Volume 6, Issue 3

Home advantage was evaluated using data from three national netball competitions: The Commonwealth Bank Trophy which ran from 1997 to 2007 in Australia, The National Bank Cup which ran from 1998 to 2007 in New Zealand, and The Co-operative Netball Superleague which ran from 2005/06 to 2008/09 in England. Mixed models were used to analyze the goal advantage in playing at home, and both resampling methods and mixed models were used to analyze the probability of winning at home. In Australia there was a significant overall goal advantage in playing at home of 1.9 goals, 95% CI (1.0, 2.7). This value is small compared to the average score for a home team of 53 goals per game. Only in 1997 and 2006 were significant goal advantages evident, both of value 3.3 goals, 95% CI's (0.5, 6.1) and (0.6, 6.0) respectively. In the Australian competition, across all years, there was a significantly higher probability of winning at home, p = 0.54, 95% CI (0.51, 0.56). For New Zealand and England there was neither a significant home goal advantage nor home win advantage. These are unexpected results as netball is derived from basketball which has been shown to have a large home win advantage.

In the National Basketball Association (NBA), there are high expectations for the post-season among the teams having the league's best regular season records. However, not every team who plays great basketball in the regular season will succeed in the playoffs. The Phoenix Suns, for example, had the third best regular season record from the 2004–05 through 2006–07 seasons; however, not once did they reach the NBA Finals during those years. We hypothesized that how teams win games in the NBA differs between the regular season and the playoffs. This paper discusses the relative importance of performance factors in winning basketball games in the past 10 years of the NBA (between the 1999–2000 and 2008–2009 seasons). Specifically, we examined the contributions of overall efficiency (offensive and defensive ratings), along with the Four Factors (effective field goal percentage, turnover percentage, rebound percentage, and free throw rate) to winning games in the regular season and the playoffs, using a multiple linear regression and a logistic regression analysis. The results of these analyses indicate that efficient offense and defense are both essential to be successful in the regular season and the playoffs, but the importance of defense in winning games may be greater in the playoffs than in the regular season. Shooting efficiency on both ends of the floor (offensive and defensive effective field goal percentages) seems to be the most critical aspect of the game in the regular season as well as the playoffs. In addition, committing fewer turnovers could be another key to winning games, especially in the regular season. It appears that defense becomes more important for winning playoff series as a team advances further in the post-season. Lastly, rebounding may play a significant role in deciding the outcome of the Conference Finals where two teams most likely have similar shooting efficiency and turnover rates.

Two related studies compared the consistency of two different methods of interpreting and applying scoring criteria in Muay Thai that are normally used by officials in the UK and that are used by officials in Thailand. In the first study, levels of consistency were determined by comparing judge's scores (n=270) from forty-five bouts judged by UK officials and forty-five judged by Thai officials. In the second study the original forty-five bouts judged by UK judges were compared with forty–five bouts judged by UK officials using Thai judging criteria. Consistency was examined in both studies using two methods. The first method compared differences in the range of the highest vs. lowest points awarded by judges for each bout. The second method compared homogeneity of variance between judges' scores. Results suggested that the Thai officials were more consistent than their UK trained counterparts but also that UK judges were more consistent when adopting the Thai judging criteria. It was suggested that the use of very clearly defined criteria and concrete operationalization of otherwise subjective concepts used in applying the system used in Thailand was the main reason for the findings.

The LRMC method for predicting NCAA Tournament results from regular-season game outcomes is a two-part process consisting of a logistic regression model to estimate head-to-head differences in team strength, followed by a Markov chain model to combine those differences into an overall ranking. We consider replacing each of the two parts of LRMC with alternative models, empirical Bayes and ordinary least squares, that attempt to accomplish the same goal. Computational results show that replacing the logistic regression with either of two empirical Bayes models yields a statistically-significant improvement when the probabilities are jointly conditioned.

The 2007 Cooper River Bridge Run (CRBR) dataset has over 28,000 observations. The histogram of finishing times has a bimodal shape and varies in location and scale with the participants' gender and age. Four different mixture models are developed and assessed in terms of their ability to describe the features of this dataset. We discuss the "label switching" problem in the present context, review current solutions, and how they may be inadequate when covariates are present. The Bayes factor and the more modern deviance information criterion (DIC) are compared as devices for model selection. MCMC output is presented with plots of the model fits. We conclude with remarks on unanswered questions with regard to Bayesian mixture modeling, and the potential impact of this analysis for future Cooper River Bridge Runs. Raw data and BUGS programs corresponding to each model are available.

