Volume 7, Issue 3

Using a unique dataset, this paper empirically tests the Peltzman effect by investigating the behavior of Formula One racecar drivers. Estimates suggest that drivers become more reckless as their cars become safer, ceteris paribus. From 1963-1973, safety changes, on average, are estimated to leave the number of driver casualties unchanged. Furthermore, this is the first attempt to estimate specifically how drivers respond to changes in the conditional probability of fatality given an accident. Results provide evidence that the behavioral response of drivers is larger when the analysis is confined to changes in the conditional probability of a fatality given an accident.

This study investigated the ability of discriminant analysis to predict the offensive play calling of the 2005 Atlanta Falcons. Data was collected on each of the 988 offensive plays run from scrimmage by the Atlanta Falcons during the 2005 NFL season. Independent variables included game location (home vs. away), down, yards to go, field position, score, offensive formation, opponent’s defensive rank against both the run and the pass, weather and field surface (turf vs. grass). The response variable was categorized into either a short pass (5 yards or less), medium pass (6 to 15 yards), long pass (more than 15 yards), run, or scramble (by Michael Vick).A linear discriminant function was developed to predict play calling based on the independent variables. Based on a cross validation procedure, the model was able to correctly predict the play called 40.38 percent of the time. While this rate is not high, the model was able to predict each play with greater accuracy than the relative frequency that each play was run. Considering that the Falcons coaches said they only use frequencies, the use of discriminant analysis is an intriguing possibility for NFL coaches.

We use the theoretical framework of “tournament theory” to obtain a statistical foundation for the most popular contest function used in the economics literature. We show that once one solves the issue of measuring “output” as it appears in tournament theory, one can obtain maximum likelihood estimates of the parameters in the contest function based on the past performance of the competitors. The findings are used to predict the odds of winning a horse race and the results compared with the odds generated by the actual wagers.

The goal of this paper is to develop an adjusted plus-minus statistic for NHL players that is independent of both teammates and opponents. We use data from the shift reports on NHL.com in a weighted least squares regression to estimate an NHL player's effect on his team's success in scoring and preventing goals at even strength. Both offensive and defensive components of adjusted plus-minus are given, estimates in terms of goals per 60 minutes and goals per season are given, and estimates for forwards and defensemen are given.

APBA baseball is a sophisticated baseball simulation game. Each major league player is represented by a card, which has numbers on it that reflect his performance in a particular season. Two people play a game by rolling dice and looking on their players’ cards to see what is the outcome of the roll of the dice.In this article, we use Markov chains to analyze certain aspects of this game. For example, we can tell whether one player's batting card is more valuable than another’s, and we can make informed decisions about strategy in the game.

This paper introduces the integration of nonuniform weighting for sports ranking. While the ideas of the paper can be applied to any ranking method, a careful investigation is conducted on incorporating weighting in two of today's most popular ranking algorithms: the Colley and Massey methods, which were both developed for sports ranking applications and have since become the baseline standards there. The article introduces how to adapt both methods in order to weight some factors, such as late season play, home court advantage, or a winning streak, more heavily in computing the ratings of teams. To illustrate the utility of such weighting, the paper applies the algorithmic ideas in the area in which both Colley and Massey motivated their methods: sports. As such, the target application is producing brackets for the Division I NCAA Men's Basketball Tournament also known as March Madness. All the methods were used to produce brackets in the 2010 tournament and their results are given, including several mathematically-produced brackets that were better than 90 percent of the nearly 5 million brackets submitted to ESPN's Tournament Challenge.

Does lineup protection exist? Observers of baseball frequently invoke the idea of lineup protection in which a batter will walk less and hit for more power if he is followed in the batting order by a high-quality hitter. Previous attempts to measure protection in Major League Baseball have sometimes found evidence of lower walk rates but never an impact on power hitting. I argue that these efforts fail to uncover such evidence because lineups are selectively chosen by managers, introducing endogeneity bias into ordinary linear regression and batting split comparisons. To remedy this problem, I use injuries to batters’ “protectors” as a natural experiment that quasi-randomly changes the level of protection received by batters. Using this approach, I find evidence that protected batters hit for more power, hitting 9.7 percent more extra-base hits if the protector’s OPS is 100 points higher. These effects are strongest among 3rd hitters, who hit 26 percent more extra-base hits under the same scenario. Supporting the previous literature, I find that batters walk more, especially intentionally, when left unprotected.

