How much trouble is early foul trouble?

It’s a classic conundrum for any NBA coach. A star player gets saddled with two early fouls in the opening six minutes of a game, which prompts the question: Do you pull your guy to help ensure he’ll be available later on when the foul trouble has subsided? Or does keeping your starter on the floor, to help keep the game competitive, outweigh the risk of the player fouling out down the line? Philip Z. Maymin, Allan Maymin and Eugene Shen sought the answer to that endless debate in their research paper, “How Much Trouble Is Early Foul Trouble?” Before the guys got into specifics, they first had to create a set standard for foul trouble. They decided on a formula, based on coaches’ tendencies to pull their starters. They define foul trouble as at least one more foul than the current quarter or put simply by the formula “Q +1.” For example, if you have three fouls in the second quarter, you meet in the criteria, until the third quarter that...