A strategy to predict association football players’ passing skills

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A Strategy to Predict Association

football players' passin

g

skills

Jorge Tovar

Andrés Clavijo

Julián Cárdenas

Documentos

CEDE

ISSN 1657-7191 Edición electrónica.

No.

6

3

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Serie Documentos Cede, 2017-63

ISSN 1657-7191 Edición electrónica.

Noviembrede 2017

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Universidad de los Andes | Vigilada Mineducación

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A strategy to predict association football players’ passing skills

Jorge Tovar*

Andrés Clavijo†

Julián Cárdenas‡ Abstract

Transfers are big business in association football. This paper develops a

generalized additive mixed model that aids managers in predicting how

a football player is expected to perform in a new team. It does so by

using event‐level data from the Spanish and the Colombian football

leagues. Using passes as a performance proxy, the model exploits the

richness of the data to account for the difficulty of each pass attempt

performed by each player over an entire season. The model estimates

are then used to determine how a player transferred from the

Colombian league should perform in the Spanish league, taking into

account that teammates and rivals’ abilities are different in the latter.

Keywords: Generalized additive mixed models, football, sports forecasting, passing.

JEL: C53, Z21, Z22

* _Associate _professor, _economics _department, _Universidad _de _Los _Andes _(Bogotá _– _Colombia). _Email: jtovar@uniandes.edu.co. Website: http://economia.uniandes.edu.co/tovar

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Una

Estrategia

para

Predecir

la

Habilidad

en

el

Pase

de

Jugadores

de

Fútbol

Jorge Tovar*

Andrés Clavijo†

Julián Cárdenas‡ Resumen

Las transferencias de jugadores es uno de los grandes rubros en el

millonario negocio del fútbol. Este trabajo desarrolla un modelo

generalizado aditivo mixto para predecir cómo se espera que se

desempeñe un jugador de fútbol en un equipo nuevo. Con base en

datos a nivel de evento de la liga española y colombiana se utilizan los

pases como proxy de desempeño. El modelo explota la riqueza de los

datos para controlar por la dificultad de cada pase que realiza un

jugador a lo largo de una temporada. Una vez se estima el modelo, se

utilizar para establecer como un jugador transferido de Colombia a

España debería desempeñarse, teniendo en cuenta que allí encontrar

nuevos compañeros y rivales.

Palabras claves: Modelos general aditivo mixto, fútbol, predicción deportiva, pases.

JEL: C53, Z21, Z22.

*_Profesor _asociado, _departamento _de _economía,_Universidad_de_Los _Andes_(Bogotá _– _Colombia)._Correo

electrónico: jtovar@uniandes.edu.co. Página Web: http://economia.uniandes.edu.co/tovar

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Introduction

Transfers are a big business in association football.1_According_to_the_FIFA₂₀₁₇_Global_Transfer

Market Report, in 2016 there were 14.591 international transfers for a total value of USD 4.79 billion.

The South American Market is a major player in this scenario, representing 17% of the World total

transfers. In 2016, there were 685 direct transfers from South America to European Leagues for a total

of USD 101 million.2_Players_move_across_countries_and_continents_and_are_expected_to_perform

according to the investment that they represent. However, managers at their destination teams have

little quantitative information on how a player should perform given the new environment it faces. This

paper contributes to filling this gap.

To predict the performance of any given player in a new environment, we use detail event‐level

data. The use of such data in football is not a new phenomenon. In fact, the analysis of detailed match‐

level data in football goes back, at least, to Reep and Benjamin (1968). Nevertheless, as stated by the

New York Times in 2010 “people in soccer have historically paid little attention to statistics, arguing that

the only way to judge players is to see them in action.”3_{Consequently,}_the_engagement_of_football_clubs

with event‐level data widely differs from that observed in American sports, particularly baseball.

