Economics may have failed the housing market, the labor market and general economy. But economics have finally solved one of the most pressing and perplexing questions in modern times: When do you pull your starters when they get into foul trouble in basketball?

Researchers Allan Maymin, Philip Maymin, and Eugene Shen applied "insights and tools from finance" (alright!) to conclude that NBA teams perform significantly worse if a starter with foul trouble is allowed to remain in the game, especially in the third quarter.

What's more, they estimate that applying their lessons could save a hypothetical couch up to five games a year. Most years, five games is more than the difference between an 8th-place playoff spot and an early trip home for the off-season.

The key finding:

A hypothetical coach who plays on average two starters through foul trouble for the second half of the third quarter rather than playing them without foul trouble for the first half of the fourth quarter in otherwise close games would hurt his probability of winning by about six percent. Thus in expectation over an 82-game regular season of otherwise close games he would lose about five games that he could have won by yanking his foul-troubled starters.

Read the full story in this paper (PDF).