A Skellam Regression Model for Quantifying Positional Value in Soccer

TL;DR

This paper introduces an open, data-driven Skellam regression model to quantify individual player contributions in soccer, leveraging publicly available data to evaluate positional value and inform salary allocation.

Contribution

The paper develops a novel open framework using Skellam regression to estimate soccer players' contributions from publicly available data, addressing previous proprietary data limitations.

Findings

The model estimates the importance of different positional lines in winning games.

It translates contributions into expected league points above a replacement player (eLPAR).

Market undervalues defensive players relative to goalkeepers in the dataset.

Abstract

Soccer is undeniably the most popular sport world-wide and everyone from general managers and coaching staff to fans and media are interested in evaluating players' performance. Metrics applied successfully in other sports, such as the (adjusted) +/- that allows for division of credit among a basketball team's players, exhibit several challenges when applied to soccer due to severe co-linearities. Recently, a number of player evaluation metrics have been developed utilizing optical tracking data, but they are based on proprietary data. In this work, our objective is to develop an open framework that can estimate the expected contribution of a soccer player to his team's winning chances using publicly available data. In particular, using data from (i) approximately 20,000 games from 11 European leagues over 8 seasons, and, (ii) player ratings from the FIFA video game, we estimate through a Skellam regression model the importance of every line (attackers, midfielders, defenders and goalkeeping) in winning a soccer game. We consequently translate the model to expected league points added above a replacement player (eLPAR). This model can further be used as a guide for allocating a team's salary budget to players based on their expected contributions on the pitch. We showcase similar applications using annual salary data from the English Premier League and identify evidence that in our dataset the market appears to under-value defensive line players relative to goalkeepers.