TaShawn made an interesting statistical point in a different thread, related to last night's game against the Knicks. With 22 seconds left in the first OT and the Pistons up 3, Stephon went up for a 3-pointer, and Chauncey contested it, but ended up fouling him. Stephon made all 3 FTs. TaShawn said:

Here is the thing about Chauncey fouling Marbury.

Marbury shoots .314 from 3-point land.
Marbury shoots .723 from the free throw line.

The odds of Marbury making all 3 free throws are
.723 X .723 X .723 = .378

.378 is greater than .314, but not significantly. When you consider that Chauncey would have pressured the shot cleanly most of the time, and gotten away with a little contact some of the time, I think that it was the right play to challenge. He was probably decreasing the odds that Steph would actually make the jumper to < 15% by getting up in his grill.I pointed out that if we instead calculate the expected value for total points scored on that play, it comes out differently:

(a) He shoots the 3 with no foul: .314*3 = 0.942
(b) He gets fouled: .723*1*3 (.723 pts expected on each FT) = 2.17

So fouling in that situation dramatically increases the expected points scored. TaShawn pointed out that he was only calculating the odds of the Knicks tying the game in that situation, though with 22 seconds left on the clock, I would argue that with that much time left, preventing them from scoring was the most important thing.

It's an interesting statistical question. Here are two extreme examples:

Ben Wallace shoots 42% on FTs for his career, and 4-34 on 3s, which is 12% (last-second halfcourt heaves probably account for more than a few of those; obviously Ben never shoots 3s by design but it's still a fun thing to contemplate). So if you foul him on a 3, his odds of making all three FTs is .42^3 = 7.4%, which is even less than his normal three-point percentage of 12%!

Kobe's career FT percentage is 83.5, so if you foul him shooting 3, the chance that he makes all 3 of them is .835^3 = 58%. This is much higher than his career 3-point rate of 33.6%, so obviously fouling him on a 3 is always the wrong thing to do.

But even a guy who shoots an OK percentage on FTs is into the territory where fouling him on a 3 might be worth it, in terms of preventing him from scoring 3 points. Rasheed is a 71.1% FT shooter for his career, which comes out to .711^3 = 36% chance of making all 3 FTs, as opposed to 34% on 3-point shots. Those are almost even.

In the end, my argument would still be that unless there are under 5 seconds left in the game, you never want to think about fouling intentionally while you have the lead--the chance that they'll get the ball back again is very high, so I would argue that expected points is the right measurement in that situation, not the odds of tying the game on one play. And with under 5 seconds left, you should just foul before they have a chance to shoot the 3 anyway. Still, interesting question!

Edit: actually TaShawn wasn't arguing for an intentional foul either, of course, just pointing out that the downside of closely contesting that 3 was perhaps less than what it seemed.

There are many factors here.

The reason that conventional wisdom tells you not to foul a jump shooter is because those guys usually shoot a high enough % from the FT line to make it a stupid play mathematically. Sheed and many others fall into this strange territory where they shoot a high 3 point % and a relatively low FT%.

There is a also a large gray area. Maybe you can contest a shot, but be very careful about it. There is a whole range of effort that you can give. The harder you try, the lower % the shooter will shoot, but the higher your odds of fouling him. I think that we can all agree that you don't just go into the fetal position when they take the crucial shot.

Another factor is that a player's FG% is pretty much a contested FG%. This means that if you don't give the normal effort to stop him, the % could be much higher. I saw a stat once that said that Ray Allen hits > 70% of his wide-open 3-point looks.

As far as the question of fouling intentially before they shoot, a good analysis can be found below. This analysis led to the decision to foul intentially by many coaches in this situation.

End-Game Strategy (http://www.sportsquant.com/endgamestrategy.htm)

The reason that conventional wisdom tells you not to foul a jump shooter is because those guys usually shoot a high enough % from the FT line to make it a stupid play mathematically. Sheed and many others fall into this strange territory where they shoot a high 3 point % and a relatively low FT%.

Yeah, but the "don't foul a jump shooter" rule is for general purposes, not just last-second situations. My argument about expected values is essentially a re-statement of that rule--you're giving up more points by fouling than by not fouling. That's still clearly true for guys like Sheed who aren't super-high percentage FT shooters.

To just change the scenario slightly....With less than 10 seconds left and a 2 or 3 pt lead, the team on the defense could possibly just foul a player without the ball just to avoid the three ball make or the three foul attempts, but I assume it would be called an intentional foul and the team would probably get two FT's and the ball back.

We have seen players grab the player with the ball before he takes the shot, but even then, you have to be aware of the clock and anticipate when the player will actually shoot it. In last nights game, Starbury took the shot with 22.5 seconds left after dribbling for 3 seconds and then lofting the shot in CB's face. No way CB should have thought about fouling before or after the shot attempt in my opinion unless the clock was less than 7 seconds.

The bad part about CB fouling him was that he kind of aknowledge that he made the mistake by looking off all of his teammates and literraly dribbling out the clock before launching his 3 ball trying to be the hero.

