When Should a Soccer Manager Insert His Subs?

Nifty article in today’s Journal about a nifty study by Bret Myers of Villanova:

The pace and flow of soccer generally make it difficult for managers to affect the outcome of a match once it begins. Since soccer has almost no stoppages for coaches to draw on clipboards or strategize with their players, a manager’s most critical in-game decision may be choosing when to utilize their three substitutions. …
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.

I don’t know if there’s much of an empirical literature about substitution for other team sports (this baseball study, e.g., is more about optimizing matchups). It does strike me that as much as “conditioning” is appreciated in sports, the role of fatigue — mental and physical — is perhaps underappreciated. Yet another reason to think about using an “opener” in baseball?
At the top of this column is a (poor) photo I snapped in Barcelona in December, of Lionel Messi getting subbed in the 54th minute in a Copa del Rey match against Bilbao. (Below is a photo of Messi in action in that same match.) The other subs: David Villa at 63 minutes and Adriano at 79 minutes — just right, according to Myers’s research. But it didn’t work out for Barca. Neither Messi nor the others provided much of a spark as a sub, and the match was a 0-0 draw. He was nevertheless wonderful to watch.