Performance diagnostics in sports is employed to obtain the current status of an athlete, for longitudinal as well as cross comparisons and for adjusting the subsequent training phase. A diagnostic set-up consists of certain tests that yield specific quantitative parameters. In this paper, we show how to analyze large amount of test data and possibilities to reduce the complexity of a diagnostic set-up. For the data collected from about 200 German elite ski jumpers and Nordic combined athletes between 2004 and 2008, we performed a factor analysis in order to find latent factors that would reduce the number of parameters measured and interpreted so far. Our calculations resulted in three latent factors: 1. general jump ability and relative maximum strength, 2. general maximum strength and dynamic strength, and 3. force rate development. We propose to reduce the number of measured parameters to a) one of the variables that load high on the three factors and b) those that do not measure any factors at all. This way, we come up with ten instead of the initial 23 parameters, while a high proportion of variance can be explained. These findings need to be checked in actual testing settings for practical relevance.

The aims of this study were to describe match actions in ice sledge hockey on a team level and identify the differences between successful and less successful teams. Eight ice sledge hockey matches in the Winter Paralympics 2010 were recorded and analyzed using the Dartfish TeamPro 5.5 analysis program. The variables for the analysis were chosen based on the performance indicators commonly used in invasion games and nine variables with sufficient reliability were reported. The number of different match actions and the percentages of successful actions were compared between the winning and losing teams, teams in different categories (team’s position in the final ranking 1-4 or 5-8), and between different player roles (forwards and defensemen). Also a scoring analysis for 23 goals was executed. The average number of actions per team in a single match was 507 (±54). The most frequent actions were passes (36 percent of the analyzed actions), dribbles (18 percent), and received passes (16 percent). The success percentages for passes, received passes, dribbles and face-offs were 65±4, 82±4, 74±8 and 50±12. The scoring analysis showed that 96 percent of the goals were shot from a close distance. The most common attack types leading to a goal were possession in the attacking zone and attacks after conquered puck and the most common shot types dribbling+shot and receiving+shot. The average scoring efficacy was 6.2±4.7 percent. The match analysis revealed only slight differences between the winning and losing teams and teams in different categories. Thus, it seems evident that individual skills and mistakes most often determined the final outcomes of the matches.

This paper determines that rankings in both the Media and Coaches college football Top 25 Polls are significantly accurate at their tops, insignificantly accurate towards their bottoms, and significantly more accurate at their tops than their bottoms. The computer-based Sagarin Poll is significantly accurate at both its top and bottom, and significantly more accurate at its top than its bottom. Comparing the Media and Coaches Polls to the Sagarin Poll suggests that the Media and Coaches Polls have diminishing accuracy because of both imperfections in voter behavior and smaller actual differences in team quality at lower ranks.

This paper introduces a new model and methodology for estimating the ability of NBA players. The main idea is to directly measure how good a player is by comparing how their team performs when they are on the court as opposed to when they are off it. This is achieved in such a way as to control for the changing abilities of the other players on court at different times during a match. The new method uses multiple seasons’ data in a structured way to estimate player ability in an isolated season, measuring separately defensive and offensive merit as well as combining these to give an overall rating. The use of game statistics in predicting player ability will be considered. Results using data from the 2008/9 season suggest that LeBron James, who won the NBA MVP award, was the best overall player. The best defensive player was Lamar Odom and the best rookie was Russell Westbrook, neither of whom won an NBA award that season. The results further indicate that whilst the frequently-reported game statistics provide some information on offensive ability, they do not perform well in the prediction of defensive ability.

National Football League (NFL) teams spend substantial time and money trying to predict which college quarterbacks eligible to be drafted into the NFL will have successful professional careers. But despite this investment of resources, it is common for quarterbacks to perform much better or worse than anticipated. Prior work on this “quarterback prediction problem” has concluded that NFL teams are poor at determining which quarterbacks are likely to be successful based on information available prior to the draft. However, these analyses have generally focused only on quarterbacks who played in the NFL, ignoring those who were drafted but did not appear in a professional game. Using data on all quarterbacks drafted since 1997, we considered the problem of predicting NFL success as defined by two metrics (games played and Net Points), based on when a quarterback was drafted and his performances in college and at the NFL Combine. Our analyses suggest that college and combine statistics have little value for predicting whether a quarterback will be successful in the NFL. Contrary to previous work, we conclude that NFL teams aggregate pre-draft information—including qualitative observations—quite effectively, and their inability to consistently identify college quarterbacks who will excel in the professional ranks is a consequence of random variability in future performance due to factors which are unlikely to be observable.