To just change the scenario slightly....With less than 10 seconds left and a 2 or 3 pt lead, the team on the defense could possibly just foul a player without the ball just to avoid the three ball make or the three foul attempts, but I assume it would be called an intentional foul and the team would probably get two FT's and the ball back.

Yeah, I think that rule comes into effect with under 2 minutes left. If you go to an all-out Hack-a-Ben/Hack-a-Shaq strategy where you just grab him every time the other team gets the ball, even before they pass it to him, you can only do that if there are more than 2 minutes left in the quarter. After that point, you can only avoid the intentional foul call if you hack him while he has the ball.

Actually the most extreme case there is of a guy who shoots well on 3s but not well from the FT line is, of course, Bruce Bowen. His career averages are 39.4% on 3s, but only 56.8% on FTs!

I had forgotten that in 2003, Bowen shot 44% on 3s, which led the league, but only 40.4% on FTs. That's gotta be the only time anyone's ever shot BETTER from 3-pt range than from the FT line. If not for issues of foul trouble and getting into the bonus, those numbers would dictate that fouling him on EVERY SINGLE 3-pointer would be the right strategy, no matter how much time was left in the game! :pound:

The Bruce Bowen case is very weird. You would think that he could move back behind the line a few feet and shoot jumpers instead of set shots on FT's to increase the %.

Oh, another stat that I found to be funny, is that players don't really shoot a worse FT% on the road. That means that all of the action behind the basket by the fans is a big waste of time.

I think that the ideal method of distracting a shooter would be to silence the crowd and have 1 designated heckler try to get inside his head.

No one mentioned this angle:

If a player shoots 40% from 3 point range, chances are greater that he will miss than make. Therefore, no points.

However, if that same player has 3 chances to make a FT, chances are better (greater than 50% in most cases) that he will make each FT shot. 1 point is more than none. 2 is even better.

So you would risk fouling a 49.99% 3-point shooter, but not a guy who shoots 50.0001%?

So you would risk fouling a 49.99% 3-point shooter, but not a guy who shoots 50.0001%?

Haha, getting technical there tashawn, but first find me all the players who average over 49% from 3pt range. Not a scenario that is very likely to happen.

PS - this season there are 6.

Over the course of a whole season, last season nobody averaged over 46%

No one mentioned this angle:

If a player shoots 40% from 3 point range, chances are greater that he will miss than make. Therefore, no points.

However, if that same player has 3 chances to make a FT, chances are better (greater than 50% in most cases) that he will make each FT shot. 1 point is more than none. 2 is even better.

Actually I sort of did, linwood...that's the idea behind the "expected value" argument I mentioned in the first post of this thread.

Another way of saying it is that even if the worst-cast scenario for the defense--the opposing team getting 3 points, either by hitting the 3 or making all three FTs--is more likely to occur when the other team shoots a 3, the best-case scenario for the defense (other team gets 0 points) is usually far less likely to happen when you commit the foul, because the chances of the other team getting at least 1 point out of it suddenly become much better when you foul the 3-pt shooter.

Here is a good way to think about the difference between expected value and odds of tying.

Your football team scores a touchdown with no time remaining to pull within 2 points. Do you kick the extra point, which has an expected value of about .97 points, or do you go for the 2-point conversion, which has an expected value of about .80 points (2 * 40%, which is the % of success on such attempts).

The answer is that you are forced to go for the option that gives you the highest chance of tying the game. 0% for option 1, and 40% for option 2.

If it were the end of the first half instead, maybe you would elect to just kick the extra point and maximize your expected value.

Actually I sort of did, linwood...that's the idea behind the "expected value" argument I mentioned in the first post of this thread.

Another way of saying it is that even if the worst-cast scenario for the defense--the opposing team getting 3 points, either by hitting the 3 or making all three FTs--is more likely to occur when the other team shoots a 3, the best-case scenario for the defense (other team gets 0 points) is usually far less likely to happen when you commit the foul, because the chances of the other team getting at least 1 point out of it suddenly become much better when you foul the 3-pt shooter.

I had to read it three times, and then draw a diagram... but we are in total agreement. And, you did mention it first.

The best strategy for a good defender is not to foul the three point shooter.

My head hurts.
:reading::eek::lecturer::dizzy2::confused::boom:

Delfino apparently subscribes to the theory that you should foul a shooter intentionally with < 2 seconds left in a tie game. I'll do the math and get back to you with whether or not it was a good decision.









Nope, it wasn't.

They punish you for not being aggressive.
Kobe blew it tonite at the Bobcats.

Delfino apparently subscribes to the theory that you should foul a shooter intentionally with < 2 seconds left in a tie game. I'll do the math and get back to you with whether or not it was a good decision.

Nope, it wasn't.
:rofl: :rofl:

I'm dissapointed in the lack of discipline lately... too much reaching and not enough positional footwork... the reaching will more than not lead to a foul... one thing that LB taught was anticipating where the player was going or the flight of the shot... not playing where the player currently is.... playing like eager rooks lately.

Heres the real point....Cb did not 'attempt" to foul a 3pt shooter. There was no 'strategy' involved. It was just a stupid play by a point guard with a grand total of 2 blocked shots all year.