Why Two For One?

A few weeks ago we addressed the somewhat specious platitude that finishing a quarter strongly is particularly important. We neglected, though, to address another end-of-quarter oddity. When a team takes possession of the ball with, say, between 48 and 35 seconds remaining in a quarter (save the fourth), coaches sometimes advise their charges to quickly put up a shot so that the opposing team gets it with no less than, say, 30 seconds left. This way, the first team will get the ball back with no less than, say, 6 seconds left, and can try for one more shot. The strategy is called "Two For One". The idea is to get two possessions before the quarter ends.

There are a couple concerns here.

First, if the first team gives the second team the ball back with a bit more than 35 seconds left, then the second team can try its own Two-For-One strategy. Thus, the first team must manage its initial possession to make a shot quickly, but not too quickly.

Second, are two low-probability shots better than one high-probability possession? Assume a frenzied drive at the 0:40 mark, without first setting up holes in the defensive alignment, has a 30% chance of success, and then a desperate 3-point heave at the 0:03 mark has a 10% chance of success. By my calculation, the expected points scored there is 0.45. Meanwhile, your opponent gets a full shot clock to work a set play sandwiched between your two possessions; perhaps the opponent has a 45% chance of scoring, with expected points scored of 0.9. So your expected +/- for that Two-For-One sequence is -0.45. On the other hand, if you took possession at 0:40 and worked the shot clock to the fullest, you have a 0.45 chance of success, with expected points scored of 0.9. Your opponent takes possession at 0:16 and, with somewhat less time to work with, has only a 0.3 chance of scoring, with expected points scored of 0.6. Your expected +/- for that sequence is thus +0.3.

Obviously my mathematical assumptions can be tweaked to make the Two-For-One strategy seem a bit more favorable, but you get the idea.