The concept of "foul trouble" is a commonly held assumption that has trickled down into all levels of basketball. When someone got two fouls for John Chaney at Temple, they'd sit until the second half. Every time. But why is that? Before I take a hack at it, I'd like to direct you to a forward by Spurs blog Pounding the Rock for a terrific article on turnovers.
The way sports are analyzed is based on certain assumptions, and I think most people (myself included) are completely blind to most of those assumptions. They are the way we understand the game we watch, and the context in which we view each performance. When we say that someone played well, we've made an evaluation that's not just based on previous experience, but also guided and shaped by hundreds of principles that we never consciously consider.
So do your best to spit up the apple you've been fed your whole basketball-watching life and attempt to be a little more open-minded as I try to tear down your beliefs after the jump.
Most of the time, I don't think there's a reason coaches take players out once they've been deemed "in foul trouble". I think they've been bred to believe that once a player has gotten two fouls in the first quarter or three fouls in the first half, they have to sit. Why? Because they have three fouls. But why? Because they could foul out?
What is the main concern about players fouling out? Answer: That they wouldn't be able to play as many minutes. So by taking this player out, the coach is already assuring that they won't be playing as many minutes. Yes they're available on the bench in case something happens, but they don't allow the player to be on the court, playing into the opponent's hand anyway.
Let's consider an example. Lavoy Allen, to be topically relevant. Lavoy played roughly 8 minutes in the first half. He picked up three fouls, so Doug Collins decided to sit him for the last 7:43 of the second quarter. He didn't want him to pick up his 4th foul. That's understandable. But by sitting him down, he had to go to Spencer Hawes to cover Kevin Garnett, and the defense (and offense) struggled mightily. Even as KG hit jumper after jumper while Hawes hung out five feet away, Doug kept Lavoy on the bench. Well, he may as well have fouled out then.
Lavoy would go on to play 12 minutes in the second half, picking up two more fouls, and finished the game with 20 minutes of play and 5 fouls. He had a foul to spare. The game was obviously out of hand by midway through the third, but Lavoy managed to get called for two more fouls and still not foul out. What would have happened if Collins left him in the game in the second? After he exited for Spence, the Sixers got outscored by 15 points until the next time he checked in. If Collins kept him in, maybe the Sixers aren't down 11 at the half.
So your next point could be: "Hey asshole, he did it so Lavoy can play at the end of the 4th quarter when it matters most." That's definitely going to be the coach's explanation for that, but my retort is: Why? From a purely mathematical point of view, points matter just as much in the second quarter as they do in the 4th. Yes, definitely yes, points are harder to come by in crunch time, but if you're already down 20, that doesn't exactly matter much, does it? Sort of similar to the Closer situation in baseball. An out is an out is an out. You want to have them in before things get out of hand.
There are definitely instances when taking players out due to fouls is the right move. I just don't think it has to be a hard and fast rule. The Sixers haven't had any players foul out of a game in the playoffs, and have only fouled out 7 times as a team this year (Thad three times, Jrue twice, Brand once, Evan once).
Now that's definitely because Collins has exercised caution in playing guys in foul trouble, but that also means he's assured fewer minutes for a player "in foul trouble" than leaving it up to the player to not foul and be able to play more minutes. And who knows what could have happened in last night's blowout if Collins had let Lavoy play through it.