain how to evaluate team de-

fenses using metrics such as GVDEP. We analyzed

the teams that advanced to Round 16 in UEFA

EURO 2020, with each team evaluated over four

A Generalized Valuation Method for Team Defense by Estimating Probabilities in Football Games

matches (three group-stage matches and one Round

16 match). This selection ensured a balanced number

of teams and matches. First, we deﬁned the defen-

sive evaluation metrics, gain value, attacked value,

and gvdep value for each team as expressed in the

following equations:

gain value =

|Ev

∑

j∈Ev

∆P

gains

), (10)

attacked value =

|Ev

∑

j∈Ev

∆P

attacked

), (11)

gvdep value =

|Ev

∑

j∈Ev

gvdep

), (12)

where Ev

was deﬁned as defending events caused by

team te, and |Ev

| was the total number of the events.

In other words, gain value represented the average

change in the probability of gaining the ball during

defense; a higher gain value indicated that the team

was more effective in increasing the likelihood of re-

gaining possession. In contrast, attacked value rep-

resented the average change in the probability of be-

ing effectively attacked; a higher attacked value sug-

gested that the team was more successful in reducing

the probability of conceding effective attacks. Addi-

tionally, gvdep value represented the average V

gvdep

during defense, with a higher gvdep value indicat-

ing better defensive quality according to our proposed

metric.

Using these metrics, we analyzed team defenses

from four perspectives: a comparison of (a) at-

tacked value versus gain value, (b) gvdep value

versus the total number of goals conceded,

gain value versus the total number of goals conceded.

(a) was similar to a previous study (Toda et al., 2022)

and indicated whether a team prioritized gaining the

ball over preventing effective attacks. (b) compared

total goals conceded with GVDEP to evaluate defen-

sive effectiveness. (c) examined which term in the

GVDEP formula contributed most to the defensive

evaluation. (d) assessed whether gain value was a

reliable metric of defensive quality based on total

goals conceded.

3 RESULTS

3.1 Validation of Player Features

Figure 2 shows the results of the impact of the number

of player-related features on the classiﬁcation model

for each label (scores, concedes, gains, and effec-

tive attacks). In this ﬁgure, the horizontal axis in-

dicates n nearest, the count of attackers and defend-

ers closest to the ball used in the feature set, and the

vertical axis represents the evaluation metric. Each

box plot reﬂects the evaluation metric values from

the ﬁve test datasets during a 5-fold CV for each

value of n nearest. The Brier Score (Figure 2(a)) re-

mained consistent regardless of changes in n nearest

for all event types. The ROC AUC (Figure 2(b))

also showed no signiﬁcant variation with different

values of n nearest for scores and effective attacks.

While the concedes exhibited some variance across

the folds, the average score remained unchanged. For

gains, we saw slight improvement when increasing

n nearest from 0 to 1, but no further improvement be-

yond that. The F1 Score (Figure 2(c)) showed simi-

lar trends: no signiﬁcant changes for scores, a slight

degradation for concedes when n nearest increased

from 0 to 1, but no further changed afterward. How-

ever, for gains, we saw signiﬁcant improvement when

n nearest increased from 0 to 1 and minor improve-

ment from 5 to 6. For effective attacks, a slight im-

provement was observed when increasing n nearest

from 0 to 1, but no further changes after that.

3.2 Evaluation of the Team Defenses

Figure 3 presents the analysis and evaluation of de-

fensive strategies for the 16 teams that advanced to

Round 16 in UEFA EURO 2020. First, Figure 3(a)

represents gain value and attacked value. Higher x-

values indicate a stronger defensive effort to increase

ball recovery chances, while higher y-values focus

on reducing effective attacks. This ﬁgure highlighted

the defensive approaches of England, the runner-up,

and Denmark, a semiﬁnalist, both of which demon-

strated balanced defenses aimed at gaining posses-

sion while limiting effective attacks from opponents.

Italy, the tournament winner, focused more on pre-

venting effective attacks, whereas Spain, a semiﬁnal-

ist, prioritized gaining the ball. Portugal achieved

the highest attacked value, while Spain recorded the

highest gain value. Figure 3(b) shows the x-axis as

the total goals conceded by each team and the y-axis

as the GVDEP value, with lower x-values indicating

fewer goals conceded and higher y-values indicating

stronger defensive performance per GVDEP. The four

semiﬁnalists conceded fewer goals than the tourna-

ment average, and their GVDEP values (a metric in-

troduced in this study) were also above average. In

contrast, Portugal, Germany, and France—eliminated

in Round 16—conceded more goals than average but

still had above-average GVDEP values, with Por-

tugal’s being the highest. This result prompts us

icSPORTS 2025 - 13th International Conference on Sport Sciences Research and Technology Support

