Volume 7, Issue 2

The search for great goalscorers in football has been traditionally tunnel-visioned. Prestigious individual football awards, such as the Golden Boot and the Ballon d’Or, are almost automatically given to the player with the highest goal count. Simple. There is nothing usually complicated about this selection process—except, this one-dimensional approach may be missing some less-than-obvious gems of goalscoring by not considering the overall contributions a player makes to his team’s offensive performance as indicated by more subtle measures. The contributions made during the 2009-2010 season by the 20 leading goal scorers from each of the six most prestigious football leagues in Europe—the English Premier League, Spanish La Liga, Italian Serie A, German Bundesliga, French Ligue 1, and the Dutch Eredivisie—are examined. Statistical methods are used to (1) adjust for the significant disparity in the goal scoring prevalence between these leagues that promote unbiased comparisons and (2) account for the shorter, 34 game season used by two of the leagues as compared to the more common 38 game season.

By definition, giving 100 percent effort all of the time is sustainable, but begs the question of how to define 100 percent effort. As a corollary, once a benchmark for defining 100 percent effort is chosen, it may be possible, even optimal, to give a greater amount of effort for a short period of time, while recognizing that this level of effort is not sustainable. This dynamic effort provision problem is analyzed in the context of effort and performance by National Basketball Association (NBA) players over the course of a season. Within this context, several benchmarks for sustainable effort are considered, but these are rejected by the data. Meanwhile, the data are consistent with the proposition that NBA players put forth optimal effort, even if such effort is not always sustainable.

The existence of home advantage in Australian Rules football (AFL) has been well documented in previous literature. This advantage typically refers to the net advantage of several factors which, generally speaking, have a positive effect on the home team and a negative effect on the away team. However, this practice excludes the in-course dynamics of home advantage throughout the match including the interrelationship between pre-game and in-game team characteristics. The aim of the present study is to calculate the intra-match home advantage for each quarter in AFL by incorporating the interaction between team quality and current score. Archival AFL data was obtained from seasons 2000 to 2009 which consisted of year, round, quarter, (nominal) home team, away team, home team score and away team score. Analysis of variance (ANOVA) on margin of victory was used to determine if there was a distinct difference between team quality (favourite/underdog) within current score (ahead/behind). Since the in-game team characteristics (current score) are likely to be caused by pre-game characteristics (team quality) the margin of victory is adjusted for team quality. The results provide marginal evidence that home underdogs in the third quarter irrespective of whether they were ahead or behind at half time receive a greater advantage than home favourites. Furthermore, home advantage is greatest in the final quarter when there is a high level of uncertainty about the outcome of the match.

The purpose of this study was to examine the relationship between leader experience and team performance. Major League Baseball managers from 1903 to 2006 provided the context within which the relationships were studied. Experience was conceptualized in terms of games managed and seasons managed at the occupational and organizational levels. Cross-sectional analyses revealed a small but significant positive relationship between all types of experience and team performance after controlling for team ability. Analyzing the data longitudinally with random coefficient modeling, however, revealed only one significant experience-performance relationship. After controlling for team ability, there is evidence that managers improve team performance until a peak at about 1200 games. There is no evidence of a positive linear relationship of any kind or that this improvement transfers to other teams.

In this paper, I estimate adjusted odds ratios by fitting stratified logistic regression models to binary response variables, games won or lost, with plus/minus statistics as explanatory variables. Adapted from ice hockey, the plus/minus statistic credits an NBA player one or more points whenever his team scores while he is on the basketball court. Conversely, the player is debited minus one or more points whenever the opposing team scores. Throughout the NBA season, the league’s better players are likely to have positive plus/minus statistics as reported by Yahoo!Sports and 82games.com. Crude or unadjusted odds ratios estimate the relative probabilities of a player having a positive plus/minus in a win, versus a negative plus/minus in a loss. Home and away games are twin strata with teams playing 41 home games and 41 road games during an 82-game regular season. Stratum-specific odds ratios vary because some players perform better at home than on the road and vice versa. In order to adjust for home court advantage, stratified odds ratios and their 95 percent confidence intervals are estimated for each of the Los Angeles Lakers during the 2009–2010 regular season.

This article examines the dependence and direction of dependencies between on the field performance variables, winning percentage, and payroll in Major League Baseball using team data from 1985-2009. Particular focus is given to the relationship between winning and payroll. The method is to employ the PC algorithm, which is an implementation of graph theoretic methods in order to identify these dependence relationships. Results indicate that winning percentage directly depends on fielding percentage, on-base percentage, and saves while payroll directly depends on fielding percentage, strike outs against, and winning percentage. Using this results panel, models are estimated to assess the magnitudes of the relationships. Further, a system based on these relationships is estimated to examine the effects of winning and payroll on each other over time using impulse responses. Those responses show that payroll has a temporarily positive effect on winning but not permanently so. Finally, some cautions are offered in interpreting the results and some suggestions for future research.

