Volume 7, Issue 1

One measure of sports league competitive balance uses a ratio: the standard deviation of team winning percentages is divided by the so-called ideal standard deviation, which assumes a game between evenly-skilled teams is equally likely to be won by either team. In fact, a team is more likely to win when playing at home than when playing on the road. The extent of this advantage differs across sports leagues. Home advantage reduces the variability of season-long team records. Ignoring home advantage biases upward the traditionally measured ideal standard deviation and bias downward the ratio of standard deviations. The authors derive a balanced league standard deviation formula that accounts for home advantage, use it to recompute the ratio of standard deviations for major sports leagues, and consider how the adjustment affects comparisons of competitive balance across those leagues.

Three of the most celebrated football leagues in the world include the English Premier League (EPL), Italy’s Serie A, and Spain’s La Liga. To date, little football research has been conducted that attempts to determine why these leagues are so successful. What is it that the EPL, La Liga, and Serie A do that fosters such a high caliber of play, and what pitch factors, if any, either (1) contrast or (2) connect these prestigious leagues? The paucity of rigorous inquiry has not deterred popular speculation—common folklore has not waited for hard data. Experts rush to characterize the perceived performance characteristics of these leagues with little hesitation. And these assumptions have, to some degree, taken on a life of their own: football’s answer to urban legend.This paper searches for key similarities and differences between these leagues that are bolstered by statistically significant findings as well as evidence to identify the key pitch factors that are associated with a team’s ultimate success within its respective league.

The purpose of this study was to gain an understanding of the bank shot and ultimately determine the optimal target points on the backboard for the bank shot in men’s basketball. The study used over one million three-dimensional simulations of basketball trajectories. Four launch variables were studied: launch height, launch speed, launch angle, and aim angle. The shooter’s statistical characteristics were prescribed to yield a 70 percent free throw when launching the ball seven feet above the ground with 3 Hz of back spin. We found that the shooter can select a bank shot over a direct shot with as much as a 20 percent advantage. The distribution over the court of preferences of the bank shot over the direct shot was determined. It was also shown that there is an aim line on the backboard independent of the shooter’s location on the court. We also found that at 3.326 inches behind the backboard, there exists a vertical axis that aids in finding the optimal target point on the backboard. The optimal target point is the crossing of the vertical axis and the aim line that is in the shooter’s line of sight.

This article presents a multivariate analysis of Olympic decathlon data based on maximum likelihood factor analysis. All results explicitly account for model selection uncertainty, which is inherent in any data-based selection process but mostly ignored in reports related to multivariate sports data. For this purpose, some well-established frequentist procedures that have so far been applied almost exclusively to regression analysis are adopted and transferred to the factor analytical context. The findings support the claim that decathlon contests consist of three dimensions. These dimensions seem to be similar to, but not exactly the same, as those found by Cox and Dunn (2002) via hierarchical cluster analysis.

Existing performance metrics utilized by the PGA TOUR have biases towards specific styles of play, which make relative player comparisons challenging. Our goal is to evaluate golfers in a way that eliminates these biases and to better understand how the best players maintain their advantage.Through a working agreement with the PGA TOUR, we have obtained access to proprietary “ShotLink” data that pinpoints the location of every shot taken on the PGA TOUR. Using these data, we develop distance-based models for two components of putting performance: the probability of making the putt and the remaining distance to the pin conditioned on missing. The first is modeled through a logistic regression, the second through a gamma regression. Both models fit the data well and provide interesting insights into the game. Additionally, by describing the act of putting using a simple Markov chain, we are able to combine these two models to characterize the putts-to-go for the field from any distance on the green for the PGA TOUR. The results of this Markov model match both the empirical expectation and variance of putts-to-go.We use our models to evaluate putting performance in terms of the strokes or putts gained per round relative to the field. Using this metric, we can determine what portion of a player’s overall performance is due to advantage (or loss) gained through putting, and conversely, what portion of the player’s performance is derived off the green. We demonstrate with examples how our metric eliminates significant biases that exist in the PGA TOUR’s Putting Average statistic. Lastly, extending the concept of putts gained to evaluate player-specific performance, we show how our models can be used to quickly test situational hypotheses, such as differences between putting for par and birdie and performance under pressure.

