Volume 5, Issue 3

The objective of this research is to provide a statistical measurement to predict the likely winners of international football tournaments with particular reference to the Euro 2008 football tournament. This research argues that there exists a positive relationship between the competitive balance and success in international football tournaments. The level of the competitive balance in a domestic football league is measured by the seasonal coefficients of variation (CV) of the end-of-season points. The CV values are employed as ranking indicators between the contesting countries in international football tournaments to predict the likely winners.The seasonal CV values are computed from the top division football leagues of participating countries of Euro 1996, Euro 2000, Euro 2004, and Euro 2008, in order to rank and to predict the likely winner of these tournaments. The results indicate that the higher the level of domestic competition the better chance of winning an international football tournament. The CV ranking is also compared to the UEFA ranking and to the odds of some well known bookmakers in predicting the likely winners of the Euro 2008 football tournament. On the basis of the overall results, this research predicts that the likely winners of the Euro 2008 football tournament would be France, Spain or Germany.

In football leagues, a won match produces three points (all for the winner) whereas a drawn match produces only two (one for each team). Here, the total resource from the viewpoint of league points is not constant and the gain of the match for both teams changes depending on the result of the match. To cater for this situation, we propose a formulation for modelling tactical changes of formation in an association football match as a non-zero-sum game using game theory. In this paper, we focus on two well-known teams in the J. League and analyse their offensive and defensive strengths based on their formation, i.e., a combination of the number of each type of outfield player on the pitch. Using these estimated offensive and defensive strengths, we develop the mathematical formulation for analyzing tactical changes of these teams' formations from the viewpoint to increase their expected number of league points gained in a match, and quantitatively demonstrate not only the effect of the introduction of the league point system on the tactical change, but also the effect of cooperation between managers which could make both teams benefit in terms of the expected number of league points gained in a match.

The issue of competitive balance is not normally considered in the study of home advantage. This paper focuses on home advantage, assessing and comparing it between seasons. The strength of the teams is estimated and linked with competitive balance. The results support that, in both the eighties and early nineties, the home advantage is more visible. After that, it tends to decrease. Meanwhile, competitive balance increases until the nineties and after that, the trend becomes unclear. The changes in the structure of the championship and the reward point system have affected the Portuguese league.

The following paper examines potential sources of bias in National Basketball Association (NBA) playoffs. Employing NBA playoff data from 2003 through 2008, we investigate the expected margin of victory by the favored team. This method, by incorporating potentially mitigating variables, can also be used to test for potential bias and manipulation in tournament results.We find that the regular season winning percentage, used as the method for seeding teams for the NBA playoffs, is a good predictor of post season play. In addition to regular season play, we find confirming evidence of the home court advantage hypothesis suggested by previous studies. However, the analysis does indicate potential bias in playoff results in favor of large market teams. A team from a larger market is expected to win by a larger margin in the case of being the better team (stronger seed) or lose by a smaller margin in the case of being the worse team (weaker seed). Bias is also detected which would indicate closer margins of victory in early playoff series games which increases the probability of a longer series. While financial motivation for playoff manipulation is discussed, the findings only suggest bias and do not indicate its source.

A control chart is developed specifically for monitoring batting performances in cricket. Issues associated with the need to retain extreme values and limited sampling opportunities are overcome by using a parametric approach to obtain theoretical quartiles from the distribution of individual batting scores. A mixed distribution, named the Ducks 'n' Runs distribution, is proposed. A beta distribution models zero scores (ducks) and a geometric distribution describes the distribution of non zero scores (runs). This suitability of this probability distribution model is demonstrated using data from New Zealand first class batsmen in domestic three day cricket over a four year period. Changes in the process (player performance) are detected using rules adapted from the supplementary rules for Shewhart control charts.

