Volume 15, Issue 3

Existing methods for player evaluation in American football rely heavily on proprietary data, are often not reproducible, lag behind those of other major sports, and are not interpretable in terms of game outcomes. We present four contributions to the study of football statistics to address these issues. First, we develop the R package nflscrapR to provide easy access to publicly available play-by-play data from the National Football League (NFL). Second, we introduce a novel multinomial logistic regression approach for estimating the expected points for each play. Third, we use the expected points as input into a generalized additive model for estimating the win probability for each play. Fourth, we introduce our nflWAR framework, using multilevel models to isolate the contributions of individual offensive skill players in terms of their wins above replacement (WAR). We assess the uncertainty in WAR through a resampling approach specifically designed for football, and we present results for the 2017 NFL season. We discuss how our reproducible WAR framework can be extended to estimate WAR for players at any position if researchers have data specifying the players on the field during each play. Finally, we discuss the potential implications of this work for NFL teams.

We test for the existence of relative age effects in professional American football. In a sample of 18,898 football players born on or after 1940, there is an excess of January and February births – consistent with a relative age effect associated with calendar year – as well as a slight increase in September births – consistent with the fact that some football players we analyze attended high school in states with fall school cutoff dates. We consider the possibility that relative age effects may affect skilled football positions more than positions relying heavily on player weight, and we find suggestive evidence of this. Lastly, and contrary to what has recently been shown in professional hockey, we find no evidence that misguided preferences for relatively older players lead to selection-based inefficiencies in football player drafting. Our results have implications for evaluating potential football players and speak broadly to the role of physiological factors beyond player control on athletic success.

In this paper we conduct an equilibrium analysis of the 2015–2016 NBA record breaking season culminating in the dramatic final series upset produced by the Cleveland Cavaliers (CLE) over the Golden State Warriors (GSW). A Stackelberg equilibrium (Conitzer and Sandholm 2006) is constructed for each pair of NBA teams, as a pair of mixed offensive strategies defined over 2- and 3-point shot court locations. The first component corresponds to Team A’s offensive strategy playing against team B’s defense, and the second component is team B’s offensive strategy playing against team A’s defense. The results support the following insights. First, the results suggest that future NBA 3-point averages are headed higher to 37.9%, in contrast with current regular and playoff season averages for the 2015–2016 of 28.6% and 30.9%, respectively. Second, the results provide a means for evaluating the influence of an opposing team’s defense upon offensive strategy. Third, the results provide a strategic interpretation of the final NBA 2015–2016 playoff series where CLE upset GSW. GSW started close to their predicted strategy and then almost monotonically shifted further away whereas CLE moved closer to their predicted strategy. Realized outcomes correlate with these strategic trends.

In basketball, a point scored on offense carries a nearly identical on-court (win) value as a point denied on defense (e.g. within the Pythagorean expected wins model). Both outcomes bear the same score margin implication. As such, a win-maximizing team is expected to value the two outcomes equally. We ask whether the salaries of NBA players reveal such an equality among NBA teams. If not, a win-maximizing team would enjoy a disequilibrium arbitrage opportunity, whereby the team could improve, in expectation, even while reducing roster payroll. We considered the 322 National Basketball Association (NBA) players during the 2016–2017 season who were on a full-season contract for which the salary was not stipulated under the NBA Collective Bargaining Agreement. We estimated the implied marginal wage of an additional point created on offense (denied on defense) per 100 possessions. Namely, we constructed a set of fixed effects, ordinary least squares regression models that specify a player’s pre-assigned 2016–2017 player salary as a function of primary team fixed effects, offensive adjusted plus minus, defensive adjusted plus minus, position-of-play, and control variables such as age. We conclude that a win-maximizing NBA team currently faces a substantial arbitrage opportunity. Namely, one unit of offense carries the same estimated implicit salary as approximately two and a half to four units of defense. We also find moderate between-team variation in adjusted plus minus return on payroll allocations.

Game theory is the study of tractable games which may be used to model more complex systems. Board games, video games and sports, however, are intractable by design, so “ludological” theories about these games as complex phenomena should be grounded in empiricism. A first “ludometric” concern is the empirical measurement of the amount of luck in various games. We argue against a narrow view of luck which includes only factors outside any player’s control, and advocate for a holistic definition of luck as complementary to the variation in effective skill within a population of players. We introduce two metrics for luck in a game for a given population – one information theoretical, and one Bayesian, and discuss the estimation of these metrics using sparse, high-dimensional regression techniques. Finally, we apply these techniques to compare the amount of luck between various professional sports, between Chess and Go, and between two hobby board games: Race for the Galaxy and Seasons .

Many empirical studies on competitive balance (CB) use the ratio of the actual standard deviation to the idealized standard deviation of win percentages (RSD). This paper suggests that empirical studies that use RSD to compare CB among different leagues are invalid, but that RSD may be used for time-series analysis on CB in a league if there are no changes in season length. When schedules are unbalanced and/or include interleague games, the final winning percentage is a biased estimator of the true win probability. This paper takes a mathematical statistical approach to derive an unbiased estimator of within-season CB that can be applied to not only balanced but also unbalanced schedules. Simulations and empirical applications are also presented, which confirm that the debiasing strategy to obtain the unbiased estimator of within-season CB is still effective for unbalanced schedules.