State transitions among groups of cyclists in cycling points races.

This study analyzed the global state of groups formed by cyclists competing in three different points races and considered the behaviour of individual cyclists in those races. We measured the time difference between the front cyclist and the other cyclists when they crossed the centrelines of home and back straights in order to quantify the global configuration of cyclists in terms of their density and features of states, extracted using principal components analysis (PCA). We examined whether the group separation and group density that characterize the cycling race can be extracted by PCA. We interpreted the PCA results to explain the separation and density of the group using the first and second principal components. Then, we defined the state of configuration of the cyclists in each lap in the plane of the first and second principal components. Subsequently, the state transition probabilities were obtained. States 1, 2, 3, and 4 corresponded to the third, second, first, and fourth quadrants, respectively. State 1 represented a state comprising one dense group, state 2 represented one stretched group, state 3 represented a divided group, and state 4 represented an escape group far from a single dense group.HighlightsAn approach to understand the collective behaviour of cycling points races through principal component analysis was effective for quantifying the configuration of the cyclists.Principal component analysis of the global configuration of the cyclists in the points races revealed the fission-fusion dynamics was characterized by two components. The density of a group and number of groups, and transitions among four states was defined by these two components.State transition probabilities indicate that the group separation states were more frequent in the latter half of the sprint interval, and it was difficult to re-combine the separated groups into one.The riders and coaches need to be aware of the stretching and separation of the group, even if it does not occur immediately before the sprint as the positioning of a cyclist in the group would be important at that time.