However, times have changed, and the use of sophisticated event‐level data has gained

importance over the past decade in football. Still, with very few exceptions, (maybe the Danish club

Midtjylland a remarkable exception), there has been no Moneyball cases where data analytics has

successfully driven a team’s performance.4

The lack of successful experiences has much to do with the need to understand the analytics of

football better. Currently, a wide range of European football clubs uses data analytics to complement

the traditional training and game process. The use of such data in other areas of the world, mostly due

to the lack of data and resources, is much scarcer. Consequently, countries such as England understand

1_Association_football_refers_to_what_commonly_is_known_as_football_in_Europe_and_Latin_America,_and_soccer_in_the

United States. In this paper, henceforth, we will refer to it simply as football.

2_A_number_of_South_American_players_are_transferred_within_Europe_and_arrived_to_Europe_from_other_regions. 3_The_New_York_Times,_visited_September₄th_,_2017:

http://www.nytimes.com/2010/07/09/sports/soccer/09soccerstats.html

4_Midtjylland_is_a_team_that_won_the_2014/15_Danish_Superliga_under_the_hypothesis_that_a_football_club_could_be

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much better how its football performs, while others, Latin American countries in particular, know little

about the analytics behind their game.

This paper adds to the literature (and to the football industry) by estimating and implementing a

model that offers a quantitative measure of how a player should perform when transferred to a new

league. It does so by evaluating the passing ability of football players in the case of a little‐studied

football competition. Specifically, it reviews a strong South American league recently ranked by the

International Federation of Football History and Statistics (IFFHS) as the second‐best league in 2016.5

The Colombian league might be by almost any standard inferior to the major European football leagues,

but the high position in the ranking does suggest that football beyond the traditional five associations is

worth studying.6_To_evaluate_how_Colombian_players_should_perform_when_moving_to_Spain,_we_need_to

estimate the model for LaLiga, the Spanish first division football league, undoubtedly one of the top

tournaments in the World.

We estimate the probability of a pass being successful using a generalized additive mixed model

as proposed by Lin and Zhang (1999). This particular estimation technique, to the best of our knowledge,

has only been used in the past by Szczepański and McHale (2016) and McHale and Relton (2017), in both

cases using data for the English Premier League. The technique, ideal because it takes into account the

difficulty of any given pass, has never been implemented using data from Spain or any South American

league. The model in the past has been used to understand the player´s passing abilities and to use the

estimated probabilities as weights in a passing network. We test the validity of the model and once

finding that the model accurately predicts the player’s passing skills move on to implement a practical

application.

The novelty of our paper relies on the model’s ability to predict how a player that participated in

the 2016‐I Colombian League should perform over the following season in another league, the 2016/17

Spanish LaLiga.7_The_model_generates_predictions_for_all_players_that_participated_in_the_Colombian

league. That is, our strategy can benefit potential employers as they can anticipate how a given player is

expected to perform under a new environment. In practice, during our sample period, three players

moved from Colombia to Spain. For each of these players, we analyze in detail the passing ability

predictions and compare them to how they actually performed.

5_IFFHS_link_visited_September₅th_,_2017:_{http://iffhs.de/strongest}_‐_national_‐_league_‐_world_‐₂₀₁₆_‐_spain_‐_since_‐_2010/ 6_The_top_five_leagues_include_the_English,_French,_German,_Italian_and_Spanish_domestic_{competitions.}

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The use of event‐level data is relatively new, mainly when using South American data. There

have been detailed data‐based studies of South American football in the past (see for instance Flores et

al., 2012 or Tovar, 2014) but, to best of our knowledge, no approach as the one implemented in this

paper has been used in the past. The relevancy of the paper exceeds academia as the technique is of use

to the football industry. South America is the source of some of the best players in the football industry

that, bred in local clubs, will eventually end up playing in Europe’s top leagues. A better understanding

of the abilities of these players while playing in South America, and predicting how their passing

performance abroad should be, will aid European clubs to optimize their investment.

Data

We use proprietary data provided by www.golyfutbol.com for the Colombian League, and LaLiga, the Spanish football league.8_In_both_cases,_the_data_is_available_for_one_complete_season._The

Spanish League, available for the 2016/17 season, is played under the traditional format of most

European leagues: a double round‐robin. The Colombian League, with a new champion every six

months, follows a single round‐robin schedule.9_The_eight_top_teams’_then_compete_in_knockout_playoffs

(with home and away games) until a champion is declared. We use data for the first semester of 2016. We have data available for 208 games in the Colombian League, and 378 in the Spanish League.

