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Using principal component analysis and process behavior charting to answer “Is Secretariat the fastest U.S. racing thoroughbred to date?”
Abstract
Statistical evidence is presented to answer the title question using graphical tools from process behavior charting as well as ranking methods based on principal component analysis. These tools provide strong data evidence to answer the question convincingly.
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A comprehensive comparative survey is presented, covering official rating systems as published by internationally recognized sports federations. Mind sports and physical sports are both included. As of November 2010, competitions in 159 international sports are organized by sports federations recognized by the IOC, Sport Accord and by Wikipedia identified under “List of International Sport Federations.†Of the 159 sports, 18 are combat sports in which opponents are in direct physical contact as in boxing and wrestling, 74 are independent sports in which significant contact is not allowed as in swimming and archery and 67 are object sports in which indirect contact is allowed while opponents attempt to control an object as in basketball and chess. Of the 159 sports, 60 sports have no rating system, two combat sports have a subjective rating system, 84 sports have an accumulative system in which points accrue non-decreasingly over some window of time, and 13 sports have an adjustive system in which a rating self adjusts based on the difference between some observed result and a prediction of that result based on past performance. For accumulative rating systems, features include converting results to points, ageing results more than one year old, and possibly adjusting points using other performance measures. Such systems are favored by tournament organizers who want to encourage many top competitors to enter as for skiing and tennis. The adjustive systems include Elo, probit and averaging methods. These systems are favored for their technical sophistication by sports such as chess, draughts, go, cricket, and women’s soccer. This study thus identifies the observed successful methodology used by the various sports federations to publish comparative ratings. Predictive success of certain rating systems are tabulated for FIBA world championship basketball, Grand Slam tennis and FIFA men’s world cup soccer.
Racing data provides a rich source of analysis for quantitative researchers to study multi-entry competitions. This paper first explores statistical modeling to investigate the favorite-longshot betting bias using world-wide horse race data. The result shows that the bias phenomenon is not universal. Economic interpretation using utility theory will also be provided. Additionally, previous literature have proposed various probability distributions to model racing running time in order to estimate higher order probabilities such as probabilities of finishing second and third. We extend the normal distribution assumption to include certain correlation and variance structure and apply the extended model to actual data. While horse race data is used in this paper, the methodologies can be applied to other types of racing data such as cars and dogs.
This article describes a method for predicting the outcome of National Hockey League (NHL) games. We combine a model for goal scoring and yielding, and one for penalty commission, in a Markov-type computation and a simulation model that produce predicted probabilities of victory for each team. Where these differ substantially from the market probabilities, we make “bets” according to a simple strategy. Our return on investment is both positive and statistically significant.
Many games and sports, including races, involve outcomes in which competitors are rank ordered. In some sports, competitors may play in multiple events over long periods of time, and it is natural to assume that their abilities change over time. We propose a Bayesian state-space framework for rank ordered logit models to rate competitor abilities over time from the results of multi-competitor games. Our approach assumes competitors’ performances follow independent extreme value distributions, with each competitor’s ability evolving over time as a Gaussian random walk. The model accounts for the possibility of ties, an occurrence that is not atypical in races in which some of the competitors may not finish and therefore tie for last place. Inference can be performed through Markov chain Monte Carlo (MCMC) simulation from the posterior distribution. We also develop a filtering algorithm that is an approximation to the full Bayesian computations. The approximate Bayesian filter can be used for updating competitor abilities on an ongoing basis. We demonstrate our approach to measuring abilities of 268 women from the results of women’s Alpine downhill skiing competitions recorded over the period 2002–2013.
That we cannot make all pieces of a given kind of product identically alike is accepted as a general truth. It follows that the qualities of pieces of the same kind of product differ among themselves, or, in other words, the quality of product must be expected to vary. The causes of this variability are, in general, unknown. The present paper presents a scientific basis for determining when we have gone as far as it is economically feasible to go in eliminating these unknown or chance causes of variability in the quality of a product. When this state has been reached, the product is said to be controlled because it is then possible to set up limits within which the quality may be expected to remain in the future. By securing control, we attain the five economic advantages discussed in Part III.
The Kentucky Derby, Preakness and Belmont Stakes: A Comprehensive History
- R Sowers