Volume 4, Issue 1

Age effects in baseball are estimated in this paper using a nonlinear fixed-effects regression. The sample consists of all players who have played 10 or more "full-time" years in the major leagues between 1921 and 2004. Quadratic improvement is assumed up to a peak-performance age, which is estimated, and then quadratic decline after that, where the two quadratics need not be the same. Each player has his own constant term. The results show that aging effects are larger for pitchers than for batters and larger for baseball than for track and field, running, and swimming events and for chess. There is some evidence that decline rates in baseball have decreased slightly in the more recent period, but they are still generally larger than those for the other events. There are 18 batters out of the sample of 441 whose performances in the second half of their careers noticeably exceed what the model predicts they should have been. All but 3 of these players played from 1990 on. The estimates from the fixed-effects regressions can also be used to rank players. This ranking differs from the ranking using lifetime averages because it adjusts for the different ages at which players played. It is in effect an age-adjusted ranking.

We propose a Markov chain model of a best-of-7 game playoff series that involves game-to-game dependence on the current status of the series. To create a relatively parsimonious model, we seek to group transition probabilities of the Markov chain into clusters of similar game-winning frequency. To do so, we formulate a binary optimization problem to minimize several measures of cluster dissimilarity. We apply these techniques on Major League Baseball (MLB) data and test the goodness of fit to historical playoff outcomes. These state-dependent Markov models improve significantly on probability models based solely on home-away game dependence. It turns out that a better two-parameter model ignores where the games are played and instead focuses simply on, for each possible series status, whether or not the team with home-field advantage in the series has been the historical favorite - the more likely winner - in the next game of the series.

The streaky hitting patterns of all regular baseball players during the 2005 season are explored. Patterns of hits/outs, home runs and strikeouts are considered using different measures of streakiness. An adjustment method is proposed that helps in understanding the size of a streakiness measure given the player's ability and number of hitting opportunities. An exchangeable model is used to estimate the hitting abilities of all players and this model is used to understand the pattern of streakiness of all players in the 2005 season. This exchangeable model that assumes that all players are consistent with constant probabilities of success appears to explain much of the observed streaky behavior. But there are some players that appear to exhibit more streakiness than one would predict from the model.

In soccer, a scoreless draw is typically considered as an unwanted result that often jeopardizes the spectacle value of the game. In the present work, we tried to investigate a) how common scoreless draws are, and b) the relationship between scoreless draws and other indices of a football team's performance using machine learning techniques. Using data from 54 competitions around the world, Bayesian networks, least squares support vector machines and Hybrid Monte Carlo multi-layer perceptrons were used to investigate which combination of indices best predicts a team's season proportion of scoreless draws and to see exactly what predictions these indices make. There was ample variability in the proportion of scoreless draws, both when comparing individual teams and countries. For individual teams, the percentage scoreless draws varied between 0 and 30%. On average, nearly 9% of all games ended in 0-0. Not surprisingly, the most important parameter appeared to be the total number of goals per game. More interestingly, the earned points per game were also linked to the proportion of scoreless draws. Games of average and bad-to-average teams more often resulted in a scoreless draw, in particular when the games of these teams saw few goals. Such a team could end up having 20% scoreless draws in one season. A suggestive result that more spectators may be associated with less scoreless draws is also presented.