Figure 2: Box-and-whisker plots illustrating the impact of the number of player-related features on classiﬁcation model

performance for various event types. Each plot displays the distribution of evaluation metrics across ﬁve test datasets from

a 5-fold cross-validation. The horizontal axis, labeled ”The number of nearest attacker/defender to the ball (n nearest),”

represents the count of attackers and defenders closest to the ball whose positional features were included in the model,

ranging from 0 (no player features) to 11. The vertical axes represent the performance metrics: (a) Brier score, measuring

prediction accuracy (lower is better); (b) ROC AUC, indicating the model’s ability to distinguish between classes (higher

is better); and (c) F1 score, the harmonic mean of precision and recall, especially useful for imbalanced datasets (higher

is better). For each n nearest value, the box plots show the median (middle line), interquartile range (box), and data range

(whiskers), with individual points representing outliers. Green triangles indicate the mean value for each n nearest.

to explore whether GVDEP signiﬁcantly affected

attacked

). Figure 3(c) indicates a strong correla-

tion, as shown by Pearson’s correlation coefﬁcient

(r = 0.9711, p = 4.155 × 10

−10

). This ﬁgure rep-

resents that the x-axis is attacked

value, and the y-

axis is gvdep value. Additionally, the weighting val-

ues varied considerably, with w

gains

= 0.009657 and

attacked

= −0.02415, underscoring that this method

favored teams like Portugal and Italy that prioritized

preventing effective attacks. Finally, Figure 3(d) ex-

amines whether gain value effectively predicts defen-

sive performance by comparing it with total goals

conceded. The x-axis represents the total goals con-

ceded, and the y-axis shows gain value. Although

Belgium, with the lowest gain value, conceded fewer

goals than Spain, which had the highest gain value,

the gain value tended to worsen as the goals conceded

increased.

4 DISCUSSIONS

In this study, we ﬁrst examined how the number

of player-related features affected the model perfor-

mance for the four events considered (scores, con-

cedes, gains, and effective attacks). The results,

shown in Figure 2, indicated that including informa-

tion for up to six players (attackers and defenders)

was sufﬁcient to maintain model performance in pre-

dicting future ball possession. Next, we evaluated

the defensive performance of teams that advanced to

Round 16 in UEFA EURO 2020. Figure 3 illustrated

that while the top four teams demonstrated solid de-

fensive characteristics, some teams with higher goal

A Generalized Valuation Method for Team Defense by Estimating Probabilities in Football Games

Figure 3: Comprehensive team defensive evaluations for the 16 teams that advanced to the knockout stage in UEFA EURO

2020. These plots illustrate various aspects of defensive performance based on our proposed GVDEP metric and its com-

ponents. (a) gain value versus attacked value: This plot compares a team’s average change in ball recovery probability

(gain value on the x-axis) against its average change in effective attack probability prevented (attacked value on the y-axis).

Higher values in either dimension indicate stronger defensive performance in that aspect. (b) Total number of goals conceded

versus gvdep value: This plot displays the relationship between a team’s total goals conceded (x-axis) and its average V

gvdep

(gvdep value on the y-axis). Lower x-values indicate fewer goals conceded, while higher y-values suggest stronger overall

defensive quality according to GVDEP. (c) attacked value versus gvdep value: This plot examines the correlation between a

team’s attacked value (x-axis) and its gvdep value (y-axis), highlighting which term in the GVDEP formula contributes most

to the defensive evaluation. (d) Total number of goals conceded versus gain value: This plot assesses whether gain value

(y-axis) effectively predicts defensive performance by comparing it with the total number of goals conceded (x-axis). All

gain value, attacked value, and gvdep value metrics represent average changes in probabilities per event for a team, as de-

ﬁned in Subsection 2.5.

concessions also received favorable defensive ratings.

The following sections provide further discussion.

First, this study validated the impact of the num-

ber of players used as features on each classiﬁca-

tion model for the four target events: scores, con-

cedes, gains, and effective attacks. Using 5-fold

cross-validation, we inferred and calculated evalua-

tion metrics on ﬁve test datasets. The results show

low Brier scores (Figure 2(a)) and F1 scores (Fig-

ure 2(c)), while ROC AUC values (Figure 2(b)) were

high. This was caused by the label imbalance in the

data used in this study. As shown in Table 3, the target

events were highly imbalanced, with very few posi-

tive instances. This imbalance likely caused the Brier

score and ROC AUC to indicate high model accuracy,

even if the model predicts all outcomes as non-events

(zero). As described in (Decroos et al., 2019; Toda

et al., 2022), the Brier scores and ROC AUC values

similarly showed accuracy. Likewise, the F1 scores

obtained when using n nearest = 11 (with data from

all players) were similar to those reported in (Toda

et al., 2022). Thus, these results were likely due to

data imbalance rather than overﬁtting.

