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. 2017 Jun 2;12(6):e0178458.
doi: 10.1371/journal.pone.0178458. eCollection 2017.

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

Affiliations

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

Clive B Beggs et al. PLoS One. .

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.

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Conflict of interest statement

Competing Interests: Clive Beggs and Simon Shepherd have nothing to disclose. Stacey Emmonds holds a coaching position at Doncaster Belles women’s football team for which she receives financial support for research activities. Ben Jones has received financial compensation from Leeds Rugby for coaching and consultancy services, the Rugby Football Union for research, and holds a position with Rugby Football League for which he receives financial support for research activities. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

Figures

Fig 1
Fig 1. Small web containing just four web pages.
Fig 2
Fig 2. Graph for user preference rating example.
The nodes represent the films and the edges represent the user ratings, with edge scores representing the numerical difference between the user ratings for the two nodes.
Fig 3
Fig 3. Connectivity networks between athletes after: (A) the first three races; (B) the first six races; and (C) all ten races.
Fig 4
Fig 4. Scatter plot of the paired PageRank scores and points (calculated using the 2016 points system) awarded to the top 23 athletes.
Fig 5
Fig 5. Scatter plot of the paired user preference scores and points (calculated using the 2016 points system) awarded to the top 23 athletes.

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