Volume 2, Issue 3

All sports have components of randomness that cause the “best” individual or team not to win every game. According to many spectators this uncertainty is part of the charm when following a competition or a match. Have different sports more or less of this unpredictability? We suggest here a general measure, a tournament stability index, together with its associated p-value which we denote the "coin-tossing-index." These indexes are aimed to quantify the randomness factor for different tournaments, and different sports. As an illustration we exemplify and discuss these measures for basketball, squash, and soccer. Some additional results will also be given on a few tournaments in ice-hockey, and handball. Furthermore, we discuss a couple of combinatorial optimization questions that turned up on the way.

This paper considers a variance decomposition of offensive baseball performance. Estimating the variance components of offensive baseball performance allows one to determine how much of the variability in performance can be accounted for by differences among teams and how much of the variability lies at the level of individual differences within teams. In addition to variance components, this paper examines the reliability estimates of the true team means in offensive baseball performance. Using offensive baseball data from the 2000 season, and replicated again for 2003, intra-class correlations and parameter reliabilities are obtained under the correct probability model for the performance measure in question. The results show that most of the variability in offensive baseball performance lies at the individual level with only a small number of measures where a sizeable amount variance is accounted for by differences among teams. Changes in the variance components and parameter reliabilities are observed from 2000 to 2003. Team level predictors are added to demonstrate the flexibility of the modelling approach. The paper concludes with a summary of the findings and implications for examining the contextual effects in baseball.

This paper first presents a brief review of potential rating tools and methods for predicting success in the NCAA basketball tournament, including those methods (such as the Ratings Percentage Index, or RPI) that receive a great deal of weight in selecting and seeding teams for the tournament. The paper then proposes a simple and flexible rating method based on ordinal logistic regression and expectation (the OLRE method) that is designed to predict success for those teams selected to participate in the NCAA tournament. A simulation based on the parametric Bradley-Terry model for paired comparisons is used to demonstrate the ability of the computationally simple OLRE method to predict success in the tournament, using actual NCAA tournament data. Given that the proposed method can incorporate several different predictors of success in the NCAA tournament when calculating a rating, and has better predictive power than a model-based approach, it should be strongly considered as an alternative to other rating methods currently used to assign seeds and regions to the teams selected to play in the tournament.

This paper combines an estimated expected run value equation with a probability model on the outcome of batted balls to isolate the game within a game. Using linear regression we were then able to determine the percentage of the outcome of an at bat that is controlled by a pitcher and the percentage that is controlled by the batter.