Lastly, Figure 3(a) shows a trade-off in our team

defensive evaluations between the tendency to gain

possession and the ability to prevent effective attacks,

consistent with previous ﬁndings (Toda et al., 2022).

For instance, teams like England and Denmark, which

performed well in the tournament, maintained a bal-

ance between these strategies, keeping their goals

conceded below the average. In contrast, Italy fo-

cused on preventing effective attacks, conceding only

once—from a corner kick—demonstrating a strong

defensive approach.

icSPORTS 2025 - 13th International Conference on Sport Sciences Research and Technology Support

Portugal achieved a higher GVDEP value than the

four semi-ﬁnalists and, like Italy, emphasized pre-

venting penetration into their penalty area. However,

they conceded seven goals—the third highest among

the Round of 16 teams—likely due to challenging

group-stage matchups against strong teams such as

Germany, France, and Hungary. This intense com-

petition may have contributed to player fatigue. Por-

tugal, Germany, and France, all high-ranking teams in

their group, had high GVDEP values but were elim-

inated in the Round of 16 after conceding multiple

goals.

In contrast, Belgium and the Czech Republic had

relatively low GVDEP values but conceded few goals,

likely due to the strength of their goalkeepers. Cour-

tois and Vacl

ık, the goalkeepers for Belgium and the

Czech Republic, respectively, kept clean sheets in

three of their ﬁve matches leading up to the quarterﬁ-

nals (UEFA, 2021). However, since our metric does

not focus on individual player abilities, it cannot cap-

ture the speciﬁc contributions of these goalkeepers.

5 CONCLUSIONS

In this study, we proposed GVDEP, a team defense

evaluation metric weighted by goals scored and gen-

eralized to better capture changes in defensive pro-

cesses. In validating the classiﬁcation models with

different numbers of player-related features, we also

found that only a limited number of player features

were needed for event prediction. This suggests ama-

teur teams can evaluate their defenses using only self-

recorded or broadcast videos. Our analysis also ex-

plained the defensive characteristics and strengths of

the top four teams in UEFA EURO 2020. However,

the results suggested factors outside this metric could

account for why some strong teams conceded more

goals than expected or why weaker teams conceded

fewer.

We present the limitations and future directions

of this study. First, it is essential to consider the

impact of different data sources. In this study, we

validated the models using 360 data, which included

information on players visible in broadcast video

frames during each event. This data has been re-

leased in recent years and remains relatively small

in scale. Due to the volume of data, the results of

cross-validation may be overly optimistic, limiting

the scope of analysis and potentially distorting the in-

terpretation of GVDEP’s sensitivity to defensive per-

formance through survivorship bias. Therefore, test-

ing whether similar validation results can be obtained

using other datasets, such as complete tracking data

for all players, is necessary. In addition, if larger

360 data can be obtained, more rigorous time series

segmentation and comparison, as well as examina-

tion of broader training-testing approaches, can be

considered for future research, along with an eval-

uation of all teams using models trained on other

datasets. Next, we discuss GVDEP itself. Figure

3(c) shows that this metric was heavily inﬂuenced by

∆P

attacked

). While preventing opponents from en-

tering the penalty area or taking shots is a clear in-

dicator of good defense, effective defense may also

involve quick transitions, such as regaining posses-

sion in the opponent’s half or slowing down the oppo-

nent’s attack by transitioning quickly to a defensive

structure. Future work should explore the compari-

son or integration of metrics for proactive defensive

actions, such as Passes Per Defensive Action (PPDA)

(Trainor, 2014) and Buildup Disruption Percentage

(BDP) (Soccerment, 2022), to provide a more com-

prehensive evaluation that accounts for pressing in-

tensity. Third, GVDEP is primarily an evaluation

metric and does not provide speciﬁc actionable in-

sights. While it could be helpful for scouting or re-

cruitment, it does not offer speciﬁc guidance on what

players should do during a game or how to prepare

for the next one. Future research should explore met-

rics that offer direct improvement suggestions, such

as evaluating defensive positioning using counterfac-

tuals (Umemoto and Fujii, 2023). Fourth, this study

does not account for defensive evaluations based on

player relationships. Speciﬁcally, actions such as

positioning between the passer and receiver to limit

passing lanes or standing between the goal and the at-

tacking player to block shots were only analyzed by

inputting player coordinates, without features indicat-

ing whether players are teammates. Therefore, con-

sidering player, pitch, and ball interactions, it is nec-

essary to develop defensive evaluation metrics. For

instance, this could involve graph neural networks, as

employed in previous studies on pass-receiver predic-

tion (Rahimian et al., 2023).