The data provided follow all events such as passes, shots, goals, interceptions, and recoveries. It gives us

the precise x,y coordinates on the pitch, and records the minute and second it occurred. In that sense, it

is similar to the dataset used in Szczepański and McHale (2016). It primarily differs, however, with the

detail tracking data used in McHale and Relton (2017) which captures each player’s position ten times

per second. Using our data we identify when and where a player passes the ball, but we do not know

where players (either teammates or opponents) surrounding the man with the ball are.

The key event used in the paper refers to the number of pass attempts. For Colombia, we have

20 teams, 536 players and 101,573 (correct and incorrect) passes. The corresponding figures for LaLiga

are 20, 535 and 234,827.

We expect the Spanish League to be superior in quality than its counterpart. The passing skill of

a player is arguably one of the most reliable indicators of player performance in a given game (See for

8_Data_Factory_originally_collected_the_data.

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instance Anderson and Sally, 2013 or Tovar, 2014). Table 1 suggests that measured by the number of

passes per game, the game is faster and precision is higher in Spain.

Table 1

Passing ability: comparative across competitions

A primary objective of the paper is to control for the pass’ difficulty. It is relatively well‐known

that, on average, the chance of completing a pass differs by the players’ position. Defenders tend to face

little opposition, while forwards encounter stronger resistance as they are closer to the opposing goal.

Table 2

Passing accuracy

Table 2 shows that LaLiga players pass with greater accuracy than those playing in the

Colombian League regardless of the position. The raw figures in this section reveal the expected

strength of the Spanish League relative to its South American counterpart.

The

Model

To estimate the probability that a player k, k=1..K, successfully makes a pass, recall that our data

is defined at the event‐level, i.e., each observation is a pass attempt by player k, at game g, g=1…G, in

any of the two leagues considered.10_In_other_words,_we_are_observing_a_group_of_players’_actions

(passes) over time (the same game), under the same conditions, but the success probabilities vary from

player to player. To deal with this type of data, we would need to estimate a generalized linear mixed

model (GLMM) which uses a parametric mean function to model covariates effects while adding random

effects to deal with overdispersion and correlation (Lin and Zhan, 1999).

10_We_estimate_a_separate_model_for_each_competition.

Competition Percentage of successful passes Number of passes per game

LaLiga 16/17 87.66% 618

Colombian League 2016‐I 84.08% 475

Source: www.golyfutbol.com. Own calculations

Competition Goalkeeper Defender Midfielder Forward

LaLiga 16/17 86.03% 88.72% 88.11% 82.72%

Colombian League 2016‐I 83.06% 84.82% 85.70% 79.72%

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The available data is precise enough to position each pass (whether successful or unsuccessful)

on a specific coordinate on the pitch. For covariates such as this, an appropriate functional form is

unlikely to be known in advance. The need to model non‐parametrically this type of covariates calls for

the use of a generalized additive mixed model (GAMM), as developed by Lin and Zhan (1999) and

implemented for the English Premier League by Szczepański and McHale´s (2016), and McHale and

Relton´s (2017).

Let oi denote the outcome for the ith pass where oi = 1 if the pass is successful and oi = 0 if the

pass is unsuccessful. Assuming that the distribution of pass outcomes follows a Bernoulli distribution

with the probability of success represented by the inverse logit function of the linear predictor



_i, we

have:



ok



i



~ Bernoulli

 

pi

where

 

i

i i

p



exp

1 exp





The linear predictor



_i is given by:



iend i iend



i



W

i





Z

i

b



s

x

i

,

x

,

y

,

y

,



[1]

where W_iis a row vector of covariates and Z_iis a design matrix selecting the elements of the random

effects vector

b

that corresponds to the ith_pass_executed_by_a_given_player._Lastly,_s_is_a_smooth

function used to model the coordinates of the passing event, i.e., origin and destination.

The

W

matrix includes in principle the distance of the pass, whether it is a forward pass, game

time, the pass number in the current sequence of passes, the time on the ball the player had it before

passing and an indicator variable on whether his team was playing at home or away.

