Statistical analysis of top performers in sport with emphasis on the relevance of outliers

Abstract

This paper presents the findings of statistical analysis of the top career performances by men in a range of well-known sports. The analytical techniques applied are commonly used in engineering hydrology for the analysis of extreme rainfalls, floods and droughts. Initially, the raw data sets were assumed to be normally distributed but because the data sets were often highly skewed, the results from logarithmically transformed data sets were preferred in most instances. For each activity analyzed in each sport studied the main results were the Z-score and performance ratio of the rank 1 performer. These parameters are both dimensionless, and hence it was possible to use these parameters to directly compare the rank 1 performers in each of the sports studied. While for most data sets the very top performances were of similar standing from a statistical viewpoint there were several notable exceptions, which appeared to be classical statistical outliers. These suspected outliers were the performances of Don Bradman, an Australian cricketer; Jack Nicklaus, an American golfer; David Campese, an Australian rugby union player; and Wayne Gretzky, a Canadian and American ice hockey player. Longevity, as a top sportsman, was an important factor in the great performances of Nicklaus and Campese and, to a lesser degree, Gretzky. However, longevity was not an important factor in Bradman's career. Hence it was concluded that Bradman's performances were more extraordinary than any other sportsman and that it can be strongly argued that he, was the greatest ever sportsman.