In conclusion, the GVDEP proposed in this study

offers a nuanced quantitative measure of defensive

performance, holding signiﬁcant potential for macro-

level decision-making in practical applications. This

includes aiding in scouting by assessing a team’s suit-

ability based on its emphasis on particular defensive

styles, and facilitating tactical analysis to identify a

team’s strengths and weaknesses within speciﬁc de-

fensive phases during a match. However, it is crucial

to acknowledge that this study validates GVDEP us-

ing data exclusively from UEFA EURO 2020. Conse-

quently, its generalizability across different leagues,

tournaments, or varying levels of play warrants fur-

A Generalized Valuation Method for Team Defense by Estimating Probabilities in Football Games

ther comprehensive investigation. Future research

should actively explore the application of GVDEP to

broader datasets to thoroughly assess its robustness

and adaptability, while also considering necessary ad-

justments for diverse playing styles and unique data

acquisition methodologies inherent to these new con-

texts.

REFERENCES

Anzer, G., Bauer, P., Brefeld, U., and Faßmeyer, D. (2022).

Detection of tactical patterns using semi-supervised

graph neural networks. In 16th MIT sloan sports ana-

lytics conference, pages 1–15.

Chen, T. and Guestrin, C. (2016). Xgboost: A scalable

tree boosting system. In Proceedings of the 22nd acm

sigkdd international conference on knowledge discov-

ery and data mining, pages 785–794.

Decroos, T., Bransen, L., Van Haaren, J., and Davis, J.

(2019). Actions speak louder than goals: Valuing

player actions in soccer. In Proceedings of the 25th

ACM SIGKDD international conference on knowl-

edge discovery & data mining, pages 1851–1861.

Fernandez, J. and Bornn, L. (2018). Wide open spaces: A

statistical technique for measuring space creation in

professional soccer. In Sloan sports analytics confer-

ence, volume 2018.

Friedman, J. H. (2001). Greedy function approximation: a

gradient boosting machine. Annals of statistics, pages

1189–1232.

Fujii, K. (2021). Data-driven analysis for understand-

ing team sports behaviors. Journal of Robotics and

Mechatronics, 33(3):505–514.

Fujii, K. (2025). Machine learning in sports: Open ap-

proach for next play analytics.

Fujii, K., Kawasaki, T., Inaba, Y., and Kawahara, Y. (2018).

Prediction and classiﬁcation in equation-free collec-

tive motion dynamics. PLoS Computational Biology,

14(11):e1006545.

Gregory, S., Robertson, S., Aughey, R., and Duthie, G.

(2022). The inﬂuence of tactical and match context

on player movement in football. Journal of sports sci-

ences, 40(9):1063–1077.

Liu, G., Luo, Y., Schulte, O., and Kharrat, T. (2020). Deep

soccer analytics: learning an action-value function for

evaluating soccer players. Data Mining and Knowl-

edge Discovery, 34:1531–1559.

Llana, S., Madrero, P., Fern

andez, J., and Barcelona, F.

(2020). The right place at the right time: Advanced

off-ball metrics for exploiting an opponent’s spatial

weaknesses in soccer. In Proceedings of the 14th MIT

Sloan Sports Analytics Conference.

Mehrasa, N., Zhong, Y., Tung, F., Bornn, L., and Mori, G.

(2018). Deep learning of player trajectory represen-

tations for team activity analysis. In 11th mit sloan

sports analytics conference, volume 2, page 3.

Nakahara, H., Tsutsui, K., Takeda, K., and Fujii, K. (2023).

Action valuation of on-and off-ball soccer players

based on multi-agent deep reinforcement learning.

IEEE Access, 11:131237–131244.

Pappalardo, L., Cintia, P., Ferragina, P., Massucco, E., Pe-

dreschi, D., and Giannotti, F. (2019). Playerank: data-

driven performance evaluation and player ranking in

soccer via a machine learning approach. ACM Trans-

actions on Intelligent Systems and Technology (TIST),

10(5):1–27.

Pollard, R. and Reep, C. (1997). Measuring the effective-

ness of playing strategies at soccer. Journal of the

Royal Statistical Society Series D: The Statistician,

46(4):541–550.