A previous article (Trono, 2005) documented how two different rating systems "outperformed" the Las Vegas betting line on NCAA bowl games when they individually disagreed with the line on which team should be favored. This article addresses several shortcomings in one of the two aforementioned systems, extends the analysis in a few new directions for both systems, adds the five most recent years of bowl games to this investigation, and includes one more recently published ranking system in this extensive study that goes back to 1983.

Classification method in a team chess championship has long been an issue of great concern. In quest of the “golden standard," Chess Federation officials applied many different ranking methods. As part of the “improvements," significant changes were introduced at the 2009 Serbia Team Chess Championship. In this paper, we will examine results of the 2008 and 2009 tournament by applying the statistical ranking method. Our aim was to compare classification in these two tournaments and for the first time quantitatively evaluate the rankings method in team chess championships. Some significant results were obtained during the process and we see them useful for the quality evaluation procedure of the classification methods. The correlation between 2008 Serbia Team Chess Championship ranking and the ranking based on the I-distance method was very significant with r=0.9639 and p<0.001. On the other hand, in the 2009 Championship our results clearly showed that the proposed “soccer ranking method" is inadequate for chess competitions. We propose the I-distance method of ranking as a possibility of rankings improvement and achievement of impartial results by any team.

A plethora of statistics have been proposed to measure the effectiveness of pitchers in Major League Baseball. While many of these are quite traditional (e.g., ERA, wins), some have gained currency only recently (e.g., WHIP, K/BB). Some of these metrics may have predictive power, but it is unclear which are the most reliable or consistent. We address this question by constructing a Bayesian random effects model that incorporates a point mass mixture and fitting it to data on twenty metrics spanning approximately 2,500 players and 35 years. Our model identifies FIP, HR/9, ERA, and BB/9 as the highest signal metrics for starters and GB%, FB%, and K/9 as the highest signal metrics for relievers. In general, the metrics identified by our model are independent of team defense. Our procedure also provides a relative ranking of metrics separately by starters and relievers and shows that these rankings differ quite substantially between them. Our methodology is compared to a Lasso-based procedure and is internally validated by detailed case studies.

In recent years predictions of athletic records have acquired a special significance in the scientific community. This article presents a method for calculation of probabilities of future records through modeling the tail of the distribution for performance measures. It utilizes an estimation method based on ideas from classical extreme-value theory that avoids difficulties associated with the maximum likelihood estimation. To improve the predictions, whenever possible, it utilizes information such as the survival time of the latest record and the time interval between the last two records. The article also presents alternative prediction methods based on order statistics and the theory of records, and includes a method for prediction of ultimate records. Application of tail modeling to men's long jump produces reasonable results. For long jump the last two records 8.95 meters and 8.90 meters are significantly greater than the third best record, 8.35 meters, which indicates a medium or long tail model. Data for 100 and 200 meter runs exhibit a similar characteristic as the present records for these events, 9.58 seconds and 19.19 seconds respectively, are significantly lower than the previous records. Application to the men's 100 meter data for the period starting January 1, 1977, when IAAF required fully automatic timing, to September 1, 2009 shows that the probabilities of setting a new record such as 9.55 seconds or less or 9.5 seconds or less are respectively:A. 0.0102 and 0.0052, when Bolt's three records are included.B. 0.0043 and 0.0023, when Bolt's three records are excluded.Also, excluding Bolt's records the probability of setting a record of 9.58 seconds or less by other runners is only 0.0064. Application of the method to Bolt's individual performance prior to the 2008 Olympics reveals the following:A. For him, the probability of running the 200 meter in the 19.30 seconds or less was only 0.00257, indicating that his Olympic record, 19.30 seconds, was completely unexpected.B. The probability of breaking his own best record, 19.75 seconds, was only 0.0738, indicating that his Olympic performance was exceptional.Also, application of the method to his individual performance including his 2008 Olympic record reveals that his new record 19.19 seconds was even more astonishing.Application of the method for estimation of ultimate record produces the following 90% prediction intervals:A. (9.40, 9.58) when Bolt's three records are included,B. (9.62, 9.71) when Bolt's three records are excluded.Note that Bolt's last record 9.58, falls outside the interval B. This demonstrates that Bolt is in a different league.

