My friend JLW (blog link to the side) recently wrote a post about foul trouble in the NBA. Read his post here. I believe, however, that he left out a few key points which I'll address here.
First, note that in the current age of the NBA, taking players out solely for foul trouble is usually limited to big men. Rather, the best way to put it is that coaches take players out for "foul trouble" nowadays only if the player is one that is prone to fouling as part of his game. This usually applies to big men because the physicality in the paint still exists while the hand check rules on the perimeter have been long gone.
The most important point that I think JLW missed was one of effectiveness. A player who is afraid of picking up another foul and getting really close to fouling out will often play less aggressively. This results in weaker defense as well as being hesitant to take it strong to the hoop. Because the NBA is so full of talent these days, bench players are often not that much of a downgrade, and a bench player playing at 100% will often be just as effective as the "star" player who's scared of picking up another foul. More than anything, the n/6 rule of thumb tempers that fear and allows the player to play better psychologically.
As for caveat #1 in his post, I don't really see how rest factors into this at all. While in the long run, rest and playing less minutes will probably lead to better production overall, that is not necessarily true in the short term for any given game. How often do you see a player be red hot in the first half only to go cold in the second? Both being rested and being tired will affect the mechanics of a shooter, where just a slight difference might throw things off. Also, there is a matter of adrenaline. The ability to play through pain. To step up in big moments. A player being "in the zone" and wanting the ball is much more important than taking him out to rest. This is one of the reasons that even though I love bridge and poker, I cannot classify them as sports. To me, physical sports involve a pain factor that just isn't present in mind sports/games. Now, if they created the no caffeine no smoking bridge world championships, we might be a step closer.
As for caveat #2, I strongly believe that minutes/possessions are not created equal (more details in the bonus rant below). The wide-open Kerr analogy is very flawed because if it wasn't for Jordan drawing a double-team, how does Kerr get wide open? Furthermore, you want your best player in the game at the end not just for the basic stats he may provide (scoring, assists, whatever) but for his decision making. More often than not, the war is won when the opposing general is lost, rather than fighting down to last man standing. With regards to the amount of time the key player leaves the game, even at n/6, 8 minutes in the NBA is a long time, especially in the drawn out final moments.
My objections above illustrate that playing key players through foul trouble is not at all "all upside". With regards to assessing the risk of sitting the player for too long, this is often a matter of the quality of the coach himself. Gregg Popovich would NEVER make that mistake. I've often seen him take players out for foul trouble, but put them back in the moment the game might get away from them. Since this is an execution issue and not a concept issue, you can't generalize based on the bad coaches. ie. the issue here is not whether to take the guy out for foul trouble, but rather for how long.
The NBA is actually at the forefront of the quantitative, stats-driven movement amongst all the sports. Without actually following the NBA closely, one should not make judgments about how strategy is implemented as a whole. Which brings me to the bonus rant, which is actually the meat of the matter.
While JLW doesn't agree with the simple baseline model (or rather, thinks it's oversimplified), I also want to put in something here about it being just plain wrong. There was an astounding number of times when I was doing my masters work in statistics that I would hear or read some sports statistician go on and on about how "minutes/possessions later in the game being more important than minutes/possessions earlier in the game is just a common misconception". In the end, they are just plain wrong. Especially when it comes to the NBA. I don't want to get into it any further, but let's just say that my assumptions on how the game works (which are quite different from most simple models) are a huge part of my NBA2H strategy, and the results speak for themselves.
Statisticians love iid distributions and other things that can be broken down simply because it helps them fit models to data (or if you're a Bayesian, fit data to models). However, when it comes to sports, such simplicity just doesn't work. When you don't play the sport, when you don't follow the NBA nightly, and when you don't understand the grind, you can't model everything correctly. Here's a simple example from when I was a kid. I was talking to my older cousin, who played for his high school basketball team, about a friend who had remarkable accuracy shooting shots from the foul line. My cousin's response was, "Well, have him run up and down the court 50 times and see how well he shoots it then." Even though I'm a big fan of the quant/sabermetrics movement in sports, I'd rather it be done by guys who've ran up and down the court 50 times.