Volume 8, Issue 2

The following quote from Gregg Doyel in reference to the National Collegiate Athletic Association (NCAA) men’s basketball tournament appeared on CBSSports.com on March 21, 2009. “For teams with a realistic chance at winning multiple games in the NCAA tournament,…the worst seed to have is the No. 8 or the No. 9. That’s statistical certainty.” Is it really “statistical certainty”? This papers attempts to answer this question. Data concerning the number of games won by teams seeded 8, 9, 10, 11, and 12 were collected from the NCAA men’s and women’s tournament brackets dating back to 1985 and 1994, respectively. It was found that among all teams entering the tournament, the 10, 11, and 12 seeds do not appear to have a statistical advantage over the 8/9 seeds. However, if only teams that win their first game are considered, the 10 seeds have a significantly greater mean number of wins than the 8/9 seeds in the men’s tournament; and the 10, 11, and 12 seeds in the men’s tournament and the 11 seeds in the women’s tournament have advanced to the Sweet Sixteen (at least two wins) a significantly greater proportion of times than the 8/9 seeds.

This article investigates the influence of local market size on playing success in professional Spanish football. In order to examine this relationship, several regressions were run for linear, beta and fractional logit models, using various proxies of local market size as explanatory variables. The evidence emerging from our analysis suggests that the advantage of big-market teams results in substantial dominance by a very small group of clubs. Nevertheless, this advantage does not actually prevent teams that are located in areas with a small market size from having at least regular opportunities for success. Furthermore, the econometric modelling and the evidence obtained provide a rational basis for supporting the idea of promoting the creation of a cross-national league in Europe (the European Superleague).

Though athletics statistics are abundant, it is a difficult task to quantitatively compare performances from different events of track, field, and road running in a meaningful way. There are several commonly-used methods, but each has its limitations. Some methods, for example, are valid only for running events, or are unable to compare men's performances to women's, while others are based largely on world records and are thus unsuitable for comparing world records to one other. The most versatile and widely-used statistic is a set of scoring tables compiled by the IAAF, which are updated and published every few years. Unfortunately, these methods are not fully disclosed. In this paper, we propose a straight-forward, objective, model-based algorithm for assigning scores to athletic performances for the express purpose of comparing marks between different events. Specifically, the main score we propose is based on the expected number of athletes who perform better than a given mark within a calendar year. Computing this naturally interpretable statistic requires only a list of the top performances in each event and is not overly dependent on a small number of marks, such as the world records. We found that this statistic could predict the quality of future performances better than the IAAF scoring tables, and is thus better suited for comparing performances from different events. In addition, the probabilistic model used to generate the performance scores allows for multiple interpretations which can be adapted for various purposes, such as calculating the expected top mark in a given event or calculating the probability of a world record being broken within a certain time period. In this paper, we give the details of the model and the scores, a comparison with the IAAF scoring tables, and a demonstration of how we can calculate expectations of what might happen in the coming Olympic year. Our conclusion is that a probabilistic model such as the one presented here is a more informative and more versatile choice than the standard methods for comparing athletic performances.

We investigate the sensitivity of the Colley Matrix (CM) rankings---one of six computer rankings used by the Bowl Championship Series---to (hypothetical) changes in the outcomes of (actual) games. Specifically, we measure the shift in the rankings of the top 25 teams when the win-loss outcome of, say, a single game between two teams, each with winning percentages below 30%, is hypothetically switched. Using data from 2006--2011, we discover that the CM rankings are quite sensitive to such changes. To alleviate this sensitivity, we propose a robust variant of the rankings based on solving a mixed-integer nonlinear program, which requires about a minute of computation time. We then confirm empirically that our rankings are considerably more robust than the basic CM rankings. As far as we are aware, our study is the first explicit attempt to make football rankings robust. Furthermore, our methodology can be applied in other sports settings and can accommodate different concepts of robustness besides the specific one introduced here.

We study two important aspects of the home advantage for ice hockey. First we study team and season level data to uncover systematic variation in the home advantage across teams and over time. We find no systematic variation in home advantage across teams. Secondly, we use six seasons of game-level data to uncover sources of the home advantage. Our results show that additional rest for the home team has no impact on the win-loss probability. We find evidence that the home team’s rule advantage with regard to stick placement during face-offs helps to explain the home advantage, but that the home team’s rule advantage with regard to last line change opportunity does not. We find that the home advantage varies over the progression of the season, being the highest at the beginning and end of the season, and very small in the middle of the season. We also find that the home advantage is larger at the end of the season when the two teams are high in the standings. Some of these results are consistent with referee bias, but we are unable to show a causal relationship between referee bias and these results.

The NBA’s age eligibility rule is controversial. To examine the on-court efficacy of the NBA’s age eligibility rule, we test the effect of age of entry on NBA career performance. Our data set comprises the 332 players selected in the first round of the NBA draft from 1989 to 2000. Using censored normal regression models, we found that players drafted at a relatively younger age have more successful NBA careers across three different metrics. To explore a beneficial effect of one year in college, group selection bias tests were conducted by comparing differences in career success between “one and done” players and players who entered the NBA straight out of high school. The results were consistent with our main analyses – players who moved into the NBA directly from high school generally perform better than players with a single year of college experience. We find no systematic evidence in support of the on-court efficacy of the NBA’s age eligibility rule.

This paper uses conditional probability distributions to simulate batsman outcomes—that is, runs and dismissals—while a limited overs cricket match is in play. The research was motivated by the potential to assess, and reassess, the likelihood of a batsman achieving a certain score within a specified interval. These likelihoods were conditional on the batsman type, a linear combination of batsman order, strike rate and contribution to team runs, and the delivery number, both discrete variables. A Visual Basic program, SimScore, was written to simulate batsman scores from the probability distributions pertaining to the match stages of interest. The scores were then adjusted for team strength, innings and venue effects, using multiple regression. The paper demonstrates the benefits of the model by fitting log-normal distributions to simulated innings (n=500) by Australia’s Ricky Ponting in the 2011 cricket World Cup quarter final. The distributions allowed us to approximate how likely he was to achieve a certain score prior to the match and at 10-, 20- and 30-over stages. It is anticipated that real-time information of a batsman's score expectations will add confidence to wagering in individual performance markets—such as “highest individual score”—as well as making possible in-play player rating revisions.

A baseball team's offensive prowess is a function of two types of abilities: batting and baserunning. While each has been studied extensively in isolation, the effects of their interaction is not well understood. We model offensive output as a scalar function f of an individual player's batting and baserunning profile z. Each of these profiles is in turn estimated from Retrosheet data using heirarchical Bayesian models. We then use the SimulOutCome simulation engine as a method to generate values of f(z) over a fine grid of points. Finally, for each of several methods of taking the extra base, we graphically depict the surface f(z) over changes in the probability of advancing via that method. This framework allows us to draw conclusions both about optimal baserunning strategies in general, and about how particular offensive profiles affect a player's optimal baserunning strategy. We present many informative visualizations and analyze specific aspects of several well-known Major League players.