城市马拉松赛参赛者位次变化分布及其与竞争程度的关联的研究

The Study on the Correlation between Participant Ranking Variation Distribution and the Level of Competition in City Marathons

近十多年来,人类动力学领域关于时间特性和空间特性的研究迅猛发展.本文统计近十多年来纽约城市马拉松赛和近四年来波士顿马拉松赛前1 000名男子参赛者和前1 000名女子参赛者的参赛数据,分析参赛者在7个中间计时赛段中的位次变化情况,发现参赛者在各中间计时赛段中的位次变化均遵循洛伦兹分布(柯西分布).引入参赛者在各计时赛段内的位次变化的方均根值来描述该赛段内的竞争激烈程度,进一步研究各计时赛段内竞争激烈程度与位次变化分布参数的关联,发现在各中间计时赛段中参赛者的位次变化分布图形的尖锐程度能直观地反映该赛段内参赛者的竞争激烈程度,参赛者在某赛段内的竞争激烈程度越低,该赛段内参赛者的位次变化分布曲线越尖锐.

In recent 10 more years, the research of the time response and spatial characteristics in human dynamics area has been rapidly developed. The datasets from the records of the participants of top1000 male athletes and top 1000 female athletes in both New York City marathons for recent 10 years and Boston marathons for recent 4 years are counted in this paper. From the above datasets, the runners’ ranking changes in 7 different internal timing lengths are also analyzed and therefore the ranking changes are always abide by Lorentz Distribution （Cauchy Distribution） during their participation in the mediate time trials. The competition fierce degree is described through the introduction of root-mean-square value of ranking changes in all time trial stages. The fierce degree of distribution graph for ranking changes in mediate time trials is discovered via further research on the correlation between the competition fierce degree and the variation distribution parameters, which reflects intuitively the competition fierce degree in such a contest. In conclusion, the lower the participant has competition fierce degree, the sharper the ranking change distribution curve of the participant becomes in such a time trial length.