A novel application of PageRank and user preference algorithms for assessing the relative performance of track athletes in competition PageRank assessment of track athletes

Abstract

'Wei-Xing Zhou'] Ranking enables coaches, sporting authorities, and pundits to determine the relative performance of individual athletes and teams in comparison to their peers. While ranking is relatively straightforward in sports that employ traditional leagues, it is more difficult in sports where competition is fragmented (e.g. athletics, boxing, etc.), with not all competitors competing against each other. In such situations, complex points systems are often employed to rank athletes. However, these systems have the inherent weakness that they frequently rely on subjective assessments in order to gauge the calibre of the competitors involved. Here we show how two Internet derived algorithms, the PageRank (PR) and user preference (UP) algorithms, when utilised with a simple ‘who beat who’ matrix, can be used to accurately rank track athletes, avoiding the need for subjective assessment. We applied the PR and UP algorithms to the 2015 IAAF Diamond League men’s 100m competition and compared their performance with the Keener, Colley and Massey ranking algorithms. The top five places computed by the PR and UP algorithms, and the Diamond League ‘2016’ points system were all identical, with the Kendall’s tau distance between the PR standings and ‘2016’ points system standings being just 15, indicating that only 5.9% of pairs differed in their order between these two lists. By comparison, the UP and ‘2016’ standings displayed a less strong relationship, with a tau distance of 95, indicating that 37.6% of the pairs differed in their order. When compared with the standings produced using the Keener, Colley and Massey algorithms, the PR standings appeared to be closest to the Keener standings (tau distance = 67, 26.5% pair order disagreement), whereas the UP standings were more similar to the Colley and Massey standings, with the tau distances between these ranking lists being only 48 (19.0% pair order disagreement) and 59 (23.3% pair order disagreement) respectively.