Volume 12, Issue 2

Traditional NBA player evaluation metrics are based on scoring differential or some pace-adjusted linear combination of box score statistics like points, rebounds, assists, etc. These measures treat performances with the outcome of the game still in question (e.g. tie score with five minutes left) in exactly the same way as they treat performances with the outcome virtually decided (e.g. when one team leads by 30 points with one minute left). Because they ignore the context in which players perform, these measures can result in misleading estimates of how players help their teams win. We instead use a win probability framework for evaluating the impact NBA players have on their teams’ chances of winning. We propose a Bayesian linear regression model to estimate an individual player’s impact, after controlling for the other players on the court. We introduce several posterior summaries to derive rank-orderings of players within their team and across the league. This allows us to identify highly paid players with low impact relative to their teammates, as well as players whose high impact is not captured by existing metrics.

Standard measures of batting performance such as batting average and on-base percentage can be decomposed into component rates such as strikeout rates and home run rates. The likelihood of hitting data for a group of players can be expressed as a product of likelihoods of the component probabilities and this motivates the use of Bayesian random effects models to estimate the groups of component rates. By combining the separate component rates, the aggregate predictions of batting performance for subsequent seasons improve upon standard shrinkage methods. This “separate and aggregate” approach is also illustrated for estimating on-base probabilities and fielding independent pitching (FIP) abilities of pitchers.

This article describes a method for predicting the outcome of National Hockey League (NHL) games. We combine a model for goal scoring and yielding, and one for penalty commission, in a Markov-type computation and a simulation model that produce predicted probabilities of victory for each team. Where these differ substantially from the market probabilities, we make “bets” according to a simple strategy. Our return on investment is both positive and statistically significant.

This paper uses random-coefficient models and (a) finds rankings of who are the best formula 1 (F1) drivers of all time, conditional on team performance; (b) quantifies how much teams and drivers matter; and (c) quantifies how team and driver effects vary over time and under different racing conditions. The points scored by drivers in a race (standardised across seasons and Normalised) is used as the response variable in a cross-classified multilevel model that partitions variance into team, team-year and driver levels. These effects are then allowed to vary by year, track type and weather conditions using complex variance functions. Juan Manuel Fangio is found to be the greatest driver of all time. Team effects are shown to be more important than driver effects (and increasingly so over time), although their importance may be reduced in wet weather and on street tracks. A sensitivity analysis was undertaken with various forms of the dependent variable; this did not lead to substantively different conclusions. We argue that the approach can be applied more widely across the social sciences, to examine individual and team performance under changing conditions.