Beggs Clive B, Shepherd Simon J, Emmonds Stacey, Jones Ben
Institute for Sport, Physical Activity and Leisure, Carnegie Faculty, Leeds Beckett University, Leeds, West Yorkshire, United Kingdom.
Medical Biophysics Laboratory, University of Bradford, Bradford, United Kingdom.
PLoS One. 2017 Jun 2;12(6):e0178458. doi: 10.1371/journal.pone.0178458. eCollection 2017.
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.
排名使教练、体育管理机构和专家能够确定个别运动员和团队相对于其同行的相对表现。在采用传统联赛的运动中，排名相对简单，但在比赛分散的运动（如田径、拳击等）中则较为困难，因为并非所有参赛者都相互竞争。在这种情况下，通常采用复杂的积分系统来对运动员进行排名。然而，这些系统存在固有的弱点，即它们经常依赖主观评估来衡量相关参赛者的水平。在此，我们展示了两种源自互联网的算法，即网页排名（PR）算法和用户偏好（UP）算法，与一个简单的“谁击败了谁”矩阵一起使用时，如何能够准确地对田径运动员进行排名，从而避免主观评估的需要。我们将PR算法和UP算法应用于2015年国际田联钻石联赛男子100米比赛，并将它们的表现与基纳、科利和梅西排名算法进行了比较。PR算法和UP算法计算出的前五名与钻石联赛“2016”积分系统完全相同，PR排名与“2016”积分系统排名之间的肯德尔tau距离仅为15，这表明在这两个列表中，只有5.9%的配对在顺序上有所不同。相比之下，UP排名与“2016”排名之间的关系较弱，tau距离为95，这表明37.6%的配对在顺序上有所不同。与使用基纳、科利和梅西算法得出的排名相比，PR排名似乎最接近基纳排名（tau距离 = 67，配对顺序不一致率为26.5%），而UP排名与科利和梅西排名更为相似，这些排名列表之间的tau距离分别仅为48（配对顺序不一致率为19.0%）和59（配对顺序不一致率为23.3%）。特别是，UP算法对“一次性”获胜者的排名高于PR算法，这表明UP算法捕捉到了与PR算法不同的特征，PR算法可能更适合预测淘汰赛等未来赛事的表现，而不是用于钻石联赛这样的比赛。因此，这些源自互联网的算法似乎具有很大的潜力，可以客观地评估田径运动员的相对表现，而无需复杂的积分等效表。重要的是，由于这两种算法都使用“谁击败了谁”模型，它们会自动根据比赛强度进行调整，从而避免了主观决策的需要。
