Sunday, April 6, 2014
Suppose I give you $1000 and then give you 2 choices, A and B. If you choose A, there is an 80% chance of keeping your money. Choosing B, there is a 50% chance of keeping your money. In either case, if you lose your money, you will have an equal chance of getting it back in the future. Obviously, choice A is the way to go. This is the choice Bo Ryan and the Wisocnsin Badgers had in front of them when they were ahead by 2 with 16 seconds and Kentucky had possession. On the floor for the Wildcats was 5 freshmen, Julius Randle, James Young, Dakari Johnson and the Harrison twins, Andrew and Aaron. Dakari Johnson makes 45.7% of his free throws. His chance of making 2 free throws in a row is about 20%, thus Wisconsin would have a near 80% of keeping their lead given that they would gather the rebound if Johnson were to miss his second free throw. By not fouling, Wisconsin accepted the 50% probability of Kentucky tying the game, based on their FG shooting percentage for the game. Worse, they handed Kentucky a 35% chance to take the lead, based on the probablity that one of the Harrisons or James Young would attempt and make a 3-pointer. The choice becomes a little less obvious if they were forced to foul their best free throw shooter and hero of the game, Aaron Harrison. The odds of him making both free throws and tying the game increases to 63%, better odds perhaps than a Kentucky basket but taking away almost any opportunity for them to take the lead(there remains the small chance of an offensive rebound and putback on a missed second free throw). Intuition and "the book" says not to foul. An intuition informed by rather simple math realizes you can almost completely avoid the worse case(losing in regulation) and live to play at least 5 more minutes of basketball.