Rahimian, P., da Silva Guerra Gomes, D. G., Berkovics, F.,

and Toka, L. (2022). Let’s penetrate the defense: A

machine learning model for prediction and valuation

of penetrative passes. In International Workshop on

Machine Learning and Data Mining for Sports Ana-

lytics, pages 41–52. Springer.

Rahimian, P., Kim, H., Schmid, M., and Toka, L. (2023).

Pass receiver and outcome prediction in soccer using

temporal graph networks. In International Workshop

on Machine Learning and Data Mining for Sports An-

alytics, pages 52–63. Springer.

Robberechts, P. (2019). Valuing the art of pressing. In

Proceedings of the StatsBomb Innovation In Football

Conference, pages 1–11. StatsBomb.

Robberechts, P., Van Roy, M., and Davis, J. (2023). un-

xpass: Measuring soccer player’s creativity. In Pro-

ceedings of the 29th ACM SIGKDD conference on

knowledge discovery and data mining, pages 4768–

4777.

Rudd, S. (2011). A framework for tactical analysis and

individual offensive production assessment in soccer

using markov chains. In New England symposium on

statistics in sports.

Simpson, I., Beal, R. J., Locke, D., and Norman, T. J.

(2022). Seq2event: Learning the language of soccer

using transformer-based match event prediction. In

Proceedings of the 28th ACM SIGKDD Conference on

Knowledge Discovery and Data Mining, pages 3898–

3908.

SkySports (2024). Expected goals, expected assists, pres-

sures, carries, high turnovers and more — advanced

stats explained. Available at: https://www.skysports.

com/football/news/11095/12829539/expected-goals

-expected-assists-pressures-carries-high-turnovers-a

nd-more-advanced-stats-explained (Accessed: June

5, 2025).

Soccerment (2022). Measuring pressing success: Buildup

disruption percentage (bdp). Available at: https://socc

erment.com/measuring-pressing-success-buildup-dis

ruption-percentage-bdp/ (Accessed: July 23, 2025).

Spearman, W. (2018). Beyond expected goals. In Proceed-

ings of the 12th MIT sloan sports analytics confer-

ence, pages 1–17.

StatsPerform (2012). Assessing the performance of premier

league goalscorers. stats perform. Available at: https:

//www.statsperform.com/resource/assessing-the-per

formance-of-premier-league-goalscorers/ (Accessed:

June 5, 2025).

icSPORTS 2025 - 13th International Conference on Sport Sciences Research and Technology Support

ockl, M., Seidl, T., Marley, D., and Power, P. (2021).

Making offensive play predictable-using a graph con-

volutional network to understand defensive perfor-

mance in soccer. In Proceedings of the 15th MIT sloan

sports analytics conference, volume 2022.

Teranishi, M., Tsutsui, K., Takeda, K., and Fujii, K. (2022).

Evaluation of creating scoring opportunities for team-

mates in soccer via trajectory prediction. In Interna-

tional Workshop on Machine Learning and Data Min-

ing for Sports Analytics, pages 53–73. Springer.

Toda, K., Teranishi, M., Kushiro, K., and Fujii, K. (2022).

Evaluation of soccer team defense based on prediction

models of ball recovery and being attacked: A pilot

study. Plos one, 17(1):e0263051.

Trainor, C. (2014). Defensive metrics: Measuring the in-

tensity of a high press. Available at: https://www.hu

dl.com/blog/defensive-metrics-measuring-the-intensi

ty-of-a-high-press (Accessed: July 23, 2025).

UEFA (2021). Season 2020 stats — uefa euro 2020. Avail-

able at: https://www.uefa.com/uefaeuro/history/seas

ons/2020/statistics/ (Accessed: June 5, 2025).

Umemoto, R. and Fujii, K. (2023). Evaluation of team de-

fense positioning by computing counterfactuals using

statsbomb 360 data. In Statsbomb conference pro-

ceedings.

Wang, Z., Veli

ckovi

c, P., Hennes, D., Toma

sev, N., Prince,

L., Kaisers, M., Bachrach, Y., Elie, R., Wenliang,

L. K., Piccinini, F., et al. (2024). Tacticai: an ai as-

sistant for football tactics. Nature communications,

15(1):1906.

Yeung, C. and Fujii, K. (2024). A strategic framework for

optimal decisions in football 1-vs-1 shot-taking situ-

ations: An integrated approach of machine learning,

theory-based modeling, and game theory. Complex &

Intelligent Systems, pages 1–20.

Yeung, C., Sit, T., and Fujii, K. (2025). Transformer-based

neural marked spatio temporal point process model for

analyzing football match events. Applied Intelligence,

55(5):1–17.

A Generalized Valuation Method for Team Defense by Estimating Probabilities in Football Games