Volume 10, Issue 1

We consider the modeling of individual batting performance in one-day international (ODI) cricket by using a batsman-specific hidden Markov model (HMM). The batsman-specific number of hidden states allows us to account for the heterogeneous dynamics found in batting performance. Parallel sampling is used to choose the optimal number of hidden states. Using the batsman-specific HMM, we then introduce measures of performance to assess individual players via reliability analysis. By classifying states as either up or down, we compute the availability, reliability, failure rate and mean time to failure for each batsman. By choosing an appropriate classification of states, an overall prediction of batting performance of a batsman can be made. The classification of states can also be modified according to the type of game under consideration. One advantage of this batsman-specific HMM is that it does not require the consideration of unforeseen factors. This is important since cricket has gone through several rule changes in recent years that have further induced unforeseen dynamic factors to the game. We showcase the approach using data from 20 different batsmen having different underlying dynamics and representing different countries.

This paper considers the decision problem of when to declare during the third innings of a test cricket match. There are various factors that affect the decision of the declaring team including the target score, the number of overs remaining, the relative desire to win versus draw, and the scoring characteristics of the particular match. Decision rules are developed and these are assessed against historical matches. We observe that there are discrepancies between the optimal time to declare and what takes place in practice.

In this research we study the relationship between concentration of scoring production (measured with the Gini index of team points) and teams’ offensive efficiency (measured as normalised team points per minutes played and possessions) in the game of basketball. We record the aggregate box-score statistics of all teams from the 1977/1978 to the 2010/2011 seasons in the NBA, together with each player’s contribution to his respective team’s offensive production. After applying a fixed effect regression model, we find evidence of a positive relationship between concentration of production and offensive efficiency, which contradicts some recent thesis (Skinner, Brian. 2010. “The Price of Anarchy in Basketball.” Journal of Quantitative Analysis in Sports 6:Article 3) about the nature of this association. Our results suggest that that the well known mass-media concepts such as “big three” or “big four” to design successful teams make sense. Teams with more talent and with several big stars will (probably) increase its concentration of scoring, and this will be associated with an increase in its offensive efficiency.

Conference affiliation is an important consideration for institutions of higher learning, both athletically and academically. Traditionally, conference affiliation in the NCAA has been determined based largely on geography. However, recent events beg the question of what would be the result if conference affiliation, and classifications such as being a Bowl Championship Series Automatic Qualifier, were re-configured based not on traditional aspects of geography, tradition and like-mindedness, but solely on the financial and on-field performance of an institution’s football program. This paper utilizes a multivariate statistical technique (cluster analysis) to re-conceptualize conference affiliation, as well as the current Football Bowl Subdivision (FBS) hierarchy, based solely on data reflecting the performance of each FBS institution’s football programs. The analysis results in a total of 23 programs being relegated from their current status, while several programs (such as Boise State, Louisville and Rutgers) have been promoted into the highest tier of the FBS based on their performance. The paper also presents a new clustering of four “super” conferences based on this same performance data, resulting in four conferences consisting of programs with similar on-field and financial performance over the past 10 seasons.

The standard metric for American football field goal kickers is simply the percentage of attempts successfully converted. Due to variance in distance of attempts and other conditions (weather, altitude, defense, etc.), we argue that field goal percentage is an insufficient measure of kicker performance. Using three seasons of NFL data, we construct a multivariate logistic regression model for the success probability of a given attempt. This leads naturally to metrics in which a kicker’s performance is compared to model expectations, if a replacement-level player was attempting the same kicks. Player salaries correlate only weakly with our measures of field goal kicking success. We find that those kickers selected to the Pro Bowl and All-Pro teams were rather mediocre by our metrics, over the seasons studied. The relative difficulty of kicking in various stadiums is also considered. Finally, we discuss the degree to which field goal kicking is a skill that can be maintained over multiple seasons.

We present a notational analysis of offensive tactics commonly employed in elite men’s water polo and address three questions related to this objective: which tactics are most effective?, which tactical performance indicators best classify the winning team?, and how accurate are predictive models based on these performance indicators? We define a new statistic, Efficiency Rating, which quantifies the importance of a tactic via a weighted average of direct and indirect goals generated by its use. By this measure, direct shot is the most efficient even strategy despite being employed far less frequently than centre or perimeter tactics. We address our second question by measuring the effect size of winning over losing teams for 25 tactical variables and find that exclusion conversion rate is the most effective discriminatory statistic in both close and unbalanced games, correctly classifying almost 90% of all contests. To address our third question, we develop and apply a simple Binomial model based on goals generated per play which correctly predicts all eight games in the medal round of the 2012 Men’s Olympics from preliminary rounds. Success probabilities are computed based on a weighted average of offensive and defensive efficiency with an optimal weight that favors defense.

Objectives: Identifying performance indicators related to rugby sevens competition outcomes will inform development of team tactics that increase the likelihood of success. This study characterized 16 team performance indicators and quantified the effect of changes and differences in performance indicators within and between teams on team ranking in international tournaments. Design: Official tournament statistics and final ranking of each team in each of nine men’s tournaments of the 2011/2012 International Rugby Board Sevens World Series were analyzed in a retrospective longitudinal design. Methods: Novel analyses involving linear mixed modeling quantified the effects within and between teams of an increase in performance indicators from a typically low to typically high value on the logarithm of the tournament ranking. Magnitudes of effects were assessed using a smallest meaningful difference in ranking. Results: Three performance indicators had substantial within-team effects and 12 had substantial between-team effects on tournament ranking. More entries into the opposition’s 22-m zone per match, tries per entry into the opposition’s 22-m zone, tackles per match, passes per match, rucks per match and a higher percentage of tackle completion were associated with a better mean ranking. Conversely, more passes per try, rucks per try, kicks per try, errors per match, surrendered possessions per match, and missed tackles per match were related to a worse ranking. Conclusions: The most successful teams maintain ball possession by reducing errors and turnovers, are efficient in converting possession into tries, and have effective defensive structures resulting in a high rate of tackle completion.