The chosen variables are expected to capture various factors that influence the ability to pass

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probability of successfully achieving a pass.11_A_forward_pass_is_an_indicator_variable_indicating_whether

or not the pass intended to move the ball closer to the opposition goal line. The larger the sequence of

passes proxies for the pressure that the opposition players place on the player attempting to pass the

ball.

Typically, the passing precision will increase if the player has the ball for a few extra seconds,

enough to control, look and pass. However, if the player retains the ball for too long, presumably

opponents’ players will increase pressure making it harder to pass the ball successfully. Consequently,

for the time on the ball, we expect a quadratic relation.

There is a well‐known home advantage effect in football where teams playing at home tend to

perform better (Carmichael and Thomas, 2005). Given the overwhelming historical evidence of such

effect, the home/away indicator variable is included despite the existence of recent research suggesting

that, under certain circumstances, the home advantage effect can disappear (Krumer and Lechner,

2017).12

The random effects vector

b

is composed of three elements: the passing ability of each player in

the sample, the ability of the passing player’s team and the ability of the opposition to impede the pass

execution. In other words, it captures the individual’s passing skill, the team ability to facilitate the kth

player pass and the capacity of the opposition to obstruct such pass.

The last component in equation (1) is modeled as a tensor product smooth to deal with multiple

inputs that in this case represent each i pass’ origin and destination by x,y coordinates. The player’s

position on the pitch proxies for the pressure faced by the passing player and the receiving player, as

well as the difficulty of the associated pass with the location on the pitch and the pass’ distance.

The

results

We estimated the GAMM model described in the previous section separately for each of the

competitions considered using the mgcv package (Wood, 2006) in R. The variables are included in each

specification depending on whether they are statistically significant or not.

11_The_pitch_is_normalized_between_[0;1]_along_the_sideline_and_between_[0;0.65]_along_the_goal_line._This_is_based

on the standard size of a pitch, 105 meters long and 68 meters wide. Although not all pitch surfaces measured

exactly the same, we searched on the Internet the size of most of the pitch included in our datasets, and a vast

majority has, relatively, the same proportions.

12_Based_on_Bundesliga_data,_they_find_that_the_home_advantage_disappears_when_the_game_is_in_the_middle_of_the

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Table 3

Estimates of the parametric model (



elements in equation 1)

The results reported in Table 3 show the expected signs for all parametric model terms

contained in the vector



. We find that the probability of successfully passing the ball increases if

playing at home, as the game advances, and the longer the sequence of passes. The longer a player is in

control of the ball, the higher the chances of successfully passing but only for so long. As hypothesized, if

the player holds onto the ball for too long, the probability of correctly passing the ball decreases. Finally,

when statistically significant, the likelihood of success falls when the ball is passed forward. The distance

is not statistically significant, most likely because its effects are captured by the smooth tensor term for

the origin and destination, which is strongly statistically significant.

Comparative

analysis

To assess the model’s validity, we first estimate the predicted pass completion rate by

substituting the model estimates (fixed parameters, random effects, and the smooth function) into the

corresponding components of equation (1). The resulting pass completion rate for all passes attempted

is averaged and scaled over players to obtain the predicted passing rate for each k player.

Variable Estimate Std. Error z‐Value P‐Value Estimate Std. Error z‐Value P‐Value

Home dummy 0.18 0.02 10.26 0.00 0.16 0.02 6.46 0.00

Minute of the pass 0.00 0.00 10.09 0.00 0.00 0.00 9.68 0.00 Number in the pass

sequence 0.02 0.00 7.11 0.00 0.03 0.00 7.50 0.00

Time to execute pass 0.33 0.02 13.57 0.00 0.25 0.04 6.90 0.00 (Time to execute pass)2 ‐0.05 0.00 ‐10.88 0.00 ‐0.03 0.01 ‐5.38 0.00

Forward pass ‐0.11 0.03 ‐3.40 0.00

Intercept 1.77 0.06 29.95 0.00 1.38 0.07 19.72 0.00

Source: www. golyfutbol.com. Own calculations

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Figure 1

Per player predicted vs. observed passing rate

(a) LaLiga (b) Colombian League

Source: www.golyfutbol.com. Own calculations.