In soccer knockout ties, which are played in a two-legged format, the team having the return match at home is usually seen as advantaged. For checking this common belief, we analyzed matches of the UEFA Champions League knockout phase since 1994/1995. It is shown that the observed differences in frequencies of winning between teams first playing away and those which are first playing at home can be completely explained by their performances on the group stage and—more importantly—by the teams' general strength.

This study analyzes the terminating actions (serve, attack, block and opponent error) resulting in point scoring for each team. These actions are then taken as reference indicators for observing the possibility of winning or losing a set in an elite men’s volleyball competition. A total of 45 matches were studied at the European Men’s Volleyball Championship held in September 2009 in Izmir and Istanbul (Turkey). Recordings were made of a number of game actions in a total of 168 sets. Analysis of these sets showed 132 ending in 25 points (78.57 percent) and 36 sets in more even matches (21.43 percent): 27 ending in more than 25 points (16.07 percent) and nine fifth or tie break sets (5.36 percent). Statistical analysis showed attacking to be the highest point-scoring technical action, but as matches became more even (sets with more than 25 points, or fifth and tie break sets), points scored by blocking became decisive for attaining victory in top-level competition. The number of errors made by each team is considerably lower at this level and points achieved through serving tend to be even.

A country's size in terms of population and economic status play a major role in the resources available to a national soccer team. Additionally, the national expectations for the team define what a successful result is. The purpose of this paper is to present a prediction for the 2010 Federation Internationale de Football Association (FIFA) World Cup based on socioeconomic variables. Building off of models presented by Johnson and Ali (2004) as well as Dyte and Clark (2000), new models are created and presented. First, a linear regression model accounts for the ratings and rankings of the nations participating. Then, the ratings are applied to a Poisson regression to predict the outcome for each of the 64 games in the World Cup. The results predict the tournament will be won by Brazil. The model was then subjected to back-testing using the 2006 World Cup tournament. The back-tested model ranked the eventual first, second and third place finishers higher than the FIFA official rankings. The paper then presents future directions for research and notes the rationale for omissions from the model.

Using data from the Bundesliga, the top German football league (American “soccer”), we analyze the effects of yellow and red cards on the probability of victory for a team. For the team receiving the cards, we find that yellow and red cards decrease the probability of victory. However, the number of fouls called increases the probability of victory for that team. We therefore find that aggressive play is valuable, but pushing too hard is detrimental. We also find that the probability change is different for the home and away teams.

Classical performance analysis techniques in golf have focused on classes of shots, such as putting, driving, etc. Because these measures remove shots from their original context within the round, such measures do not describe a player's ability to perform a specific type of shot. Rather, these measures provide a score which is a composite score of all previous shots on the hole. This study establishes a new method for assessing the difficulty of shots in golf and a new performance indicator — Shot Quality. We call our method the “ISOPAR method,” which gets its name from the analogy we make to isobar maps used in meteorology. The method presented here relies on ball positions taken from tournament play and the associated number of shots required to hole out from each measured ball position. Data were collected from the 2009 Bavarian Junior Championship in Burgwalden, Germany. ISOPAR values are calculated which represent the average number of strokes required to hole out from any location on the green. These ISOPAR values can be visualized on an ISOPAR map. Instead of lines of equal pressure, as in the case of our meteorological analogy, the lines on the map represent the ISOPAR values at intervals of 0.2. High values can be interpreted as difficult areas on the green and low values as easy areas on the green. The Shot Quality score is the difference between the ISOPAR values of the starting position and finishing position, respectively. ISOPAR maps could potentially be used by professional golfers and caddies to characterize a green in terms of areas of difficulty and may also help them decide which putts to play more or less aggressively. Television broadcasts could also use these maps to show the audience how the field fared from various positions on the green. Finally, coaches and teachers could use the Shot Quality measure as a new performance indicator to assess shot outcomes.