No previous study on momentum in team sports has found any valid evidence for a momentum effect—i.e., an effect of success in the past few games, over and above the effect of team quality. We develop an econometric model to determine if there is a momentum effect in the NBA by examining how success over the past few games leads to a higher probability of winning the next game. The model takes into account the home vs. away strengths of the teams in the current game as well as their opponents in the previous games (to calculate measures of “adjusted success over the past few games”). Thus, success in previous games is adjusted for quality of the wins or losses. In addition, we account for rest days before the current game for both teams. Using data over three NBA seasons (2007-2009), we find strong evidence for a positive momentum effect.

Quantitative analysis of football play calling suggests that NFL coaches do not choose their strategies optimally. They tend to be overly cautious. One possible explanation for this finding is that NFL coaches are averse to risk and loss. We propose a prospect theory based model of coaches' utility and estimate the model's parameters using kickoff data from the 2009 NFL season. Using an outcome measure of points scored on the initial post-kickoff possession we analyze two strategic kickoff decisions that involve risk-reward tradeoffs: the decision to kick a surprise onside kickoff or a regular kickoff, and the decision to accept a touchback or run the ball out of the endzone. Surprise onside kickoffs may yield a more favorable mean points scored value for the kicking team than a regular kickoff, yet surprise onside kickoffs are infrequently used (and thus the same size is small and the p-value of significance test is 0.68). Coaches appear averse to the possible loss involved in the surprise onside kickoff. Running the ball out yields a higher mean points scored for the receiving team than accepting a touchback, but it entails some risk (fumbles are lost in 2 percent of returns). Nevertheless, declining the touchback option and running the ball out is very common. Coaches do not appear excessively risk averse when presented with this choice over possible gains. Prospect theory models allow for risk aversion over possible gains, as in traditional expected utility theory, and in addition they permit an asymmetric aversion to losses. A prospect theory model therefore seems suitable for our analysis of kickoff strategies. We estimate a risk aversion coefficient value of 0.66 and a loss aversion coefficient value of 1.55, where values <1 and >1 indicate risk and loss aversion, respectively. Our analysis supports the notion that NFL coaches are both modestly risk averse and loss averse. In other words, coaches display diminishing sensitivity to changes in scoring outcomes as they move further from a reference point (zero), and for scoring gains and losses of equal magnitude they suffer more from a loss than they enjoy from a gain. This result may explain their propensity for making conservative strategic choices that, at first glance, appear sub-optimal.

In low-scoring sports such as ice hockey or soccer, which team scores the first goal is critically important to game outcome. By the same token, how a team responds to scoring or conceding the first goal is also important. If a team responds well when it concedes the first goal, it may win out in the end. On the other hand, if it handles an initial setback badly, the game may be effectively over. These considerations are knit together in an accounting identity which serves as a scaffold for the present study. Performance after the first goal is controlled by two responses, how well the team which scores the first goal retains its advantage and how well the team which concedes the first goal counters its disadvantage. These two responses are both found to play large roles in which team wins the game and how many goals after the first each one scores. Both responses are highly significant and together account for most of the advantage that the home team enjoys in game outcome. The relation of these results to the frequently encountered idea of momentum is also discussed.

Generalizability (G-) theory is increasingly being used by assessment professionals in a variety of assessment contexts, especially those involving performance assessments. This study expands the use of G-theory and its possible application to highly competitive sporting events that involve judging panels. Specifically, using G-theory, this study examined both the scoring variability and reliability of all four events of the 2004 World Figure Skating Championships. For each event, it examined the independent sources of score variation contributing to the variability of scores assigned by the raters (judges), and the score reliability (or generalizability coefficient). For the Ice Dancing event, an additional examination of the impact of treating “rater” and “rating” as different facets of G-theory studies on the score reliability was conducted. The results show that rater/rating was identified as a component of concern in all events. For the Singles events, in particular, the percentages of the variance for rater (judge) reached approximately 10 percent of the total variance, indicating that there were serious concerns about the scoring reliability. The generalizability coefficients for the events of Men’s Singles and Ladies’ Singles were both 0.93. However, the generalizability coefficients for Pairs and Ice Dancing were 0.99 and 0.98, respectively, indicating that the scores for these two events were extremely reliable. Using rater vs. rating in the Ice Dancing scores appeared to result in very little difference.

The aim of present investigation was to develop the behavioural instrument for measuring the achievement motivation in sport matches. According to 5-stage behavioural measurement system, the instrument was established and was applied for Iran national soccer team among three matches. The results have revealed the good validity, intra-rater, and inter-rater reliabilities for measuring motivational behaviours in sport contexts. In addition, the repeated measure analysis of variance has shown the applicability of new instrument for studying the association of achievement behaviours with successful performance, through significant differences between achievement behaviours in different matches with varied outcomes (p<.05).It seems the developed instrument is applicable for coaches to discriminate achievement behaviours of players during the match and select their strategy and players’ substitutions according to their trends and behaviours for success.