Figure 1 compares the predicted with the observed pass completion rate. On average the model

predicts with 90% accuracy LaLiga, and with 85% accuracy the Colombian League. The predictive power

is in line with Szczepański and McHale´s (2016) estimates for the English Premier League.

The nonparametric additive function included in equation (1) controls for the origin and

destination coordinates of each pass, whether successful or unsuccessful. We visualize the observed

impact of the smooth function s, on the passing ability rate by fixing a point of origin and depicting the

predicted probability for each pass. Specifically, Figure 2 sets the pass’ source in the center of the pitch

and using the estimated linear predictor, determines the chances of successfully passing the ball for a

central midfielder.13

A central midfielder tends to be more accurate when passing towards his own half than towards

the opponents half, i.e., it is easier to pass the ball backward than forward. Figure 2 also highlights that

open passes tend to be more successful than passes towards the end zone, not a surprising result since

much of the opponents’ objective when not in possession is to impede the ball to reach their own goal.

Consequently, the chances of successfully passing the ball towards the opposing goal are slim.

Figure 2 also reveals some differences across competitions. Not surprisingly, the Spanish league

has a higher passing precision, mainly when passing backward or when opening the ball to the wings.

Remarkably, a player in the Colombian league has a surprising difficulty passing the ball towards his own

13_Using_all_available_events_in_the_dataset_(goals,_assists,_passes,_recoveries,_etc),_a_player_is_defined_as_a_center

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goal: the predicted probability in this case, near the own goal, is smaller than in LaLiga. Similarly, an

open offensive pass in the Colombian League is expected to be less successful than one executed in

Spain.

Figure 2

Value of the linear predictor by origin of the pass and player position

Center Midfield originating the pass from the center of the pitch

Note: X represents the pitch’s length. Y, the width. X2 and Y2 are the destination coordinates of the

attempted pass by length and width. The origin represents the right corner of the player’s team own

goal line.

One can conclude that a center midfielder with the ability to successfully pass towards the

penalty box (say the penalty spot) would be among the best (and presumably amongst the most

valuable) players in a given league. Indeed, according to our model, we find evidence that Tony Kroos

(Real Madrid) and Steven N’Zonzi (Sevilla) were the two most successful players in doing this in LaLiga

during the season considered. Correspondingly, for Colombia, the name that pops out is Mayer Candelo,

a locally well‐known name. Candelo, 11 caps with Colombia, was 39 years old during our sample period.

He is arguably the last of the traditional South American playmakers in the Colombian league. Like

others in the past, Carlos Pibe Valderrama the most renown, Candelo is physically slow but mentally

fast. Such characteristics made it possible for him to achieve great performance at a relatively advanced

age.

The annex presents the linear predictor for additional positions (Figure A.1 and Figure A.2). As

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center back in Colombia has a hard time passing successfully towards the opponents half. Similarly, a

Colombian center forward is very erratic when attempting anything beyond a horizontal pass.

Among the model’s strengths is its capacity to take into account that not all passes are made

equal. To calculate the ease of passing, we estimate the linear predictor setting each player’s random

coefficient to zero. The latter implies that the player‐specific passing abilities are excluded when

determining the probability of successfully passing the ball, resulting in the predicted pass completion

rate by an average player.

Figure 3

Ease of pass (average)

Note: The horizontal dotted lines represent, from left to right, the 25, 50, and 75 percent quartiles.

Figure 3 depicts the distribution of the probability of a successful pass by an average player.14

The further to the right the higher the likelihood of success, i.e., the easier the pass is. Similar to earlier

findings by Szczepański and McHale (2016), the distribution is highly skewed to the right. Comparatively

speaking there are significant differences between the Spanish and the South American competition as

passes in the latter tend to be easier than in LaLiga.

It is well‐known that the passing success varies by the nominal position held by a given player.

Figure 4 depicts the predicted pass completion rate per player’s position. As expected forwards and

midfielders’ pass are less prone to succeed, particularly true in Colombia.

