Journal of Sports Analytics 5 (2019) 23–34 23 DOI 10.3233/JSA-170235 IOS Press Modelling the financial contribution of soccer players to their clubs Olav Drivenes Sæbøa and Lars Magnus Hvattumb,∗ aDepartment of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Norway bFaculty of Logistics, Molde University College, Norway Abstract. This paper presents a framework for evaluating the financial consequences of player transfers as seen from a club’s perspective. To this end, an objective player rating model is designed based on players’ contribution towards creating a positive goals differential for their team. A regression model is then applied to predict match outcomes as a function of the players involved in a match. Finally, Monte Carlo simulation is used to predict the final league standings and the financial gains obtained as a function of sporting success. The framework is illustrated on player transfers from the 2014-2015 English Premier League season. Keywords: association, football, rating, simulation, regression 1. Introduction North American sports such as baseball or American football remain closed competitions with exclusive Soccer, or association football, is one of the largest franchise rights, they remain more profitable than sports in the world. The last two decades have seen European sports leagues practising promotion and the revenues of leading European association foot- relegation. Salary caps, player drafts, and roster lim- ball clubs rising steadily, with broadcasting windfalls its are restrictions that remain almost exclusive to in particular soaring (Dobson and Goddard, 2001). North American sports (Sloane, 2015). Meanwhile, While revenues soar, it appears that owners of Euro- in European soccer, while limits on squad size are pean soccer clubs are in general not seeking to also coming into effect in several competitions, play- maximize profits; many clubs’ losses and debts are ers are still routinely traded as part of big-money deals shown to be quite severe, while dividends are seldom negotiated by clubs with typically very little interfer- paid out. Sloane (1971) presents alternative objec- ence. American sports and their clubs are therefore tives such as maximising supporter attendances or seen as more receptive of the idea of profit max- sporting success, while the clubs’ financial security imisation and economic rationality (Sloane, 2015). must be maintained. However, with an increased competitive balance, Assuming maximisation of wins rather than resulting from a more even income through broadcast profit, competitive balance in league competition is revenue, English soccer clubs may get a competi- strengthened by increased sharing of central revenue tive advantage from using better tools to assess the (Sloane, 2015). In 2007, the top five clubs in Eng- economic consequences of player trades. land and Spain received about half and two thirds of This paper presents a framework for evaluat- all broadcast revenue, respectively (Vrooman, 2007). ing player transfers in European soccer leagues, Szymanski and Zimbalist (2005) comment that while using illustrative examples from the English Premier ∗ League. Gerrard (2014) discussed two types of player Corresponding author: Lars Magnus Hvattum, Molde Univer- valuation in soccer. First, comparative valuation is sity College, P.O. Box 2110, N-6402 Molde, Norway. Tel.: +47 71 21 42 23; E-mail: [email protected]. based on using observable market values from recent 2215-020X/19/$35.00 © 2019 – IOS Press and the authors. All rights reserved This article is published online with Open Access and distributed under the terms of the Creative Commons Attribution Non-Commercial License (CC BY-NC 4.0). 24 O.D. Sæbø and L.M. Hvattum / Modelling the financial contribution of soccer players to their clubs transactions to form an anchor that is then adjusted The first contribution of this paper is to present a based on the particular player evaluated. For soccer, coherent framework for valuing players in the con- this has been explored using multiple linear regres- text of specific clubs, so that clubs can evaluate player sion. Frick (2007) summarized early work, which transfers based on their own performance and needs uses ordinary least squares regression to find vari- rather than relying on market mechanisms to price ables that describe observed transfer fees. Typical players. That is, we show that fundamental valua- significant independent variables include age, inter- tion of players is possible in the dynamic and fluid national caps, career games played, goals scored, sport of soccer. As a second contribution, we present and attributes of the buying and selling clubs. More an improved top-down player rating system to assess recently, Sæbø and Hvattum (2015) found that a sim- the contribution of single players to the performance ple, objective player rating can explain a large portion of a team as a whole. Third, we present an extensive of the variance in observed transfer fees, with addi- computational study, including calculations