Linear models for paired comparisons, the Bradley-Terry model and the Thurstone-Mosteller model in particular, are widely used in sports for ranking and rating purposes. By their formulation, these models predict the probability that a player or team defeats another if the playing strengths of the players or teams are known.In this paper, we investigate the prediction accuracy of the two linear models by using them to describe three simple theoretical games which mimic actual sports and whose winning probability, given the playing strength of each player, can be expressed explicitly. A theoretical result is presented, which provides the basis of a linearization method that enables these games to be represented by linear models. The predicted winning probabilities from the linear models are then compared to the actual ones. Comparisons are also made in prediction accuracy between the Bradley-Terry model and the Thurstone-Mosteller model.

We propose a rank-based statistical procedure for comparing performances of top major league baseball players who performed in different eras. The model is based on using the player ranks from voting results for the most valuable player awards in the American and National Leagues. The current voting procedure has remained the same since 1932, so the analysis regards only data for players whose career blossomed after that time. Because the analysis is based on quantiles, its basis is nonparametric and relies on a simple link function. Results are stratified by fielding position, and we compare 73 Hall of Fame players up to 2010. We also consider the players on the 2011 Hall of Fame ballot as well as other potential Hall of Fame candidates. The analysis is based on the method of maximum likelihood, and results are illustrated graphically.

In every AFL season, there are usually one or two round matches that end in a draw. This situation is handled in finals matches by playing extra time. Whilst the scoring systems used in finals matches could be applied to round matches to eliminate draws, we devise new alternative systems that have better statistical properties by increasing the probability for the stronger team to win, increasing fairness and spectator interest, and reducing the likelihood of long matches occurring. Further, these new scoring systems could also be used in finals matches.

Archival data was gathered from the FIBA33 games during the 1st inaugural Youth Olympic Games held in Singapore. Data collected from 70 basketball games played by boys from 20 participating countries were gathered for analysis. Analysis of game-related statistics and FIBA33 final rankings differentiated successful from unsuccessful teams. Ninety-five percent of the cases were correctly classified using discriminant analysis and in the cross-validation (leave-one-out method) the correct re-classification was 75 percent. Data triangulated from interviews and field notes were used to determine key factors contributing to team’s success in the FIBA33 games. Results of the present study showed that players from the top 10 successful teams could be differentiated from those in the bottom 10 unsuccessful teams. The determining factors were taller, had better shooting percentages, played aggressively (i.e., recorded more team fouls and the ability to draw fouls on opponents during games). Coaches can use these results to improve player’s recruitment process, reinforce the importance of fundamental skills such as shooting, individual offensive and defensive concepts under different game situations during trainings.

In recent years, the NFL’s quarterback passer rating has become one of the most widely recognized statistics in sports. Though it has been in use since 1973, popular acceptance of the statistic took a few decades and has resulted in a great deal of debate over its ability to effectively quantify an aspect of the quarterback’s performance. Here, we will offer some background on the current quarterback passer rating system, consider some prevalent criticisms of the rating and propose some minor modifications to the rating system designed to keep the original intent of the statistic intact, while significantly improving results. Thus, rather than to offer a newly designed statistic, the goal here is to offer the simplest of modifications to the current quarterback passer rating, in line with the established calculation procedure, which will improve the effectiveness of the statistic. We will show that these modifications produce results that are far more reasonable than those achieved by the current rating.

This study examines home advantage in American college football games from a multilevel perspective. It quantifies the extent and significance of that home advantage and examines how it varies between BCS and non-BCS teams as well as analyzing the relationship between home advantage and team parity. Our results indicate that home advantage exists for most teams and conferences. It equates to a 6 point advantage for home teams and a 3-point disadvantage for away teams when controlling for team strength and other predictors. It concludes that after controlling for team ability, non-BCS teams possess a stronger home advantage than BCS teams. Such a result is likely related to the greater parity among BCS teams which leads to a “choking under pressure” effect for them in closely played games.

We propose a model to estimate the rates at which NHL teams score and yield goals. In the model, goals occur as if from a Poisson process whose rate depends on the two teams playing, the home-ice advantage, and the manpower (power-play, short-handed) situation. Data on all the games from the 2008-2009 season was downloaded and processed into a form suitable for the analysis. The model seems to perform adequately in prediction and should be useful for handicapping and for informing the decision as to when to pull the goalie.