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Figure 4

Ease of pass (by player position)

Note: The horizontal dotted lines represent the median

This section’s findings can be summarized in Figure 5 which shows that, as hypothesized, LaLiga

players tend to have superior passing abilities than players in the Colombian League.

Figure 5

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Predicting

passing

performance

The model has the capacity to predict the passing performance of any player when transferred

abroad. We derive some examples based on the estimates for the Colombian League and contrast the

prediction with actual performance. Specifically, we take the player’s estimates before moving to Spain

and, using those figures and given the team he is transferred to and the rivals he will face in Spain, we

calculate the predicted passing completion rate in his new Spanish team.

The three players considered competed in the Colombian League during the first semester of

2016 and moved to Spain for the 2016/17 season. Daniel Torres (midfielder) moved from Independiente

Medellín to Alaves, Marlos Moreno (forward) from Atlético Nacional to Deportivo de La Coruña, and

Rafael Santos Borré (forward) from Deportivo Cali to Villarreal. Note that the number of players that

moved from Colombia to Spain is irrelevant. The strength of the model is its ability to generate

predictions for any given player in the Colombian league.

The first step to determine their prospect passing performance in Spain consists of estimating

the linear predictor based on the Colombian model, setting to zero the random effects corresponding to

the own team’s ability to facilitate passes and the opposition to prevent them. These results are

averaged for each of the three players considered. The resulting predicted pass completion rate implies

that the expected passing skills depend solely on each players abilities, not on how his team aids in his

performance or on how the rivals obstruct his passing intentions. Lastly, for each of the three players,

we add his team and the opponents’ random effects for each game they can potentially play during the

2016/2017 LaLiga. The result, scaled using the inverse logit function, is the linear predictor considering

the player’s skills, and his new teammates and rivals abilities to facilitate and impede the player's passes

respectively.

Figure 6 depicts the average fixture‐specific predicted probability calculated as described above.

There are two observations for Villarreal, Deportivo, and Alavés because the players considered played

in one of these teams. Torres has the highest predicted probability consistently while Marlos Moreno

has the lowest. The predicted passing performance is relatively weak against Barcelona, consistent with

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passing of their opponents. It should come as no surprise that the order of the teams in Figure 6 follows

the x‐axis in Figure A.3, which represents the team’s ability to prevent the opponents passes. The

magnitude of the fixture‐specific prediction is determined by each player’s skills and the team’s ability to

facilitate passes, i.e., the y‐axis in Figure A.3.

Figure 6

Source: www.golyfutbol.com. Own calculations

The passing performance estimates in Figure 6 are the ones that the Spanish managers would

receive as a quantitative indicator of what he should expect from each player analyzed. During the

2016/17 season, Torres was on the pitch for an average of 74 minutes over the 20 games he played for

Alavés. Moreno averaged on the pitch 45 minutes over the 18 games he played, and Santos Borré was

fielded 16 times for an average of 24 minutes per game.

Figure 7 presents the result of games where they participated, and the observed pass

completion rate is less than one.15_The_continuous_line_in_the_graph_represents_the_identity_line

indicating that the predicted probability of successfully passing the ball is the same as the observed pass

completion rate.

Consider the case of Daniel Torres initially. The model predicts, for the most part, a fixture‐

specific probability of 90.4%. Indeed, he did achieve in most games around 90% pass effectiveness. Over

15_For_a_number_of_games_they_just_played_a_few_minutes_during_which_they_just_had_time_to_pass_once_or_twice

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the first six matches, Torres completed the entire game in five of them. In matchday 1, Alavés played

Atlético de Madrid. The model predicted an 89.9% passing accuracy and Torres delivered a passing

precision rate of 87.5%. In matchday 3, playing away against the mighty FC Barcelona, the model

predicts a passing success rate of 86.8%. His observed performance was 79%. Later on in the season,

when facing Barcelona in Vitoria (home game), the model predicted 89.7% passing accuracy. Torres’

observed rate was 88.8%. The Camp Nou, Barcelona’s stadium, sits comfortably near 100,000

spectators, the largest crowd in Europe, the second in the World. It could be argued that Torres,

relatively new in the Spanish league at the time of the match, was particularly impressed by the Camp

Nou’s atmosphere, leading to his relatively poor performance. His experience in Barcelona was useful

later on in the season, not only when Barcelona visited Vitoria (Alavés’ home city) but also when they

faced home Real Madrid, the other Spanish giant. The model predicted a 91.5% passing accuracy, pretty

close to the observed 92.7%. On average, Torres’ successful passing rate was as expected. His

unsurprising passing performance explains in great part why he was a starter in 17 games and why he

was kept in the Alavés squad for the following season.

