Key Players and Key Groups in Teams: A Network Approach Using Soccer Data
Sudipta Sarangi & Emre Ünlü
Louisiana State University
October, 2010
INTRODUCTION • Understanding the contribution of each individual to their teammates is crucial.
‐ Examples: Special Task Groups, Team Sports and R&D Groups .
• Interviews often test an applicant’s ability to be a “team player” before hiring. Recommendation letters often talk about a person’s “team ability”. • Identifying individual contributions allows for better team composition and helps with compensation and retention issues.
• In this paper, we develop a model of a Team Game by extending Ballester et al. (2006). OBJECTIVES
• Introduce a team outcome component into the payoff functions of the players.
• Provide the key player solution for the Team Game.
• Describe the game of soccer through the individual actions and interaction between the players and identify the key players and key groups in this network. • Conduct simulations to investigate how the results change when model parameters change.
• Investigate the effect of having a higher interaction with teammates on the player ratings and market values of the players.
TEAM GAME
• Individual payoff function for player i:
In the above payoff function:
 xi represents the individual actions, and αi stands for the returns on individual actions.  σii <0 captures the concavity in individual actions.
 σij stands for the complementary action of player i on player j.
 θZ is the desired team outcome defined as θ(δ1x1+δ2x2+…+δnxn) where δi
is ability parameter of player i.
TEAM GAME (cont.)
The matrix of cross effects can be written as:
TEAM GAME (cont.)
• The matrix G=[gij] is a zero diagonal nonnegative square matrix, interpreted as the adjacency matrix of g. By using the above definitions, the payoff functions are decomposed into the following expression:
•
CENTRALITY MEASURES
• Define the M matrix such that:
• Bonacich (1987) centrality measure becomes:
• Bonacich centrality measure weighted with the ability parameter:
CENTRALITY MEASURES (cont.)
• The Ballester et al. (2006) intercentrality measure (ICM) for an
asymmetric G matrix is given by: • We define a useful centrality measure which accounts for the receiving of a player weighted by her ability parameter:
CENTRALITY MEASURES (cont.)
• Team intercentrality measure (TICM) for the Team Game is:
‐
ICM takes into account the number of connections that emanates from and ends at player i.
‐
TICM differs from ICM with the last term which measures contribution of player i to team’s outcome by her ability parameter. NASH EQUILIBRIUM
• The Nash equilibrium action level of each player is proportional to her Bonacich centrality, Bonacich centrality weighted with the ability parameter in the network of local complementarities. A TEAM SPORT: SOCCER
• “There are no more crucial skills than passing in soccer because soccer is a team sport. The most effective set plays involves accurately passing and receiving the ball.” (Miller and Wingert, 1975)
• “Passing and receiving skills form the vital thread that allows 11 individuals to play as one‐ that is, the whole to perform greater than the sum of its parts.” and “Even the most talented players cannot do it alone.” (Luxbacher, 2005)
• Luhtanen et al. (2001): “The presented results show that there is a variable of successful passes at team level that explained the success in the EURO 2000.’’
UEFA EURO 2008
Source: www.uefa.com/tournament/statistics/teams
TEAM GAME FOR SOCCER
• Individual payoff function for player i:
In the above payoff function:
 xi represents kicking effort of player i and αi > 0 stands for returns on having kicks in the game. It includes shots on goal, passing, throw‐ins and corners.
 σii <0 captures the concavity in kicking.
 σij stands for the net discounted passes from player i to player j, Thus, player i's utility from interacting with player j is weighted by how often he passes to j.
. THE TEAM OUTCOME
Two ways to define team outcome:
1. θ Z represents the team outcome where Z is {‐1, 0 ,1} and θ
is the coefficient of the team outcome. ‐ This allows us to use ICM to identify the key players.
2. θZ represents the team outcome defined as: Z= θ(δ1x1+δ2x2+…+δnxn) where δi is the scoring probability of player i.
‐ This allows us to use TICM to identify the key players.
PASSING DATA
• The interactions between players can be observed from the passing network within the teams. So, elements of complementarity matrix (Σ) are constructed using this passing data.
• The passes between players are discounted and only (net) successful passes (includes corners, crosses and throw ins) from player i to player j are included.
• The passing data are collected from the Final, Semi Final and Quarter Final matches of UEFA Euro 2008.
• The data for scoring probabilities (as an ability parameter) of each player are available through ESPN but only identifies scoring probability of each player in the UEFA Euro 2008. PASSING DATA (cont.)