for sev- tional significant factors including age, nationality, eral cases of transfers to clubs in the English Premier international caps, and the remaining contract time. League for the 2014-2015 season. Ruijg and van Ophem (2015) presented an estimation In the next section we describe the proposed frame- method to correct for sample selectivity, finding that work for evaluating player transfers from a club the most important determinants for making a good perspective. The framework is based on the pres- transfer are age, average number of minutes played, ence of objective player ratings, which can be used as and not being a goal keeper. input to model match outcome probabilities, which in Herm et al. (2014) examined the ability of an online turn are used in simulation of relevant competitions. community to assess players’ market values. A real Then, the framework is used to illustrate several trans- option pricing framework for valuating players was fers involving clubs in the English Premier League, derived by Tunaru et al. (2005) and later used in estimating the economic consequences for the clubs (Tunaru and Viney, 2010), highlighting that there is a involved. Concluding remarks are provided in the last difference in the value of a soccer player for their cur- section of the paper. rent club and for potential new clubs. The valuation framework is based on an analysis firm’s performance rating system for individual players, the Opta Index, 2. Evaluation framework with each player’s performance rating acting as the underlying asset in option price modelling. While the The following presents a framework to estimate proposed valuation system does look at players’ value the influence a single player has on the sporting per- as a function of their performance, it does not consider formance of a club. Assuming that the economic club performances and direct player contributions to performance is related to the sporting performance, such. No definitions of relevant player contributions the framework can indicate how much a club should to results are offered, the Opta Index being assumed be willing to spend to secure the services of the as a sufficient measure of player quality instead. given player. The framework has three components: The second type of valuation discussed by Gerrard 1) an evaluation of each player in terms of how (2014) is fundamental valuation, which involves cal- they contribute to sporting success, 2) a prediction culating the net benefits that the holder of an asset of outcomes of future matches based on the players can expect to obtain. Regarding soccer players, this involved, and 3) a prediction of competition results includes merit payments obtained through sporting based on the ability to predict matches based on performance and revenues based on a players image player evaluations. Limitations of the framework are value. Pioneering work was done by Scully (1974) discussed in the concluding remarks of the paper. in the context of baseball: a team revenue equation based on player performance statistics fed into a team 2.1. Player ratings performance function to determine players marginal revenue contribution. Gerrard (2014) argues that it The first building block of the framework consists may be difficult to use a similar scheme for soccer, as of evaluating the active soccer players. While there baseball is a simple atomistic sport with a high degree has been some work on methods for rating and rank- of separability in player contributions, whereas soc- ing soccer teams (Constantinou and Fenton., 2013; cer is a complex sport with a hierarchical dependence Hvattum and Arntzen, 2010; Lasek et al., 2013), of player actions. the evaluation of players has received much less O.D. Sæbø and L.M. Hvattum / Modelling the financial contribution of soccer players to their clubs 25 attention. Sæbø and Hvattum (2015) proposed a plus-minus ratings for players with little playing time top-down rating model for soccer players, using a recorded are prone to large errors (Macdonald, 2011; regression model capturing the performance of play- Winston, 2009). Ridge regression, or Tikhonov reg- ers relative to their team mates and the opposition. ularisation, was proposed by Macdonald (2012) to The model was based on similar models, referred to reduce these errors. Rather than using ordinary least as adjusted plus-minus ratings, from basketball (Win- squares regression, ridge regression adds a penalty ston, 2009) and ice hockey (Macdonald, 2011, 2012). term, λβT β, to the target function, thereby preventing McHale et al. (2012) describe a rating for soccer play- values that differ strongly from 0. ers based on six subindices, the first of which uses a The regularized adjusted plus-minus rating pro- bottom-up approach to estimate the contribution of posed by Sæbø and Hvattum (2015) includes the players to match outcomes, whereas the other five following modifications: First, the duration in min- are based on the number of minutes played (in two utes, Di, of different segments may vary significantly.