Figure 7

Note: The continuous diagonal line is the identity.

The model, for Marlos Moreno, estimates an average successful passing probability of 87.5%.

The observed average passing completion rate was 92%. However, Moreno was a starter in only nine

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15 minutes and made more than five pass attempts, the observed percentage of successful passes drops

to 85.6%. Indeed Figure 7, which considers all games with a passing rate smaller than one, shows that

for games where Moreno actively participated, he, for the most part, underperformed. Added this to his

goalless record explains much on why he was unable to succeed in La Coruña.

Considering only games where Santos Borré played more than 15 minutes, i.e., when he actively

participated in the game, the observed percentage of successful passes was 83.2%. A starter in just two

games his predicted passing accuracy was 88.3%. Figure 7 shows that whenever his passing rate was

below one, he always underperformed. The latter and the fact that he only scored two goals explains in

part why Santos Borré had to move back to South America, specifically River Plate (Argentina).

The analysis suggests that players who underperform the model’s predictions have trouble to

make it to the starting eleven and to remain in the squad the following season. In our examples, only

Torres performed as the model expected. He played a large number of games, was part of the starting

eleven in most games where he played and was part of the squad for the following season. Moreno and

Santos Borré, both of who underperformed the model's expectations were dismissed at the end of the

season.

Conclusions

This paper estimates a generalized additive mixed model using event‐level data from the

Spanish and the Colombian football leagues. The model accounts for the player’s characteristics as well

as the teammates and the opposition ability to ease and deter the players’ passing effectiveness

respectively. It also models, nonparametrically, the origin and destination coordinates. In other words,

the model takes into account various characteristics of the game to assess the difficulty of the pass.

Once the model estimates are available, we show that the model predicts the passing ability accurately

in both leagues.

The model’s strength is its capacity to anticipate the passing performance of players when

transferred from one league to another. In an industry with millions of dollars at play, access to an

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In practice, a manager will be interested in the passing performance of a player during the

following season, t+1, given the player’s performance in his home league during period t. To deliver the

predictions, the model needs to be also estimated using data from the destination league in period t.

This poses no challenge. The model will be estimated during the same season for the origin and the

destination leagues. In our example, it implies that the model is calculated for the first semester of 2016

using data from the Colombia league and using data for the 2015/16 Spanish season. The player’s

destination team and its opponent’s random effects need to be extracted from the latter and plugged

into the linear predictor (as discussed in the text) using the estimates from the Colombian model. The

implicit assumption is that in the destination league, the team’s ability to facilitate and prevent passes

does not change radically from one season to another. For newly promoted teams, where no random

effect predictions are available, the estimates used will be those of the relegated teams, as done

previously in the literature.

The model has, of course, some limitations aside from the obvious data requirements in both

the origin and destination league. Passing is probably the most important skill that a football player

should have. Bill Shankly, the legendary Liverpool manager, used to say: “Above all, the main aim is that

everyone can control a ball and do the basic things in football. It’s control and pass … control and pass …

all the time”.16_However,_it_is_not_the_only_relevant_indicator_to_determine_if_a_player_is_performing_as

expected. In that sense, our model is limited to one particular, but probably the most important

performance proxy.

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Appendix

Figure A.1

Center back originating the pass from just outside the player’s team own box

goal line.

A center back is defined as the player that, given all available events, plays in the team’s defense, between the right and left backs.

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Figure A.2

Center forward originating the pass from just outside the middle of the opponents’ box

goal line.

A central forward is defined as the player that, given all available events, plays in the team’s offense,

between what would be the right and left wings.

Figure A.3