Volume 6, Issue 1

We propose two new measures for evaluating offensive ability of NBA players, using one-dimensional shooting data from three seasons beginning with the 2004-05 season. These measures improve upon currently employed shooting statistics by accounting for the varying shooting patterns of players over different distances from the basket. This variance also provides us with an intuitive metric for clustering players, wherein performance of players is calculated and compared to his cluster center as a baseline. To further improve the accuracy of our measures, we develop our own variation of smoothing and shrinkage, reducing any small sample biases and abnormalities.The first measure, SCAB or, Scoring Ability Above Baseline, measures a player's ability to score as a function of time on court. The second metric, SHTAB or Shooting Ability, calculates a player's propensity to score on a per-shot basis. Our results show that a combination of SCAB and SHTAB can be used to separate out players based on their offensive game. We observe that players who are highly ranked according to our measures are regularly considered as top performers on offense by experts, with the notable exception of LeBron James; the same claim holds for the offensive dregs. We suggest possible explanations for our findings and explore possibilities of future work with regard to player defense.

Despite the conventional wisdom of the existence of the “hot hand" in basketball, studies have found no or weak evidence for the hot hand in game situations, although stronger evidence in controlled settings. Almost all studies have tested for the hot hand in univariate frameworks, often with inadequate power. I use a sample based on all free throws during the 2005-06 NBA season. With a multivariate framework with individual fixed effects, I find evidence for the “hot hand" in that making the first free throw is associated with a significantly higher probability of making the second free throw.

Optimizing the performance of a basketball offense may be viewed as a network problem, wherein each play represents a “pathway" through which the ball and players may move from origin (the in-bounds pass) to goal (the basket). Effective field goal percentages from the resulting shot attempts can be used to characterize the efficiency of each pathway. Inspired by recent discussions of the “price of anarchy" in traffic networks, this paper makes a formal analogy between a basketball offense and a simplified traffic network. The analysis suggests that there may be a significant difference between taking the highest-percentage shot each time down the court and playing the most efficient possible game. There may also be an analogue of Braess's Paradox in basketball, such that removing a key player from a team can result in the improvement of the team's offensive efficiency.

We examine the role of attendance in home-field advantage for Major League Baseball, using a dataset of all MLB games played from 1996 to 2005. Using two-stage least squares, we find that attendance has a significant effect on the home-field advantage. Our results indicate that a one standard deviation increase in attendance results in a 4% increase in the likelihood of a home team win. We also find that if attendance as a percent of stadium capacity were to increase by 48%, we would expect the home team's run differential to increase by one run. We show that the additional home-field advantage is driven by increased home team performance.

Most professional golfers and analysts think that winning on the PGA Tour peaks when golfers are in their thirties. Rather than relying on educated guesses, we can actually use available statistical data to determine the actual ages at which golfers peak their golf game. We can also test the hypothesis that age affects winning professional golf tournaments. Using data from the web sites of the Golf Channel, the PGA Tour, the European PGA Tour, and the LPGA Tour, I calculated the mean, the median, and the mode ages at which professional golfers on the PGA, European PGA, Champions, and LPGA Tours had won between 2003 and 2007. More specifically, the ages at which golfers on the PGA, European PGA, Champions, and LPGA Tours peak their wins seem to be 35, 30, 52, and 25, respectively. The regression analysis I have conducted seems to support my hypothesis that age affects winning professional golf tournaments.

The NHL determines draft order from a lottery that favors teams that are lowest in the standings. Losing can help a franchise acquire a coveted prospect, which encourages fans to cheer against their favorite teams. Draft order based on mathematical elimination would force the teams that performed poorest into a highly competitive atmosphere. The teams that are eliminated earliest would instead have more games to earn the top picks. If substandard teams are to survive in mediocre markets, the injustice of incentives for losing must be eradicated.

Estimating the salaries of professional athletes has received a substantial amount of attention both in the press and in academic journals. A statistical technique that can be used to obtain an estimate of a player's salary with a given set of performance characteristics is the classical least squares regression analysis. This technique does not work well, however, if the data upon which the model is based contain outliers or are not normally distributed. In this paper we focus our attention on the salaries of American League baseball players in 2007 and demonstrate the usefulness of an alternative estimation approach – that of quantile regression analysis. Our results indicate that ordinary least squares regression overestimates the salaries of poor players, and underestimates the salaries of star players. This, we believe, is a compelling reason to apply quantile regression in the prediction of baseball player salaries.

Pythagorean win share has been one of the fundamental contributions to Sabermetrics. Several hundred articles, both academic and non-academic, have explored variations on Bill James' original formula and its fit to empirical data. This paper considers a variation that is previously unexplored on any systematic level, consistency. After discussing several important contributions to the line of literature, we demonstrate the strong correlation between Pythagorean residuals and several notions of run distribution consistency. Finally, we select the "correct" form of consistency and use it to construct a simple regression estimator, which improves RMSE by 11%.

The Opta Index is a prestigious performance measure used to assess English Premier League (EPL) football players. Although the Opta model is proprietary, the general structure uses a multiattribute collection of subjectively weighted pitch measures that either rewards or penalizes a player with a potential range of points based on the quality of his game performance. In addition, the specific set of measures used depends upon player position: forwards, midfielders, defenders, and goalkeepers each have their own unique set of measures even though there might be some overlap. Although the player's Opta Index is calculated for each game, it is the cumulative "grade card"—the final Opta Index calculated at the end of the thirty-eight game EPL season in May—that is of particular importance. The index, along with the large array of player pitch data, is commercially distributed to the EPL clubs and appears in a wide variety of television and print media outlets. This paper proposes an alternative to using the full set of Opta data by identifying those specific pitch actions that form a statistically significant retrodictive linear regression model for the 2007-2008 EPL season. Additionally, the importance of evaluating pitch actions historically assumed to be clearly pertinent measures—such as goals allowed per game for the goalkeeper—will be not only be appraised from a statistical viewpoint, but also from a practical perspective.