This work extends the work of Coleman (2005) which provides a football rankings system that minimizes game score violations. The modified model, called AccuV, developed in this paper incorporates several other aspects of most rankings systems including: strength of schedule, margin of victory, and home field advantage. These other components of a team's rank are included via an additional variable called the composite index. In addition to these new components, other bounding constraints have been added. These new constraints significantly reduce the solve-time of the model. The model of (Coleman, 2005) achieved a minimum of 55 game score violations for the complete 2002 season in about 36 seconds with 234,313 iterations as reported by LINGO. However, with the addition of the new constraints, the new model (without the additional ranking components) established the same minimum in only 6 seconds with a total of 55,119 iterations. This work is also easily extendable to allow the addition of other components if desired.

The aim of this study was to establish the reliability and validity of a coding system for measuring serve and return of serve locations in tennis. A notational analysis of men’s and women’s singles matches at the 2008 Australian Open was undertaken. The results revealed that the inter-rater reports were highly similar on first or second serve (r=0.972), serve landing location (r=0.999), returner’s impact location (r=0.990) and return of serve landing location (r=0.995). Hawk-Eye data were used to validate the coding measures for ball location. When comparing the coded ball location data of the researcher (n=1) and tennis coaches (n=4) to Hawk-Eye data, high correlations for the landing location of the serve (r=0.998), the impact location of the return (r=0.993) and the landing location of the return of serve (r=0.997) were registered. The match notation system analysed was shown to be reliable and valid for the study of serve and return of serve strategies and tactics in tennis. This system also provides a template for other researchers and coaches to evaluate game tactics in tennis.

We consider the problem of estimating a Major League Baseball player’s batting average in the second half of a season based on his performance in the first half. We fit two linear regression models to players’ averages from each half of the 2004 season, use these models to predict batting averages in the latter half of 2005 and compare the results to those achieved by three Bayesian estimators considered by Brown (2008). The linear models consistently outperform the Bayesian estimators in terms of four measures of error. Since the regression models use data from 2004 as well as 2005, while Brown’s estimators were based strictly on 2005 data, we also compare the performance of the linear models to that of the Bayesian estimators when the Bayesian estimators are based on the same amount of data. We find the linear models to be superior in this case as well. As a further test, we use the same methods to predict on-base percentages in the last half of the 2005 season, and we find that the linear models again do a better job. While we change the question proposed in Brown’s original paper, our results are a valuable reminder of the power of linear regression.

Dressage is an Olympic equestrian discipline with rules governed by The Fédération Equestre Internationale (FEI). After questions arose regarding dressage scoring during the 2008 Olympics, the FEI undertook studies of dressage scoring at international equestrian competitions in Europe. These studies included investigations of scoring scales and judging bias. Based on those results, the FEI recommended the use of statistics to improve the consistency of judge training in dressage competition. The authors performed a statistical analysis of dressage scores earned by riders in the United States. This work demonstrates the lack of consistency in judging in the United States. This is the first published study that looks at U.S. dressage results. It includes a very large data set considered representative of the population of riders in the U.S. Dressage is a subjectively judged sport. The final score, not the class placing, is of greatest importance when assessing rider results. The authors show how mainstream statistical tools can identify factors impacting the final dressage score. Analysis of Variance (ANOVA) was used to demonstrate the existence of key variables which impact scores. The analysis shows there are variations in scoring patterns by horse breed, as well as the existence of high-scoring and low-scoring judges. Finally, the analysis shows that there are increased standard deviations at the "extremes" of the judging scale. This would indicate there is variability in interpretation of scoring at the upper and lower ends of the scoring scale. Analysis of Means (ANOM) identified five judges whose scores were statistically different than the grand average scores.

The assessment of batsmen in cricket is largely based upon their average score: a Test average of 50 or over provides a rule-of-thumb for distinguishing great players from the merely good; Donald Bradman, with the highest Test average ever achieved (99.94), is generally regarded as the greatest of all batsmen even though many of his other achievements have been eclipsed. However, a ranking based on simple averages suffers from two defects. First, it does not take into account the consistency of scores across innings: a batsman might have a high career average but with low scores interspersed with high ones; another might have a lower average but with much less variation in his scores. Second, it pays no attention to the “value” of the player’s runs to the team: arguably, a century, when the total score is 600, has less value compared to a half-century in an innings total of, say, 200. The purpose of this paper is to suggest new ways of computing batting averages which, by addressing these deficiencies, complement the existing method and present a more complete picture of batsmen’s performance. Based on these "new" averages, the paper offers a revised ranking of the top fifty batsmen in the history of Test cricket.