How good is Tiger Woods?

A major objective of professional sport is to find out which player or team is the best. Unfortunately the structure of some sports means that this is often a difficult question to answer. For example, there may be too many competitors to run a round-robin league, whilst knock-out tournaments do not compare every player with every other player. The problem gets worse when one has to compare players whose performance varies over time. Fortunately mathematical modelling can help and in this article, we use the Plackett-Luce model to estimate time-varying player strengths of golfers. We use the model to investigate how good golf's current biggest attraction, Tiger Woods, really is

On the development of a soccer player performance rating system for the English premier league

The EA Sports Player Performance Index is a rating system for soccer players used in the top two tiers of soccer in England—the Premier League and the Championship. Its development was a collaboration among professional soccer leagues, a news media association, and academia. In this paper, we describe the index and its construction. The novelty of the index lies in its attempts to rate all players using a single score, regardless of their playing specialty, based on player contributions to winning performances. As one might expect, players from leading teams lead the index, although surprises happen

Time-varying ratings for international football teams

We present a model for rating international football teams. Using data from 1944 to 2016, we ask `which was the greatest team?'. To answer the question requires some sophisticated methodology. Specifically, we have used k-fold cross-validation, which allows us to optimally down-weight the results of friendly matches in explaining World Cup results. In addition to the central aim of the paper, we also discuss, from a philosophical perspective, situations in which model over-fitting is perhaps desirable. Results suggest that Hungary in 1952, is a strong candidate for the all-time greatest international football team

Identifying key players in soccer teams using network analysis and pass difficulty

We use a unique dataset to identify the key members of a football team. The methodology uses a statistical model to determine the difficulty of a pass from one player to another, and combines this information with results from network analysis, to identify which players are pivotal to each team in the English Premier League during the 2012–13 season. We demonstrate the methodology by looking closely at one game, whilst also summarising player performance for each team over the entire season. The analysis is hoped to be of use to managers and coaches in identifying the best team lineup, and in the analysis of opposition teams to identify their key players

To lead or not to lead : analysis of the sprint in track cycling

This paper uses a statistical analysis of match sprint outcomes to guide tactical decisions in this highly tactical contest and to provide competitors and coaches with a potential, marginal gain. Logistic regression models are developed to predict the probability of the leading rider winning at different points of the race, based on how the race proceeds up to each point. Key tactics are successfully identified from the models, including how the leading rider might hold the lead and how the following rider might optimise overtaking

A bivariate Weibull count model for forecasting association football scores

The paper presents a model for forecasting association football scores. The model uses a Weibull inter-arrival-times-based count process and a copula to produce a bivariate distribution of the numbers of goals scored by the home and away teams in a match. We test it against a variety of alternatives, including the simpler Poisson distribution-based model and an independent version of our model. The out-of-sample performance of our methodology is illustrated using, first, calibration curves, then a Kelly-type betting strategy that is applied to the pre-match win/draw/loss market and to the over–under 2.5 goals market. The new model provides an improved fit to the data relative to previous models, and results in positive returns to betting

An analysis of country medal shares in individual sports at the Olympics

Research question: Several studies report modelling relating countries’ medal shares at the Olympics to population and per capita income (host status and political system are typically included as controls). This paper uses a similar model but disaggregates to the level of the individual sport to ask questions such as whether some sports have a less steep relationship with income levels than others and whether hosting effects are more pronounced in some sports than others. Research methods: Employing a random effects tobit model, data on medal shares are modelled across 15 sports at six editions of the Games (1992–2012). Marginal effects, calculated for the case of cycling, illustrate how far many poor countries are from reasonable expectation of achieving medals. Results and findings: Income is influential on outcomes in all sports, its effects most pronounced in sports with substantial requirements for specific capital equipment; the distribution of medals is less unequal in sports practised in multi-sports venues. Gains from hosting vary in magnitude, performance tending to be elevated most in sports with outcomes strongly influenced by judges. Implications: For poorer countries, the paper identifies a small group of sports on which it would be most realistic to focus resources. For Games organisers, who must decide which sports to include, it provides information relevant to the goal of spreading success more evenly across countries. For example, proposals to exclude wrestling are shown to have been potentially harmful to medal prospects of poorer countries

On outcome uncertainty and scoring rates in sport : the case of international rugby union

In this paper we investigate the relationship between outcome uncertainty and scoring rates in the framework of a “Poisson match”. We argue that increasing scoring rates in the hope of increasing entertainment may have a detrimental impact on the popularity of sport. The basis of our argument is that higher scoring-rates decrease outcome uncertainty. We use international rugby to demonstrate our findings and show that scoring rates have indeed increased significantly over the previous half-century in this sport. Therefore, administrators should recognise our general point and we suggest that rugby union administrators in particular ought to consider the introduction of new laws to reduce scoring-rates. Scenarios in which the scoring-rate is radically reduced are illustrated through a simulation of the Rugby World Cup tournament

Maintaining market position: Team performance, revenue and wage expenditure in the English Premier League

This paper investigates the relationship between playing success andcommercial success in team sports. Utilizing a data set relating to theEnglish Premier League that combines both financial measures andindicators of playing skills and performances, our empirical analysisis based on three behavioural equations. Our analysis indicates thaton-field success can be directly related to players’ skills and abilitiesand that revenue is positively related to on-field success. Wageexpenditure is also shown to systematically reflect player skills andperformances. One interpretation of this evidence is that investmentin players’ skills and ability buys on-field success, with richer teamsbecoming ever richer and able to maintain or even build upon successby spending more on players than less successful clubs. To the extentthat richer clubs are successful in their objective there is a causal linkbetween revenue earned and competitive imbalance via investmentsin players. The implications of this tendency within a league are discussed in our conclusion, which also considers the potentially wider implications of our study as they relate to the evolution of firmsize and issues of market share