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To examine did eddie the eagle win any medals the statistical significance of B value for each manager, we generated sequences of interevent times from the exponential distribution whose mean was equal to that of the original data.

To examine the statistical significance of the cross-correlation obtained from the original data, we generated randomized sequences of formation changes as follows.

Taiji M, Ikegami T ( 1999 ) Dynamics of internal models in game players.

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As in the case of formation changes, we regarded that a manager was changed when the manager directed a team in a given match but did not do so in the next match.Empirical studies also suggest that humans obeying reinforcement learning does not improve the performance in complex environments.We did not find a significant relationship between the usage of the wsls and the probability of winning for both J-League (Pearsons.,., n ) and Bundesliga (r.,., n ) data.Proc Natl Acad Sci 95 (.In the present study, we have neglected various factors that potentially affect the likelihood of formation change because our data sets did not contain the relevant information.Hirotsu N, Wright MB ( 2006 ) Modeling tactical changes of formation in association football as a zero-sum game.In particular, a formation is a part of tactics to determine how players participate in offense and defense and considered to affect match results.The interevent time for formation changes was defined by ik tik tik ( i Nk ).The dependent variable was the occurrence or lack thereof of formation changes, which was binary.Equal probability such that the number of s in the synthesized sequence was the equal to that in the original sequence.R Core Team ( 2014 ) R: a language and environment for statistical computing.

R Foundation for Statistical Computing, Vienna.

In addition, we excluded matches immediately after a change of manager because we were not interested in formation changes induced by a change of manager.

Table 9 Results of the glmm analysis for the Fussballdaten data when all the independent variables were considered Winti (i 1, 2) is the binary variable representing whether or not the team has won the (t i)th match (0: no win, 1: win).

Because formation changes occurring as a result of a managers move or after a long absence were not considered to be strategic, we discarded the corresponding intervals.This is consistent with negative persistence effects reported in previous literature,.e., the results of the current and previous matches tend to be the opposite.Appendix E: Cross-correlation analysis To further investigate possible relationships between formation changes and match results, we measured the cross-correlation between the two.We generated a randomized sequence for each team.The results indicate that a swift implementation of a new formation in the win-stay lose-shift manner may not be a successful managerial rule of thumb.The colored bars correspond to the teams or managers that have played at least 100 matches.