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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Complex dynamics in the distribution of players' scoring performance in Rugby Union world cups
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Complex dynamics in the distribution of players' scoring performance in Rugby Union world cups

机译：橄榄球联盟世界杯球员得分表现分布的复杂动态

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摘要

The evolution of the scoring performance of Rugby Union players is investigated over the seven rugby world cups (RWC) that took place from 1987 to 2011, and a specific attention is given to how they may have been impacted by the switch from amateurism to professionalism that occurred in 1995. The distribution of the points scored by individual players, ~(Ps), ranked in order of performance were well described by the simplified canonical law ~(Ps)∝(~(r+φ)-α), where r is the rank, and φ and α are the parameters of the distribution. The parameter α did not significantly change from 1987 to 2007 (α=0.92±0.03), indicating a negligible effect of professionalism on players' scoring performance. In contrast, the parameter φ significantly increased from φ=1.32 for 1987 RWC, φ=2.30 for 1999 to 2003 RWC and φ=5.60 for 2007 RWC, suggesting a progressive decrease in the relative performance of the best players. Finally, the sharp decreases observed in both α(α=0.38) and φ(φ=0.70) in the 2011 RWC indicate a more even distribution of the performance of individuals among scorers, compared to the more heterogeneous distributions observed from 1987 to 2007, and suggest a sharp increase in the level of competition leading to an increase in the average quality of players and a decrease in the relative skills of the top players. Note that neither α nor φ significantly correlate with traditional performance indicators such as the number of points scored by the best players, the number of games played by the best players, the number of points scored by the team of the best players or the total number of points scored over each RWC. This indicates that the dynamics of the scoring performance of Rugby Union players is influenced by hidden processes hitherto inaccessible through standard performance metrics; this suggests that players' scoring performance is connected to ubiquitous phenomena such as anomalous diffusion.
机译：在1987年至2011年的七届橄榄球世界杯（RWC）上，对橄榄球联盟球员得分表现的演变进行了调查，并特别关注了他们可能会受到从业余到职业的转变的影响。发生在1995年。通过简化的经典定律〜（Ps）∝（〜（r +φ）-α）很好地描述了按表现顺序排列的各个玩家得分（〜Ps）的得分分布，其中r是等级，而φ和α是分布的参数。从1987年到2007年，参数α没有明显变化（α= 0.92±0.03），这表明职业素养对球员得分表现的影响可忽略不计。相反，参数φ从1987 RWC的φ= 1.32、1999年到2003 RWC的φ= 2.30和2007 RWC的φ= 5.60显着增加，表明最佳球员的相对表现逐渐下降。最后，与从1987年至2007年观察到的分布更不均匀相比，在2011年RWC中观察到的α（α= 0.38）和Φ（φ= 0.70）的急剧下降表明得分者之间个人绩效的分布更加均匀。并建议竞争水平急剧提高，从而导致平均水平的球员提高和顶级球员的相对技能下降。请注意，α和φ都不与传统性能指标显着相关，例如最佳球员得分，最佳球员参加的比赛次数，最佳球员团队的得分或总数每个RWC得分的百分比。这表明橄榄球联盟球员得分表现的动态受到迄今为止通过标准绩效指标无法访问的隐藏过程的影响;这表明玩家的得分表现与异常扩散等普遍现象相关。

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