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?

TrueHoop at MIT Sloan Sports Analytics Conference

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 is, when you are no longer in foul trouble.

With that idea in mind, two distinct possibilities were named and explored for when foul trouble arises for any starter. Was the team’s “current value” (playing a starter with foul trouble) a better choice than the “option value” (replacing the starter with a bench player) when it comes to the team’s future performance and achieving the ultimate goal of winning the game?

By digging through three years of NBA play-by-play data from 2006-2009, the trio’s research examined the starters of all 30 NBA teams, exploring whenever they got into foul trouble over that time period.

After plugging in that data to an advanced formula, the group’s conclusions, with few exceptions, agreed with most coaches’ conventional wisdom; benching your guy was the smartest move.

The decision to yank any starter with early foul woes had the strongest evidence in its support, with the choice to go with any option value (bench player) highly outperforming the effect of keeping said starter on the floor by anywhere from 5-10 percent in winning probability in the first half of games.

The value of keeping the affected player out of more severe foul trouble, combined with the propensity of the player to play tentatively on both ends of the floor (avoiding charges, loose defense, etc.) made the option value the better choice in nearly all situations, according to the trio’s data. The lone exception? Late in games, when there is no use in protecting your guys for later.

As a whole, the data confirmed the usual reaction by all NBA coaches on how to handle foul trouble through the years. On average, any NBA coach would sit out their players 67 percent of the time when they faced any sort “foul trouble” throughout the game.

The unsurprising outlier in that department? None other than Don Nelson, who let his players, play through foul trouble and essentially anything else during his final hurrah in Golden State.

Perhaps the most intriguing part of the research, however, was seeing how the coaches treated various players around the league when they were whistled early and often.

Incredibly, three players (Johan Petro, Quinton Ross, and Jeff Foster) were given the hook 100 percent of the time they ran into trouble. As a whole, defensive big men and stoppers made up all of the players in the top 10 in that category, largely guys who need to be able to operate aggressively on the defensive end in order to be effective.

On the opposite end of the spectrum, veteran guards and shooters brought up the rear out of players who hit the bench the least if foul trouble comes knocking. Baron Davis bottomed out the list with just a 32 percent substitution rate in those instances, with offensive stars Jason Richardson and Chris Paul following shortly thereafter.

Names like that clearly show different players and scenarios bring forth varying reactions by the coaches in how they handle any foul problems. When push comes to shove though, the numbers back conventional wisdom in this department. So next time you question your team’s coach after making his star player take an early seat, know that in the long run, the numbers back him up.