In the basketball world there has been a debate about intentionally fouling a team's worst foul shooter, let him shoot two foul shots with the idea he is probably going to miss one or both of them. Is this a good strategy? Some math can be used to try to find an answer to this.
A good probability problem might be, What is the probability makes at least one, i.e., he makes the first (event A) or second (event B) shot?
Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B) = 0.349 +0.349 - (0.349)(0.349) = 0.576 = 57.6%
But I digress. Let's answer the specific question of how would Andre do just shooting free throws each time down the court? The probability of him:
Missing both = 0.651 x 0.651 = 0.424
Miss the first and make the second = 0.651 x 0.349 = 0.227
Make the first and miss the second = 0.349 x 0.651 = 0.227
Making both = 0.349 x 0.349 = 0.122
His expected value of scoring for a possession is:
0(0.424) + 1(0.227) + 1(0.227) + 2(0.122) = 0.698
Per one hundred possessions that would be 69.8 points. That compares to the Pistons team OE of 102.5. So yes, based on this, foul him. However, there are other factors to consider. Each player can only commit six fouls before being disqualified. You may have to pick your times. That is what the opposing teams have been doing.
How about the second worst free throw shooter in the league - DeAndre Jordan at 42.1%? Doing the same math, in a hundred possessions, his free throws would account for 84.2 points. His team, the Clippers, usually score 106.2, so again - foul him.
The third worst shooter is Dwight Howard. his free throw shooting would gain 109.8 points. His team's (the Houston Rockets) OE is only 104.2.By my calculations, this fouling strategy would only be effective with two players in the entire league.
Aspiring NBA basketball players - practice your free throws.
