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

Abstract

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. In particular, the UP algorithm ranked ‘one-off’ victors more highly than the PR algorithm, suggesting that the UP algorithm captures alternative characteristics to the PR algorithm, which may more suitable for predicting future performance in say knockout tournaments, rather than for use in competitions such as the Diamond League. As such, these Internet derived algorithms appear to have considerable potential for objectively assessing the relative performance of track athletes, without the need for complicated points equivalence tables. Importantly, because both algorithms utilise a ‘who beat who’ model, they automatically adjust for the strength of the competition, thus avoiding the need for subjective decision making.

What Is Performance? A Scoping Review of Performance Outcomes as Study Endpoints in Athletics

“…The thematic analysis of the 11 articles brought to light the reporting of performance categories, themes, and constructs to describe POs within individual sports like athletics (Table 1). Two categories were identified to define the ‘performance metrics’ that represent the event or competition result: ‘continuous’ data ( n = 3) such as heights [18,19], times [18,19,20], distances [18,19], and conversion to IAAF points scores [18,19,20] or ‘ordinal’ data ( n = 9) ranked against a finishing position [19,21] or performance standards including personal bests [22,23], season’s bests [23,24,25,26,27], national records [25] or world records [28]. One article reported performance metrics according to both categories, continuous and ordinal [19].…”

“…Two themes describe the ‘framework’ within which the scope of each performance metric resides: Comparison of the result or rank with other athletes (INTER-personal scope, n = 3) [19,21,25], or comparison of the result or rank relative to one’s own previous performance (INTRA-personal scope, n = 10) [18,19,20,22,23,24,25,26,27,28]. Two articles reported performance metrics within the scope of both frameworks, intra- and inter-personal [19,25].…”

“…Two constructs were identified to ‘analyse’ the themed categories: ‘deviations’ ( n = 8) represent a divergence from a performance trend like meet, annual or career performances [18,20,23,24,27] or divergence from performance standards such as season’s best or ranking [21,25,26], and ‘associations’ ( n = 6) between the performance metric and predetermined independent variables, such as psychological factors [19,25,28], physical or physiological factors [22], and societal factors [24,27]. Three articles analysed performance metrics by both constructs, deviations and associations [24,25,27].…”

“…Correspondingly, the calibre of competition at an event may result in overvalued or undervalued rankings. An athlete may continually lose narrowly to the highest-calibre athletes and be poorly ranked; conversely, an athlete may continually beat competitors of lower calibre and be ranked unduly high [21]. Applying a contextual framework to a performance metric enables the evaluation of the resulting PO to move from a singular endpoint with limitations to a more versatile endpoint that captures and considers a broader array of factors.…”

Hidden dynamics of soccer leagues: The predictive ‘power’ of partial standings

“…While many of these methodologies remain unpublished because of confidentiality issues, others are in the public domain. For example, well established mathematical techniques such as the Colley [3–5] and Keener [4–6] algorithms aim to rank teams based on past performance in fractured competition, while techniques such as the Pythagorean expectation system [7, 8] attempt to predict future league performance based on past performance. Still other techniques, such as the Bradley-Terry [9, 10] and Elo [4, 11] methods, seek to predict the outcome of single matches using a probabilistic methodology.…”