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 consider the problem of finding checkerboard copulas for modeling multivariate distributions. A checkerboard copula is a distribution with a corresponding density defined almost everywhere by a step function on an m-uniform subdivision of the unit hyper-cube. We develop optimization procedures for finding copulas defined by multiply-stochastic matrices matching available information. Two types of information are used for building copulas: 1) Spearman Rho rank correlation coefficients; 2) Empirical distributions of sums of random variables combined with empirical marginal probability distributions. To construct checkerboard copulas we solved optimization problems. The first problem maximizes entropy with constraints on Spearman Rho coefficients. The second problem minimizes some error function to match available data. We conducted a case study illustrating the application of the developed methodology using property and casualty insurance data. The optimization problems were numerically solved with the AORDA Portfolio Safeguard (PSG) package, which has precoded entropy and error functions. Case study data, codes, and results are posted at the web.
In this work, we propose a spatio-temporal Markovian-like model for ordinal observations to predict in time the spread of disease in a discrete rectangular grid of plants. This model is constructed from a logistic distribution and some simple assumptions that reflect the conditions present in a series of studies carried out to understand the dissemination of a particular infection in plants. After constructing the model, we establish conditions for the existence and uniqueness of the maximum likelihood estimator (MLE) of the model parameters. In addition, we show that, under further restrictions based on Partially Ordered Markov Models (POMMs), the MLE of the model is consistent and normally asymptotic. We then employ the MLE’s asymptotic normality to propose methods for testing spatio-temporal and spatial dependencies. The model is estimated from the real data on plants that inspired the model, and we used its results to construct prediction maps to better understand the transmission of plant illness in time and space.
We prove and describe in great detail a general method for constructing a wide range of multivariate probability density functions. We introduce probabilistic models for a large variety of clouds of multivariate data points. In the present paper, the focus is on star-shaped distributions of an arbitrary dimension, where in case of spherical distributions dependence is modeled by a non-Gaussian density generating function.
This paper studies the identification of players’ preferences and beliefs in discrete choice games using experimental data. The experiment comprises a set of games that differ in their matrices of monetary payoffs. The researcher is interested in the identification of preferences (utility of money) and beliefs on the opponents’ expected behavior, without imposing equilibrium restrictions or parametric assumptions on utility and belief functions. We show that the hypothesis of unbiased/rational beliefs is testable as long as the set of games in the experiment imply variation in monetary payoffs of other players, keeping the own monetary payoff constant. We present conditions for the full identification of utility and belief functions at the individual level – without restrictions on players’ heterogeneity in preferences or beliefs. We apply our method to data from two experiments: a matching pennies game, and a public good game.
Predictive football modelling has become progressively popular over the last two decades. Due to this, numerous studies have proposed different types of statistical models to predict the outcome of a football match. This study provides a review of three different models published in the academic literature and then implements these on recent match data from the top football leagues in Europe. These models are then compared utilising the rank probability score to assess their predictive capability. Additionally, a modification is proposed which includes the travel distance of the away team. When tested on football leagues from both Australia and Russia, it is shown to improve predictive capability according to the rank probability score.
We propose a Markovian model to calculate the winning probability of a set in a volleyball match. Traditional models take into account that the scoring probability in a rally (SP) depends on whether the team starts the rally serving or receiving. The proposed model takes into account that the different rotations of a team have different SPs. The model also takes into consideration that the SP of a given rotation complex 1 (K1) depends on the players directly involved in that complex. Our results help to design general game strategies and, potentially, more efficient training routines. In particular, we used the model to study several game properties, such as the importance of having serve receivers with homogeneous performance, the effect of the players’ initial positions on score evolution, etc. Finally, the proposed model is used to diagnose the performance of the female Colombian U23 team (U23 CT).
We examine correlates of tenure length for professional soccer managers. Using 521 managers from Major League Soccer (MLS), Spain’s La Liga, and the English Premier League (EPL) whose tenures occurred between 2000 and 2015, we assess the association between both performance-related and non-performance variables, and manager duration. Performance variables include measures of a team’s ranking (or position) and relegation/promotion indicators. Non-performance variables include manager nationality and age, the timing of a manager’s hire, and the team’s wage bill. We employ survival analytic methods, including Cox’s proportional hazards model, to explore the effects of fixed and time-dependent covariates on coach tenure length. We find that La Liga managers have shorter survival, as do managers who were older when they were hired. Furthermore, finishing with a better ranking and, more importantly, improving on previous team performance yields longer survival. Most strikingly, however, we find a significant disparity in the comparison of domestic and foreign managers within a league. While the difference in longevity between domestic and foreign managers in La Liga and the EPL was minimal, American managers in MLS survived significantly longer than their foreign peers.