Extending the work of Connolly and Rendleman (2008), we document the dominance of Tiger Woods during the 1998-2001 PGA Tour seasons. We show that by playing 'average,' Woods could have won some tournaments and placed no worse than fourth in the tournaments in which he participated in the year 2000, his best on the PGA Tour. No other PGA Tour player in our sample could have come close to such a feat. We also are able to quantify the intimidation factor associated with playing with Woods. On average, players who were paired with Woods during the 1998-2001 period scored 0.462 strokes per round worse than normal. Although we find that Woods' presence in a tournament may have had a small, but statistically significant adverse impact on the entire field, this effect was swamped by the apparent intimidation factor associated with having to play with Tiger side-by-side.We also demonstrate that Phil Mickelson's performance in major golf championships over the 1998-2001 period was not nearly as bad as was frequently mentioned in the golf press. Although Mickelson won no majors during this period, he played sufficiently well to have won one or two majors under normal circumstances. Moreover, his overall performance in majors, relative to his estimated skill level, was comparable to that of Tiger Woods, who won five of 16 major golf championships during our four-year sample period. Thus, the general characterization of Woods as golf's dominant player over the 1998-2001 period was accurate, but the frequent characterization of Phil Mickelson choking in majors was not.

We develop a stochastic Markov chain model to obtain the probability density function (pdf) for a player to win a match in tennis. By analyzing both individual player and 'field' data (all players lumped together) obtained from the 2007 Men's Association of Tennis Professionals (ATP) circuit, we show that a player's probability of winning a point on serve and while receiving serve varies from match to match and can be modeled as Gaussian distributed random variables. Hence, our model uses four input parameters for each player. The first two are the sample means associated with each player's probability of winning a point on serve and while receiving serve. The third and fourth parameter for each player are the standard deviations around the mean, which measure a player's consistency from match to match and from one surface to another (e.g. grass, hard courts, clay). Based on these Gaussian distributed input variables, we use Monte Carlo simulations to determine the probability density functions for each of the players to win a match. By using input data for each of the players vs. the entire field, we describe the outcome of simulations based on head-to-head matches focusing on four top players currently on the men's ATP circuit. We also run full tournament simulations of the four Grand Slam events and gather statistics for each of these four player's frequency of winning each of the events and we describe how to use the results as the basis for ranking methods with natural probabilistic interpretations.

The NCAA Division I Men's Basketball Committee annually selects its national championship tournament's at-large invitees, and assigns seeds to all participants. As part of its deliberations, the Committee is provided a so-called "nitty-gritty report" for each team, containing numerous team performance statistics. Many elements of this report receive a great deal of attention by the media and fans as the tournament nears, including a team's Ratings Percentage Index (or RPI), overall record, conference record, non-conference record, strength of schedule, record in its last 10 games, etc. However, few previous studies have evaluated the degree to which these factors are related to whether a team actually wins games once the tournament begins. Using nitty-gritty information for the participants in the 638 tournament games during the 10 seasons from 1999 through 2008, we use stepwise binary logit regression to build a model that includes only eight of the 32 nitty-gritty factors we examined. We find that in some cases factors that receive a great deal of attention are not related to game results, at least in the presence of the more highly related set of factors included in the model.

In 1999, the International Volleyball Federation (IVF) changed the scoring system of volleyball, from the side-out scoring system to the rally scoring system. The main goal of the scoring system change was to make the length of the game more predictable. This short paper investigates whether the change achieved its goal. First, I use a simulation model of volleyball matches to demonstrate that the length of the matches is more predictable in the rally scoring system, regardless of the relative strength of the teams. Then, I analyze data on volleyball matches from the U.S. Women's Northern Sun Intercollegiate Conference, and compare the variance of the length of the matches before and after the scoring system change in 2000 and 2001. The empirical data shows that the length of the matches became more predictable. Also, with the help of the simulation model, I show that the scoring system change does not significantly affect the outcome of the matches.

This paper develops a robust, statistically significant, six independent variable multiple regression model that accounts for the relative success of English Premier League football clubs based on an array of twenty-four pitch actions collected during the 2007-2008 season (p<0.0000). Additionally, one-way ANOVA is used to identify those specific pitch actions that statistically separate the top 4 clubs from (1) the dozen clubs forming the middle of the pack and, (2) by a greater contrast, the bottom 4 clubs. Thirteen pitch actions yield statistically significant differences among these three tiers of clubs using this second method of analysis.