An economist’s study of the optimal timing of substitutions in football matches (spanning a bunch of 2009/10 leagues) discovered the following:
Dr. Myers analyzed the substitutions and ensuing results of every game played during the 2009-10 season in the top English, Spanish, Italian and German professional leagues, as well as the 2010 Major League Soccer season and the 2010 World Cup. He concluded that if their team is behind, managers should make the first substitution prior to the 58th minute, the second substitution prior to the 73rd minute and the third prior to the 79th minute. Teams that follow these guidelines improve—score at least one goal—roughly 36% of the time. Teams that don’t follow the rule improve about 18.5% of the time. He noted 1,037 instances the rule could have been applied and found that managers abide by it a little less than half the time. He also found that the timing of subs has no effect on the team ahead in the score or if the match is tied.