Own Half Of The Field
Opponent’s Half Of The Field
FIGURE II: Discounting the passes made in the own half of the field by “d”. KEY PLAYERS
KEY PLAYERS
SENSITIVITY CHECKS
• There is no formal proof for the effect of model parameters a
and d on identifying the key players. Counter‐examples exist!
 We conduct a sensitivity check using simulations.
• We allow “a” to vary in the interval [0, 0.125] in increments of 0.001. Simultaneously, “d” varies in the [0, 1] interval in same increments. • The identified key players according to ICM are 85% robust in the parameter ranges.
KEY GROUP
• The key group problem was initiated by Ballester et al. (2004). Temurshoev (2008) provides a new formulation and provides an algorithm for determining the key group. • Key groups provide information about the joint contribution of players to their team. ‐ This is a valuable information to the clubs, team managers and coaches who wishes to include players who provide different adjacency to their teammates.
KEY GROUP (TICM)
KEY GROUP (ICM)
PLAYER DATA • The estimated market values (EMV) of players are obtained from transfermarkt.de. Battre et al.(2008) and Torgler et al. (2008) mention it as a good and reliable source. • We obtained the other observable characteristics of players from transfermarkt.de such as: Age, club, position, number of international caps, number of international goals, preferred foot and captaincy.
• Club UEFA points and Nation UEFA points available from UEFA's website for 2008 are used to control for the quality of players. • Average ratings of the players obtained from Goal.com, ESPN and SkySports for the considered matches in UEFA Euro 2008. AVERAGE RATINGS AND INTERCENTRALITY
• Base regression model :
Avg. Ratingit = α1 + β1 (T)ICMit + γ1 Agei + θ1 Agei 2 + λ1 Positioni
+ ψ1 Club Ranki + φ1 Nation Ranki + ε1t
In the above regression model:
‐ subscript i represents player i. ‐ (T)ICM stands for the (team) intercentrality measures.
‐ Position is a dummy identifying field position of the player. ‐ Team is a dummy to identify the player’s national team.
‐ Club Rank and Nation Rank indicate the rank of the club and nation of the player i measured by UEFA points. • The above model is estimated by Population Average (PA).
AVERAGE RATINGS AND INTERCENTRALITY
• Base regression model :
Avg. Ratingi = α1 + β1 (T)ICMi + γ1 Agei + θ1 Agei 2 + λ1 Positioni
+ ψ1 Club Ranki + φ1 Nation Ranki + ε1
In the above regression model:
‐ subscript i represents player i. ‐ (T)ICM stands for the (team) intercentrality measures.
‐ Position is a dummy identifying field position of the player. ‐ Team is a dummy to identify the player’s national team.
‐ Club Rank and Nation Rank indicate the rank of the club and nation of the player i measured by UEFA points. • The above model is estimated by GLS.
MARKET VALUE AND INTERCENTRALITY
• Base regression model :
Log EMVi = α2 + β2 (T)ICMi + γ2 Agei + θ2 Agei 2 + λ2 Positioni + ψ2 Club Ranki + φ2 Nation Ranki + ε2
In the above regression model:
‐ subscript i represents player i. ‐ dependent variable is log of the estimated market value of players available from transfermarkt.de
‐ (T)ICM stands for the (team) intercentrality measures.
‐ Position is a dummy identifying field position of the player. ‐ Team is a dummy to identify the player’s national team.
‐ Club Rank and Nation Rank indicate the rank of the club and nation of the player i measured by UEFA points. .
REGRESSION RESULTS
• Note that the regression models use the (team) intercentrality measures which are calculated for specific parameters of a=0.125 and d=0.5. As a sensitivity check, we use the parameter sets as:
 a=0.1 and d={0.4, 0.5, 0.6}  a=0.125 and d={0.4, 0.6}
• One standard deviation increase in the intercentrality measure (ICM) creates on the average 9.84 percent increase in the market values of the players. • On the other hand, one standard deviation increase in TICM yields on the average 10.88 percent increase in the market values of the players.
CONCLUSION
• In this paper, we introduce a Team Game and develop a measure of identifying the key players and key groups in the teams. • Our work extends the intercentrality measure of Ballester et al.(2006) to contain an additional term. This additional term comes from the team outcome expression in the utility functions of players.
• The calculated team intercentrality measure (TICM) can be regarded as team performance index of players. The calculated group team intercentrality measure can be interpreted as the joint contribution of players to their teams.
CONCLUSION
• A key player does not need to have the highest amount of individual payoff. In addition, a key player does not need to have the highest amount of individual action (number of shots.)
• More importantly, the market value of the players increase with their intercentrality measure which is assumed to be reflected in their salaries. This effect is homogenous in the sample with respect to the field position of players. THANK YOU…