Volume 2, Issue 1

This article presents a method to measure the impact of the home field advantage for intra-conference college football. The method models longitudinal data across several years while utilizing a unique home field parameter for each individual team. Additionally, two novel yet intuitive measures of home field advantage are proposed. As a case study of the method and the definitions of home field advantage, teams with the best and worst home field advantages within their respective conferences are determined.

Many count statistics are used to evaluate pitchers such as the number of wins and losses, the number of strikeouts, the number of walks, and the number of runs allowed. For a given measure such as strikeouts, this paper focuses on the estimation of pitchers’ probabilities of striking out a batter. The variation in the season strikeout rates among a group of pitchers is due to differences in the pitchers’ probabilities and also due to chance binomial variation. Among all the various rates, we find that a strikeout rate is one of the most accurate estimates of the corresponding probability of a pitcher performing the associated task. We examine the distribution of strikeout, walk and runs-prevented “true” rates of pitchers across the years. By use of our model, we are able to judge the magnitude of a great strikeout season. A z-score statistic is used to rank the greatest strikeout seasons of baseball history and this ranking is contrasted with other traditional ways of ranking pitchers.

The Ironman triathlon was created in 1978 by combining events with the longest distances for races then contested in Hawaii in swimming, cycling, and running. The Half Ironman triathlon was formed using half the distances of each of the events in the Ironman. The Olympic distance triathlon was created by combining events with the longest distances for races sanctioned by the major federations for swimming, cycling, and running. The relative importance of each event in overall race outcome was not given consideration when determining the distances of each of the races in modern triathlons. Thus, there is a general belief among triathletes that the swimming portion of the standard-distance triathlons is underweighted. We present a nonlinear Bayesian model for triathlon finishing times that models time and standard deviation of time as a function of distance. We use this model to create “fair” triathlons by equating the standard deviations of the times taken to complete the swimming, cycling, and running events. Thus, in these “fair” triathlons, a one standard deviation improvement in any event has an equivalent impact on overall race time. We conclude that a ratio of roughly 1:4:17 for swim distance to run distance to bike distance generates appropriate distances for a "fair" triathlon. So, for example, the Olympic triathlon swim distance should be increased from 1.5 km to 2.5 km to more fairly value each discipline in the race.

We analyze the number of games played in a seven-game playoff series under various home-away sequences. In doing so, we employ a simple Bernoulli model of home-field advantage in which the outcome of each game in the series depends only on whether it is played at home or away with respect to a designated home team. Considering all such sequences that begin and end at home, we show that, in terms of the number of games played, there are four classes of stochastically different formats, including the popular 2-3 and 2-2 formats both currently used in National Basketball Association (NBA) playoffs. Characterizing the regions in parametric space that give rise to distinct stochastic and expected value orderings of series length among these four format classes, we then investigate where in this parametric space that teams actually play. An extensive analysis of historical 7-game playoff series data from the NBA reveals that this home-away model is preferable to the simpler, well-studied but ill-fitting binomial model that ignores home-field advantage. The model suggests that switching from the 2-2 series format used for most of the playoffs to the 2-3 format that has been used in the NBA Finals since a switch in 1985 would stochastically lengthen these playoff series, creating an expectation of approximately one extra game per playoff season. Such evidence should encourage television sponsors to lobby for a change of playoff format in order to garner additional television advertising revenues while reducing team and media travel costs.

I create a state space within the game of ice hockey by noting which team has possession, and in what location of the rink the puck is located. This space is used to model the game as a semi-Markov process, as data from a series of games in 2004-2005 NCAA play suggest that the system cannot be modeled as a continuous time Markov process. The model is then used to determine the average number of goals scored by a team as a function of the starting state. These scoring probabilities are used to demonstrate the effectiveness of several commonly used tactics.

The Bowl Championship Series is designed to match the two top teams in college football in a title game. To determine the top ranked teams, polls are combined with a number of quantitative ratings of the teams known collectively as the “computer ranking”. The computer ranking serves primarily to offer a validation of the polls. The individuals whose quantitative ratings are used in the computer ranking have never been given a clear objective to design their ratings for and they are limited in the inputs that they can use (for example, they can not use score or site of game). For all of these reasons, I am advocating a boycott of the Bowl Championship Series by all quantitative analysts.