Seems like the idea of fouling earlier (and gambling soon) makes sense assuming that the players can make some quick calculations in their head.

BTW, I’m a fan of throwing a second player at the primary ball handler in these cases. I’m a Portland fan and the few times that opposing coaches throw a double team at Roy in these cases, it seems to end badly (maybe not so badly now that we have Miller).

Im surprised at Sebastian here truth be told, I thought you were sharper then that Seb!

The whole “case” here appears to be based around the assumption that Davis is going to hit a contested long range two pt jumper and a 25-26ft three-pointer.

What is more puzzling/irritating is when teams who are behind let the team run down the shot clock a substantial amount and THEN foul! Getting the worse of both Worlds then. Teams dont go for the aggressive 8 second count violation enough in my view either.

If you don’t foul down 4 with 1:06 left, you can expect to get a possession starting with 0:46 left and another possession starting with around 15 seconds left. To win, realistically, you have to score on both of these possessions and hope the opponent doesn’t score on both of theirs. If you give both teams about a 50-50 chance of scoring, you find that the comeback team has about a 6% chance of making up the difference.

The goal of the comeback team is not to have the most efficient offense. The goal is to have the most variable offense. It is far better for the comeback team to have a possible +/- of -10 to +10 than to have a possible +/- of -5 to +5 (I use +/- because both teams are going to score more points if the comeback team fouls) because this puts more of the probability curve in the win-or-tie range (+4 or better).

Finally, a couple of links:
http://sports.espn.go.com/ncb/news/story?id=4982961 (third para from bottom)
http://scores.espn.go.com/ncb/playbyplay?gameId=300860096&period=2 (4:30 to end)

Thanks for making that correction to the initial situation described by Sebastian, i.e. down by 4 points with 66 seconds in the 4th quarter, opponent with possession of the ball.

What this does, however, is further accentuate why the best available strategy for the defense on that initial possession was not to foul, and then to evaluate on a possession-by-possession basis, thereafter, whether fouling [or not] on any given possession would have been a better option, considering the specific time, score, number of fouls committed, number of time-outs left, etc., they found themselves in, as time continued to tick off the clock.

It’s a false assumption in the first to believe that Team A will only get a certain limited number of possessions the rest of the way.

At any rate, the right approach is to consider the various options. The choice as to whether to foul or not may well depend on what you plan to do on subsequent possessions, so they do need to be taken into account. You can’t necessarily assume that the tactic will be to continue to foul. For instance, for the down eight with a minute left situation, I consider fouling each time, not fouling each time, or not fouling this time, but fouling subsequent times. I chose not to do that for down four, but I could do that, too. The point was less to come to a concrete conclusion (since the underlying assumptions are open to debate), but to illustrate methodology.

Either way, I think it is totally unclear that the right tactic, down four, with over a minute to go, is to foul. That seems pretty unlikely to me, but I haven’t done all the numbers.

I believe the original situation was …

- 40 secs left
- down by 4 points
- opponent with possession
- the defense decides not to foul on THIS specific possession

Although I could certainly be incorrect in my interpretation of the original scenario … from what’s actually written here, it does not appear to be the case that what’s being discussed involves the decision not to foul on ANY of the remaining opponent possessions.

That being said, the officials often make it difficult to get an intentional foul off in the waning seconds. It is by no means certain that a pair of possessions (one for each team) could be obtained in just a few seconds. At any rate, you give a number of plausible situations where fouling could help, but nothing of the sort of analysis that either I or Kevin give that would substantiate your claim that fouling is the best option mathematically. I of course agree that most coaches are loathe to foul under those circumstances.

@Kevin: That’s sort of the kind of analysis that I have in mind, but I wouldn’t short-circuit to the table, but would continue on using the sort of analysis that you use in the first possession. The reason is that these numbers–presumably derived empirically–reflect the kind of coaching decisions that we’re trying to validate in the first place! Just continue the analysis further on to the actual end of regulation. We can then assume 50-50 wins in OT. Also, the table doesn’t seem to reflect possession, unless it’s implied somewhere that I didn’t see.