I think there are occasional good reasons to sub a guy out, such as calming down a player who is clearly not in control of his game on the court, or if you were going to give a guy a breather anyway starting a minute early might not do any harmful. You also have to take into account an individual's likelihood of continuing to accumulate fouls. Some guys are far more likely to foul than others. If Kobe picks up two fouls right off the bat, that is unlikely (and not just because he's Kobe; wing players generally pick up less). He can probably make only the most minor of adjustments and remain out on the court at 99% effectiveness without real risk of fouling out. Greg Oden, on the other hand, who is in there primarily for defense and who hasn't met a foul he didn't love yet, might need to be benched if you think you'll need him for specific match-up purposes in the 4th. So, it's not optimal to have a blanket "never bench a guy with 'foul trouble'" dogma. But voluntarily giving something up to avoid the RISK of potentially giving it up just is obviously an ineffective tactic.

Most importantly, though, I'm just glad I'm not crazy!

I could be mistaken, but I think Synergy can do that.

Very true, very true. Upon a reread, I misinterpreted your initial post ("On the other hand, I don't like the way teams abandon running plays on the last possession of a quarter, half, or game)". I read it as you believed teams should 'run' the ball (e.g. uptempo looks) - which on reflection is, I think, not what you meant at all.

For teams running a 'play,' it may be that certain ones fear the inability to execute the play. At that point, it probably depends on how good of a shooter your point guard is. A team like New Orleans or Phoenix probably is much more likely to run a play at the end of a quarter (and, anecdotally, I feel like they do), because they have excellent shooting PGs. Even if David West doesn't come open off a screen, Chris Paul is still a high-percentage shooter likely to score on a jump shot.

Taking the example of the Garnett down screen, let's look at the Celtics. A team like Boston, with a PG who is extremely poor on jumpers, may feel less comfortable running their usual offense with the ball in his hands. If Garnett doesn't get free for the screen, that leaves a 20-foot Rondo jumper. I actually feel like this happened once or twice at the end of quarters in the Finals, where they attempted to free up Allen or Garnett but the play broke down.

This is all speculation and hearsay - it'd be interesting, though very labor-intensive, to put together a database of how often teams run isolation plays for 1-on-1 players at the end of quarters, vs running offensive sets, and then comparing that against jump-shooting percentage for each team's primary distributor.

#17 - Good point about the fact that Kerr/Paxson wouldn't be open w/o Jordan on the floor. My feel for what Prof. Weinstein was saying in the original post was that the points created by having the star on the floor in the final minutes aren't worth any more than those same points earlier in the game. I was simply adding that sometimes the alpha dog mentality might actually make those points harder to come by in the final minutes, because the ego of the alpha dog could cause him to make the incorrect play in the final minutes due to an obsessions with "the last shot".

Jordan didn't have that problem when he passed to Kerr/Paxson, but then again, they made the shots -- remember how the press killed LeBron when he did the same thing with Donyell Marshall (who missed)? Sometimes in the 4th quarter, there's needless pressure to make an incorrect basketball decision because of the egos involved, while that pressure doesn't exist for the same play in quarters 1-3.

Also, very interesting point about the win probability being different only in the final couple minutes... This does suggest that you should put a premium on saving him for the final sequences of the game, which is another layer of complexity you'd have to take into account in the payoff matrix.

#18 - I remember that study, and thinking about the Bill James aphorism about leaders and trailers merging at .500 because of not only RTM, but also because the team in the lead has a tendency to change to a conservative strategy while the losing team will be more aggressive. I also wonder if the seeming paradox of the team down 1 after a half winning more has anything to do with getting more possessions in the 2nd half -- maybe the leading team is up by one b/c they won the tip and had 1 more possession than the opponent, bur in the second half that advantage is perhaps erased.

That makes a lot of sense, though I think in a possession where you have 22 seconds, there's no special reason to think you couldn't run a play that required most of a shot clock. It doesn't necessarily have to be up-tempo to generate a better look than a predictable isolation. Going back to the Celtics example, Doc Rivers ran a lot of good motion to get open looks for Garnett and Allen coming out of time outs, where the play was by definition executed in the half court.

I understand that handing the ball to Pierce and telling him to dribble out the clock and shoot over Artest and Odom at the last second guarantees that LA doesn't get another shot, but is running a down screen to free up KG for an elbow jumper with a couple seconds left, a couple seconds in which the other team will have to force up a contested buzzer beater, really a worse option? I guess, as you numerically posit, it depends on your estimation of Pierce's ability to finish the isolation play.

One of the assumptions of the argument is that 5 minutes in the 2nd quarter is the same as 5 miutes in the 4th. Obviously people will debate clutchness until the end of time, but lets ignore that for the time being and focus on something else... playing from behind (or ahead).