This paper investigates how the structure of a relegation-promotion system impacts the competitiveness of a sports league. It proposes a rigorous mathematical model of a multi-division hierarchical sports league made up of teams with intrinsic skill levels (ISLs) that change from year to year. Since team skill changes over time, modification in division (or cluster) composition is necessary to optimize competitiveness. This is accomplished through promoting teams with the best records at the end of a season to a higher division and relegating teams with poor records to lower divisions. Such mechanisms are fundamental to the English football league system and the PGA Tour/Nationwide Tour. For reasons discussed in the paper, we use data from the National Basketball Association (in which there is no relegation system) to develop statistical models for year-to-year variability in ISLs and for match outcomes based on the ISLs of the two teams. We then develop a multiple season simulation model to investigate the effect of the number of teams relegated and promoted, the schedule, and the variability of year-to-year ISLs on competitiveness of the divisions. For the NBA data, we find that in a three-division league with ten teams in each division, relegating and promoting three teams at the end of the season results in the most competitive divisions as measured by the long run average within-division ISL standard deviation and the percentage of teams assigned to the correct division. The effect of schedule is minimal.

The 2007 gambling scandal involving a National Basketball Association (NBA) referee, coupled with the NBA’s follow-up investigation, put allegations of basketball referee bias in the spotlight. This paper analyzes specific allegations of bias by Miami Heat coach and general manager Pat Riley against NBA referees Steve Javie and Derrick Stafford. In the course of analyzing every referee who officiated a Miami Heat during a nine-year period, neither Javie nor Stafford exhibited systematic bias that had an adverse effect on the Miami Heat. In fact, the Heat performed slightly better than predicted when Javie officiated their games. The results provide real-world empirical evidence consistent with “confirmation bias,” a theory grounded in the finding that individuals with a vested interest in certain self-justifying outcomes may reach generalized conclusions unsupported by actual evidence.

This paper analyzes the ability of a neural network model to predict the outcome of NFL games. This model uses only readily available statistics, such as passing yards, rushing yards, fumbles lost, and scoring. A key component of this model is the use of statistical differentials to compare teams. For example, the offensive passing yards gained by one team are compared to the defensive passing yards allowed by an opposing team to create a data set of expected values for a given matchup. By using principal component analysis and derivative based analysis, we determined which statistics influence our model the most. We assessed the performance of the model by comparing its performance to that of published prediction algorithms and the Las Vegas oddsmakers over multiple seasons. Two novel aspects of this work include the use of multiple committees of machines for prediction and the use of our model to simulate virtual round-robin tournaments to establish an objective ranking of the teams.

In this paper, we consider the National Football League Pick Value Chart and propose an alternative. The current Pick Value Chart was created approximately 20 years ago and has been used since to determine the value of draft selections for trading of draft selections. For this paper, we analyze the first 255 draft selections for the years 1991 to 2001. As part of our analysis, we consider four non-position dependent metrics to measure and model player performance at each of the first 255 draft selections. We perform a nonparametric regression of each performance metric onto player's selections. A comparison is then made between each fitted line and the Pick Value Chart. Having considered these comparisons, we propose an alternative Pick Value Chart.

In Ohio high school football, playoff teams are selected and seeded using an objective point system. Roughly one-fourth of the state’s teams earn playoff berths, and higher seeds host first-round games. Even in the final week of the season, a team’s playoff chances can depend on the outcomes of dozens of other games, making direct computation of playoff probabilities impractical. To make playoff-related predictions, we first estimate win probabilities for all remaining regular-season games by applying a predictive ranking algorithm, then repeatedly simulate the remainder of the regular season. Using the aggregate results, we predict the playoff qualifiers and seeds, and also estimate conditional probabilities (based on the number of future wins) that particular teams earn a berth or a home game. In tracking the results of this model over two seasons, we find that modeling future games substantially increases the accuracy of seed predictions, but adds far less value in predicting the qualifying teams. This phenomenon may be related to the specificity of seed prediction, as compared to the more general nature of predicting a group of teams likely to qualify. That is, the additional information is most useful when making more specific predictions.

