Band 16, Heft 3

In this paper, we present a new model for ranking sports teams. Our model uses all scoring data from all games to produce a functional rating by the method of least squares. The functional rating can be interpreted as a team average point differential adjusted for strength of schedule. Using two team’s functional ratings we can predict the expected point differential at any time in the game. We looked at three variations of our model accounting for home-court advantage in different ways. We use the 2018–2019 NCAA Division 1 men’s college basketball season to test the models and determined that home-court advantage is statistically important but does not differ between teams.

Betting odds are generally considered to represent accurate reflections of the underlying probabilities for the outcomes of sporting events. There are, however, known to be a number of inherent biases such as the favorite-longshot bias in which outsiders are generally priced with poorer value odds than favorites. Using data from European soccer matches, this paper demonstrates the existence of another bias in which the match odds overreact to favorable and unfavorable runs of results. A statistic is defined, called the Combined Odds Distribution (COD) statistic, which measures the performance of a team relative to expectations given their odds over previous matches. Teams that overperform expectations tend to have a high COD statistic and those that underperform tend to have a low COD statistic. Using data from twenty different leagues over twelve seasons, it is shown that teams with a low COD statistic tend to be assigned more generous odds by bookmakers. This can be exploited and a sustained and robust profit can be made. It is suggested that the bias in the odds can be explained in the context of the “hot hand fallacy”, in which gamblers overestimate variation in the ability of each team over time.

This work is concerned with the interpretation of the results produced by the well known Elo algorithm applied in various sport ratings. The interpretation consists in defining the probabilities of the game outcomes conditioned on the ratings of the players and should be based on the probabilistic rating-outcome model. Such a model is known in the binary games (win/loss), allowing us to interpret the rating results in terms of the win/loss probability. On the other hand, the model for the ternary outcomes (win/loss/draw) has not been yet shown even if the Elo algorithm has been used in ternary games from the very moment it was devised. Using the draw model proposed by Davidson in 1970, we derive a new Elo-Davidson algorithm, and show that the Elo algorithm is its particular instance. The parameters of the Elo-Davidson are then related to the frequency of draws which indicates that the Elo algorithm silently assumes games with 50% of draws. To remove this assumption, often unrealistic, the Elo-Davidson algorithm should be used as it improves the fit to the data. The behaviour of the algorithms is illustrated using the results from English Premier League.

In assessments of sports-related injury severity, time loss (TL) is measured as a count of days lost to injury and analyzed using ordinal cut points. This approach ignores various athlete and event-specific factors that determine the severity of an injury. We present a conceptual framework for modeling this outcome using univariate random effects count or survival regression. Using a sample of US collegiate soccer-related injury observations, we fit random effects Poisson and Weibull Regression models to perform “severity-adjusted” evaluations of TL, and use our models to make inferences regarding the recovery process. Injury site, injury mechanism and injury history emerged as the strongest predictors in our sample. In comparing random and fixed effects models, we noted that the incorporation of the random effect attenuated associations between most observed covariates and TL, and model fit statistics revealed that the random effects models (AIC Poisson = 51875.20; AIC Weibull-AFT = 51113.00) improved model fit over the fixed effects models (AIC Poisson = 160695.20; AIC Weibull-AFT = 53179.00). Our analyses serve as a useful starting point for modeling how TL may actually occur when a player is injured, and suggest that random effects or frailty based approaches can help isolate the effect of potential determinants of TL.

Drawing on the golf-related example of regression to the mean as presented by Kahneman in his best-selling book, Thinking Fast and Slow , this study shows how the regression-to-the-mean phenomenon is revealed in first- and second-round scoring in 11 different golfer populations, ranging from golfers with the highest level of skill (professional golfers on the PGA TOUR) to amateur groups of much lower skill. Using the mathematics of truncated normal distributions, the study introduces a new method for estimating the mix between variation in scoring due to differences in player skill and that due to luck. Estimates of the skill/luck mix are very close to those obtained using the regression-based methodology of Morrison and are nearly identical to those implied by fixed effects regression models where fixed player and round effects are estimated simultaneously. The study also sheds light on the “paradox of skill,” originally suggested by Gould and developed further by Mauboussin, as it relates to golf by showing that luck plays a more important role in determining player scores in higher-skilled golfer groups compared with lower-skilled groups.

We study the stability of a time-aware version of the popular Massey method, previously introduced by Franceschet, M., E. Bozzo, and P. Vidoni. 2017. “The Temporalized Massey’s Method.” Journal of Quantitative Analysis in Sports 13: 37–48, for rating teams in sport competitions. To this end, we embed the temporal Massey method in the theory of time-varying averaging algorithms, which are dynamic systems mainly used in control theory for multi-agent coordination. We also introduce a parametric family of Massey-type methods and show that the original and time-aware Massey versions are, in some sense, particular instances of it. Finally, we discuss the key features of this general family of rating procedures, focusing on inferential and predictive issues and on sensitivity to upsets and modifications of the schedule.