A study was done by Johan Berger and Devin Pope of Wharton University in which it found that college teams were more likely to win a game when down a point at halftime than up only a point. The reason (linked to Prospect Theory) is that they team that is losing can see victory being down only a little and will thus play harder to win while the team winnin will likely not play any harder and thus play less hard relative to the opposition.

So in this situation, if the coach decides to bench the foul plagued player then he is "betting" on his team keeping the game close enough that when the player returns the whole teams effort will improve as they can see the victory and will try harder to reach it. On the other hand, if he plays the player and that player fouls out and the game is still within reach by the opposition, the impact of losing a player and the other team being close to victory could lead the other team to "play harder" and win the game.

The basic puzzle using this logic is which is more likely to occur, The player continues to play and if he fouls out the team will have generated a large enough lead to overcome a final push by the opposition or by benching him will the remainder of the team keep the game close enough so that he can return and lead them to a final push to win the game in the end.

The study would suggest that the last 5 minutes are more important in a close game than 5 minutes in the second quarter (even ignoring clutchness).

@15 - "Obviously, Paxson and Kerr were open because Jordan was doubled, but the best option is sometimes for your "finisher" to pass for the good of the team."

I don't think that's the point some readers are trying to make. I think the point is, if the 'finisher' isn't on the court, Paxson/Kerr/etc aren't open at all. That star player necessitates the double-teams. Now, Paxson/Kerr/etc have to HIT the shot, and 'finisher' X has to have the willingness to pass the ball, but the finisher still NEEDS to be on the court to create that good look.

@13 - I think it's because there's still a high value in depriving the opponent of a possession. Let's imagine the following:

1) Team A scores 1.2 PPP when running up-tempo, usually scoring within 10 seconds. Team A scores .7 PPP when isolating its best 1-on-1 player(so we've got a HUGE delta here between offensive options).
2) Team B scores 1 PPP when running up-tempo, and .8 when isolating its best player.
3) Let's say a half-court heave type play (plays run with 2 or less seconds) returns .1 PPP.

If Team A has the ball with 22 seconds left in the quarter, it has 2 options:
It can try to run its uptempo offense, which results in an average of 1.2 points and leaving 12 seconds on the clock (PLENTY of time for a regular possession). Or, it can run an isolation set and effectively run out the clock for a shot.

BUT, if Team A plays up-tempo, Team B gets a final possession in the quarter with a reasonable amount of time to shoot - let's say Team B plays iso on final possessions basically every time they have enough time to do so. Their PPP is then .8 on this possession.

So we set up the payoffs for each team based on Team A's chosen strategy:

If Team A runs, they'll earn 1.2 points on average, and Team B will earn .8 points on average - Team A increases its lead an average amount of .4 points.
If Team A isolates, they'll earn just .7 points on average. But Team B earns only .1 points on average (flings at the basket and full-court passes, etc) - Team A increases its lead an average amount of .6 points.

Possessions are valuable, and by playing isolation at the end of quarters, a team can effectively guarantee itself an extra one relative to its opponent for that quarter.

@Neil's original article - I actually got into a brief email correspondence with that article's author, Prof. Jonathan Weinstein. Unfortunately, he didn't have enough time to respond to all of my questions. One that he didn't really address, I'll reprint here:

If I may, I'd like to refer to http://dberri.wordpress.com/2009/03/05/modeling-win-probability-for-a-college-basketball-game-a-guest-post-from-brian-burke/ (Berri's models have their flaws, but this post is a guest post by Brian Burke; admittedly, his data does come from college basketball). To quote:

"One thing I’ve already noticed that’s interesting about basketball is that the win probability equation is the same for nearly the entire game. In other words, a 6-point lead for the home team in the first 10 minutes of the game yields the same WP of 0.86 as a 6-point lead with 10 minutes to go in the 2nd half. This surprised me. I would have expected any certain lead to be more decisive as the game went on, gradually becoming more and more insurmountable. In the graph I cited above, the “slope” of the curve would theoretically get steeper and steeper as the game goes on. When I went to make a graph of selected times in the game to show how the curve steepens, I could only see a single curve. I thought I had made some kind of error in Excel, but the curves were just superimposed. Not until the final couple minutes do the curves become very steep, when ultimately a 1-point lead with zero seconds remaining is as decisive as a 10-point lead."

... Coaches, with their years of experience, can be extremely well-tuned to the proper response to a lead or deficit for their respective teams, and adjust their in-game strategies accordingly. As such, they prefer to have all of their resources available for as long as possible. And, in evidence, as the game begins to get more 'out-of-hand' (i.e. as the deficit increases) you're much more likely to see coaches put back in players who are in 'foul trouble.' That's because they ARE aware that being blown out in the 2nd quarter makes a game hard to win in the 4th... But if their reserves can keep the game close in the 2nd (which sometimes happens, sometimes doesn't) they much prefer to have their star players available to improve win probability late in games.