Volume 9, Issue 1

Whether the nature of the risks associated with climbing high-altitude (8000 m) peaks is in some sense “controllable” is a longstanding debate in the mountaineering community. Well-known mountaineers David Roberts and Ed Viesturs explore this issue in their recent memoirs. Roberts views the primary risks as “objective” or uncontrollable, whereas Viesturs maintains that experience and attention to safety can make a significant difference. This study sheds light on the Roberts-Viesturs debate using a comprehensive dataset of climbing on Nepalese Himalayan peaks. To test whether the data is consistent with a constant failure rate model (Roberts) or a decreasing failure rate model (Viesturs), it draws on Total Time on Test (TTT) plots from the reliability engineering literature and applies graphical inference techniques to them.

Gender gaps in absolute performance at the Olympics are well-established, while gender differences in relative performance have not been considered. We analyzed time trends in male and female performance improvement for medal results in all individual athletics and swimming events in Olympic years with male and female competition. Performance improvement was defined as the percentage change in performance over the gold-medal result of the previous Olympic year. In mixed effects models that accounted for the effects of the order of finish, event, and year, we found a non-significant average difference in performance improvement of <0.5% for events in running, jumping, throwing, and swimming. Since the mid-twentieth century, the record at the Summer Games shows that gains in the performance of female Olympic medalists have kept pace with men.

Sports teams have incentives to put more effort into games with an immediate effect on standings compared to games that do not, possibly affecting outcome uncertainty. We develop a measure of game outcome uncertainty, game importance (GI), that captures how each game affects a team’s standing and can be calculated for individual games. Results show that observed variation in GI explains observed variation in attendance, game outcomes, and margin of victory at MLB games over the 1994 through 2010 seasons, suggesting that GI is an influential indicator in fans’ attendance decisions, consistent with the uncertainty of outcome hypothesis.

A rating system provides relative measures of superiority between adversaries. We propose a novel and simple approach, which we call pi-rating, for dynamically rating Association Football teams solely on the basis of the relative discrepancies in scores through relevant match instances. The pi-rating system is applicable to any other sport where the score is considered as a good indicator for prediction purposes, as well as determining the relative performances between adversaries. In an attempt to examine how well the ratings capture a team’s performance, we have a) assessed them against two recently proposed football ELO rating variants and b) used them as the basis of a football betting strategy against published market odds. The results show that the pi-ratings outperform considerably the widely accepted ELO ratings and, perhaps more importantly, demonstrate profitability over a period of five English Premier League seasons (2007/2008–2011/2012), even allowing for the bookmakers’ built-in profit margin. This is the first academic study to demonstrate profitability against market odds using such a relatively simple technique, and the resulting pi-ratings can be incorporated as parameters into other more sophisticated models in an attempt to further enhance forecasting capability.

Nowadays many approaches that analyze and predict the results of football matches are based on bookmakers’ ratings. It is commonly accepted that the models used by the bookmakers contain a lot of expertise as the bookmakers’ profits and losses depend on the performance of their models. One objective of this article is to analyze the role of bookmakers’ odds together with many additional, potentially influental covariates with respect to a national team’s success at European football championships and especially to detect covariates, which are able to explain parts of the information covered by the odds. Therefore a pairwise Poisson model for the number of goals scored by national teams competing in European football championship matches is used. Moreover, the generalized linear mixed model (GLMM) approach, which is a widely used tool for modeling cluster data, allows to incorporate team-specific random effects. Two different approaches to the fitting of GLMMs incorporating variable selection are used, subset selection as well as a Lasso-type technique, including an L1-penalty term that enforces variable selection and shrinkage simultaneously. Based on the two preceeding European football championships a sparse model is obtained that is used to predict all matches of the current tournament resulting in a possible course of the European football championship (EURO) 2012.

What is the best male and female athletics performance in history? We seek to answer this question for Olympic distance track events by simultaneously modelling race performances over all Olympic distances and all times. Our model uses techniques from a branch of statistics called extreme value theory, and incorporates information on improvements over time using an exponential trend in addition to a process which identifies the changing ability of the population of athletes across all distances. We conclude that the best male performance of all time is the 1968 world record of Lee Evans in the 400 m, and that the best female performance of all time is the current 1988 world record of Florence Griffith-Joyner in the 100 m. More generally, our approach provides a basis for deriving a ranking of track athletes over any distance and at any point over the last 100 years.

A detailed study of the bank shot trajectory was performed with a focus on breaking it down into its significant features. The bank shot’s effectiveness was examined in terms of the player’s ability to accurately impart launch speed, back spin, pitch angle, and side angle. It was shown that the bank shot is more forgiving than the direct shot in launch speed and launch angle and has about the same level of forgiveness in side angle at particular locations on the court. This paper concludes that the bank shot can be extremely advantageous over the direct shot to the shooter who learns how to accurately impart side angle.

In this paper we examine the relationship of the speed of a set in volleyball with the outcome of the attack. A total of 1777 sets of a single male university level volleyball team were photographed using high speed cameras so that the time the set was in the air could be measured with accuracy to 1/100 th of a second. Data were analyzed using a logistic regression model implemented using the Bayesian paradigm. Using these methods the probability of a kill resulting from a set of a particular speed could be calculated. In general, sets that traveled a further distance had significant increases in the probability of success with a faster set. No trends were seen with sets that were delivered to hitters that were closer to the setter. Decreasing outside set time from 1.53 to 0.85 s, significantly increased probability of a kill from 0.31 to 0.58 for the team studied. The speed of the set when the attacker is not near the setter appears to be an important component in the success of the attack in male collegiate volleyball.

We present a regularized logistic regression model for evaluating player contributions in hockey. The traditional metric for this purpose is the plus-minus statistic, which allocates a single unit of credit (for or against) to each player on the ice for a goal. However, plus-minus scores measure only the marginal effect of players, do not account for sample size, and provide a very noisy estimate of performance. We investigate a related regression problem: what does each player on the ice contribute, beyond aggregate team performance and other factors, to the odds that a given goal was scored by their team? Due to the large- p (number of players) and imbalanced design setting of hockey analysis, a major part of our contribution is a careful treatment of prior shrinkage in model estimation. We showcase two recently developed techniques – for posterior maximization or simulation – that make such analysis feasible. Each approach is accompanied with publicly available software and we include the simple commands used in our analysis. Our results show that most players do not stand out as measurably strong (positive or negative) contributors. This allows the stars to really shine, reveals diamonds in the rough overlooked by earlier analyses, and argues that some of the highest paid players in the league are not making contributions worth their expense.