Unlike many other sports where only the top ten or twenty participants have a realistic shot at victory, when 144 players tee it up at a PGA tournament every participant has a legit chance at winning. In golf, even the greatest players lose more often than they win, and long-shots and unknowns win some of the most prestigious events. With such parity, random chance plays a large part in determining the winner. This is evident by the world ranking of four major champions in the 2009: 69th, 71st, 33rd, and 110th. While statistical modeling is commonplace in many sports, particularly baseball, the golf world is largely untapped. Using historical data from one of golf’s major championships, the Masters, this paper establishes a technique for modeling hole-by-hole results. This research has two major benefits: the opportunity to calculate real-time winning percentages and definition of the performance coefficient—which quantifies the level of performance within the player’s capability. For instance, 2009 Masters winner, the 69th rated Angel Cabrera, only had a seven percent chance of defeating both Phil Mickelson and Tiger Woods over 72 holes. However, his performance coefficient of .01 signifies that he performed close to his optimal performance. While Tiger Woods and Phil Mickelson performed above average with performance coefficients of .37 and .17, respectively, on this given week they were unable to better Cabrera.

In previous studies for analyzing the batting order of baseball games, the order is evaluated by its expected number of runs scored in a game, under the Markov chain model on the D’Esopo and Lefkowitz runner advancement model. However, the order to maximize the expected number of runs may not be the best order in the sense that it may not get more than 0.5 in probability of winning the game against other possible batting orders. In this sense, the best batting order is reconsidered, and it is tried to find better orders than the order which maximizes the expected number of runs. In this paper, the existence of such orders and the difference between the best orders and the order to maximize the expected number of runs are concretely shown by taking into account of not only the expected number of runs but also the standard deviation of runs, based on the data of Major League teams.

Sports fans can be freed from cheering against their favorite team for a draft pick. Draft orders based on how teams perform after becoming mathematically eliminated from playoff contention trigger highly competitive atmospheres that inspire fans with passion and optimism. The worst teams receive the handicap of playing more games to earn the top draft pick. Using the reverse standings to determine draft order creates the distressing paradox where success and failure become synonymous. Each fan’s right to cheer for their favorite team, from the first game to the last, is more important than the attempt to list teams from the worst to best. Advanced mathematical formulas and rigorous computer algorithms create the demand for professional sports franchises to make the pursuit of winning unlimited. After presenting on October 16, 2010, performance among eliminated teams dropped by 34.32 percent, and the St. Louis Blues are awarded the first overall draft pick.

This publication presents a formulation of an extension to the Pythagorean expectation for association football and other sports in which a draw result is a nontrivial event. Instead of estimating win percentage as in baseball, the extended Pythagorean estimates points won per game. A least-squares algorithm is used to fit offensive and defensive goal distributions to a three-parameter Weibull distribution, of which the parameter of interest is the Pythagorean exponent. Further analysis reveals that the league Pythagorean exponent remains stable across multiple leagues in the same calendar year and within a single league over multiple seasons, which gives support to the notion of a “universal” Pythagorean exponent. Application of the extended Pythagorean to results of domestic soccer leagues in Europe, Asia, and the Americas shows excellent agreement between goal statistics and league records for a majority of teams, and it indicates the teams that strongly overperform or underperform with respect to their expected performance.

Pitcher intent, as measured by the position of the catcher's glove before a pitch is thrown, is an element of baseball that is regularly observed by commentators (“he's missing his spots”) but remains an uncaptured aspect of statistical analysis of the game, offering many potential aspects on pitcher performance that have yet to be exploited. In order to collect this data systematically for public consumption (a far from trivial task), I propose and design a number of mechanisms for manual collection of this data from video playback using an offine charting approach, the direct indication of catcher position on the video, or a combination of the two. Through a pilot study conducted via a web applet, I find that there are considerable advantages to the direct-on-video method of charting catcher spots, including a higher inter-rater reliability as a consequence of higher precision and fewer replays needed of each pitch for a measurement to be taken, suggesting that direct video analysis, rather than lower-tech zone assessment, will be the preferred method for collecting catcher spotting data as the method becomes more popular.

Before the space race and computer games, 1957 was a simpler time. Baseball card collectors, mostly young boys, had few distractions to advance their hobby. In 1957, there were 16 major league baseball teams. The Kansas City Athletics, moved from Philadelphia in 1955, was the farthest west team. For others west of Saint Louis, baseball appetites were fed with the TV Game of the Week with Dizzy Dean, KMOX—the St Louis radio station, the Sporting News, baseball cards, or some combination. The young baseball fans of the period were the “baby boomers” who most likely were the major collectors in 1957. We examine several factors that influence the values of the Topps 1957 baseball card issue through the years and show how this baseball card set avoided the price collapse of the post-1980 baseball card issues.