People say "well you can lose if he hits the 3 and makes the free throw."
I hate that argument. It displays a complete lack of understanding of probability -- or woefully pessimistic thinking.
Yeah, sure, fouling adds the infinitesimal chance of losing in regulation. It also
decreases the chances of losing in overtime. The goal isn't to avoid losing in regulation. The goal is to win the ****ing game!
Let's say you don't foul. Because you know the 3 attempt is coming, you defend it tighter than usual (unless you're Ryan Boatright), and the chance of making it is 20%. Then you have a 50/50 chance of losing in overtime.
You lose 10% of the time.
Before discussing what happens when you foul, I'll first estimate that the chances of scoring 2 from either a basket or a foul on rebounding action in under 2 seconds is 10%.
Now let's say you foul. Let's also say there's a 10% chance of doing it "wrong" (while shooting a 3) and a 90% chance of doing it "right" (non-shooting).
1) On shooting foul -- 10% it's a shooting foul * an 80% free throw shooter makes 3 free throws in a row 50% of the time -- 5%, and you lose in overtime 50% of that --
2.5% losing
+ 10% * 65% chance of making 2 free throws * 20% chance of missing * 10% of scoring on rebounding action --
0.13% losing
+ 10% * 32% chance of making 1 of 2 * 90% chance of missing on purpose * 10% of scoring on rebounding action * 50% losing in OT --
0.13% losing
+ 10% * 5% that he makes the 3 while being fouled * (80% of making the free throw + 20% chance of missing * 50% chance of losing in OT) --
0.5% losing
2) On a non-shooting foul -- 90% it's a non-shooting foul * 80% makes the first * 90% missing on purpose * 10% scoring on rebounding action * 50% losing in OT --
3.3% losing
Sum all those up, and, with fouling,
you lose 6.6% of the time.
You can quibble with the exact percentages, but for the love of God, avoiding the risk of losing sooner doesn't justify doing something that actually
increases your overall chances of losing.
When you foul, surely, there are more
different things that can go wrong, but the sum of them all occurring are no more probable than if you give your opponent the chance to hit a 3!
P.S. Belichick was right to go for it on 4th down at Indy.