King,

I agree completely that not fouling when down by 2 or 3 pts with under a minute left is insane. I was muttering at my TV about that at more than one game this weekend.

I disagree with you, though, on fouling when up by three points. Yes, teams that are up at that point should definitely closely guard the opposition when the ball is being brought up the court. If an accidental foul happens while applying, the pressure that's fine. Fouling on purpose though the right call sometimes, is not the right call in all cases.

The big problem with fouling while up by three points is that you give the other team a chance to do two things they want to do that you don't want to do: they get the clock stopped and they get a high percentage chance to score. Depending on the exact circumstances, those may be risks that you want to take as the team that's ahead, but it is far from a cut and dried case.

The one case when it definitely makes sense to foul is when the other team isn't in the bonus yet. In that case you can disrupt their rhythm

and make it more difficult for them to setup a decent shot. Effectively, even though you are stopping the clock, you are wasting time by stopping the other guys from getting set up. Of course this case is pretty rare in the end of college games. Teams almost never make it to the last minute with less than 6 fouls.

There are other situations that also make a relatively strong case for fouling with a three point lead. If the other team is still in the single bonus, if you foul them it is much more likely that they will get no points out of it and you will get the ball back.

Or if you can find a really bad free throw shooter to foul. Here again you make the other team getting 0 or 1 point more likely, making the risk that the other team will get the rebound or steal the inbound pass easier to deal with.

Or if the other team has really good or really hot three point shooters, then a better case can be made for making the foul as well.

Let's look at a specific case. Team A is up by 3 with 15 seconds left after hitting a free throw and Team B is in the double bonus. Let's say a player on Team A fouls a player on Team B with 12 seconds left. Let's say the player that fouled shoots the typical 70% for free throws. In that case, assuming that he tries to make them both, there is a 49% chance that he will make both, a 9% that he will miss both, a 21% chance that he will make the first and miss the second, and a 21% that he will miss the first and make the second. So there is a 91% will have cut the Team B will have cut Team A's lead to 1 or 2 points. So now if Team got a rebound on a missed second shot or makes a steal, they can shoot a high percentage shot, instead of being limited to 3 pointers. Plus they still have 12 seconds left to try it.

On the other hand if Team A doesn't foul, let's say Team A's defense breaks down and a a 35% three point shooter (a fairly typical value) from Team B gets a three pointer up with 5 seconds left. So there is a 35% chance he will make and Team B will have 4 seconds or so to try to drive the length of the court and make a shot to avoid overtime. There is a 65% chance that he will miss. In if Team A gets the rebound they likely get fouled, and they most likely have won the game. If Team B gets the rebound (maybe a 1 in 3 chance), they have 4 seconds or so to find an open shooter and heave up another three pointer. It is a chance, but I don't think that it is a good chance.

Well, I have gone on with this too long already, but hopefully it is clear to thee three people who read this far, that this case is far from clear cut. To really get a good idea of how the possible scenarios might play out, someone should do some statistical simulations, but I don't have the time for that this afternoon.

King, you asked about typical foul shots. here is a nice link that I found while writing my previous post that goes into a lot of detail about free throw percentages: http://www.post-gazette.com/pg/07070/768555-291.stm

In there it says that the long time season team average is 69%. Individual player averages probably do drop a bit at the end of games, but then again I also think that the better shooters get put on the line more at the end of games. Some teams succeed in fouling people who shoot foul shots badly, but it seems to me that it is the good shooting guards who end up taking most of those foul shots.