Volume 21, Issue 1

This paper presents a new framework for player valuation in European football, by fusing principles from financial mathematics and network theory. The valuation model leverages a “passing matrix” to encapsulate player interactions on the field, utilizing centrality measures to quantify individual influence. Unlike traditional approaches, such as regressing on past performance-salary data, this model focuses on in-game performance as a player’s contributions evolve over time. Consequently, our model provides a dynamic and individualized framework for ascertaining a player’s fair market value. The methodology is empirically validated through a case study in European football, employing real-world match and financial data. This cross-disciplinary mechanism for player valuation adapts the effect of connecting pay with performance, first seen in Scully ((1974). Pay and performance in major league baseball. Am. Econ. Rev. 64: 915–930), to include in-game contributions as well as expected present valuation of stochastic variables.

This paper proposes novel approaches to measuring team productivity and evaluating trading efficiency in Major League Baseball (MLB) from 1995 to 2021 through an application of portfolio theory. The performance of individual players is measured using a structural approach relating player outcomes to team runs developed by Lindsey (1963. An investigation of strategies in baseball. Oper. Res. 11: 477–501). Using a portfolio theory framework, we treat MLB teams as a portfolio of players (assets), each of which can be defined by an expected contribution of runs per game and the variance of this measure. It is found that both the expected value and variance have a positive impact on team runs scored. Given our definition of teams characterized by their expected values and variances, we evaluate trading efficiency between teams given their pre-trade expected values and variances and the acquired player’s pre-trade expected value and variance. We find that trade efficiency has improved over our timeframe, consistent with the growth in data-driven decision making used in MLB front offices.

While the use of expected goals (xG) as a metric for assessing soccer performance is increasingly prevalent, the uncertainty associated with their estimates is often overlooked. This work bridges this gap by providing easy-to-implement methods for uncertainty quantification in xG estimates derived from Bayesian models. Based on a convenient posterior approximation, we devise an online prior-to-posterior update scheme, aligning with the typical in-season model training in soccer. Additionally, we present a novel framework to assess and compare the performance dynamics of two teams during a match, while accounting for evolving match scores. Our approach is well-suited for graphical representation and improves interpretability. We validate the accuracy of our methods through simulations, and provide a real-world illustration using data from the Italian Serie A league.

Count data play a crucial role in sports analytics, providing valuable insights into various aspects of the game. Models that accurately capture the characteristics of count data are essential for making reliable inferences. In this paper, we propose the use of the Conway–Maxwell–Poisson (CMP) model for analyzing count data in sports. The CMP model offers flexibility in modeling data with different levels of dispersion. Here we consider a bivariate CMP model that models the potential correlation between home and away scores by incorporating a random effect specification. We illustrate the advantages of the CMP model through simulations. We then analyze data from baseball and soccer games before, during, and after the COVID-19 pandemic. The performance of our proposed CMP model matches or outperforms standard Poisson and Negative Binomial models, providing a good fit and an accurate estimation of the observed effects in count data with any level of dispersion. The results highlight the robustness and flexibility of the CMP model in analyzing count data in sports, making it a suitable default choice for modeling a diverse range of count data types in sports, where the data dispersion may vary.

Identifying success factors in football is of sporting and economic interest. However, research in this field for national teams and their competitions is rare despite the popularity of teams and events. Therefore, we analyze data for the UEFA EURO 2020 and, for comparison purposes, the previous tournament in 2016. To mitigate the challenges of perceived multicollinearity and a small sample size, and to identify the relevant variables, we apply the ‘LASSO Cross-fitted Stability-Selection’ algorithm. This approach involves iterative splitting of data, with variables chosen via a ‘least absolute shrinkage and selection operator’ (LASSO) model (Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Stat. Soc. B 58: 267–288) on one half of the observations, while coefficients are estimated on the other half. Subsequently, we inspect the frequency of selection and stability of coefficient estimation for each variable over the repeated samples to identify factors as relevant. By that, we are able to differentiate generally valid success factors such as the market value ratio from on-field variables whose importance is tournament-dependent, e.g. the tackles attempted. As the latter is connected to a team’s tactics, we conclude that their observed relevance is correlated to the results of the linked playing style in the specific tournaments. We also show the changing effect of these playing-styles on success across tournaments.