End game spots in basketball are my favourite strategic spots to think about. One thing I think many people get wrong is going for a quick 2 when down by 3 points at the end of game (I’m looking at you announcers who love to say “you don’t need a 3”). I figured I would run through some quick math based on actual results of ~20 years of NBA games to show that teams should be more aggressive going for 3 in these spots.
To do this analysis we need to get a rough idea of a team’s win percentage based on the score margin and time remaining. I could use a win probability model but instead I’m just going to look at the historical win percentages for different score margin and time remaining states. I looked at all final minute possessions where the score margin was within 5 points in all NBA games since 2000 and found how often teams won the game. For example how often does a team with the ball down 2 and a possession starting with 30 seconds remaining win the game. The results are shown in the graph below from the perspective of the team with the ball. I smoothed things out a bit by looking at all possessions +/- 5 seconds of the given time, so in the graph below the spots with 30 seconds remaining represent how often a team wins with that score margin and possessions starting with between 25 and 35 seconds remaining.
It is important to note how rare it is to win when down 3 with 20-30 seconds remaining because I think one of the reasons people like to say “you don’t need a 3” in these spots is because if you miss, and don’t get the rebound, the game is pretty much over, but before you have even taken a shot your chances of winning aren’t very good. We can see from this graph that teams down 3 with the ball with 20-30 seconds left win around 10-15% of the time. We can also see that teams up 1 with the ball and 15-20 seconds remaining win around 85% of the time, so teams down 1 without the ball win around 15% of the time. This means that going from down 3 with the ball to down 1 without the ball doesn’t increase your chances of winning by very much. This is why I like to call the quick 2 the slow loss. By scoring 2 points you are really just extending how long it is before you have no chance of winning - you are likely to just end up back in the same spot, down 3 with the ball, but with less time remaining, and eventually you will miss a shot and the game will be over. You should be trying to maximize your chances of winning the game, not maximizing the time until you have no chance to win.
To look at it another way let’s say if you shoot a 3 you will make it 25% of the time (I am intentionally choosing a low percentage here to demonstrate that even a low percentage 3 is a fine shot). Even if we assume that if you miss the shot you have 0 chance of winning (which we know is not true - missed 3s are offensive rebounded ~20% of the time), given that teams without the ball in a tie game when the other team can hold for the last shot win 35-40% of the time, you win 9-10% of the time if you take that 3. Compare this to the 15% of the time teams down 1 without the ball and 15-20 seconds left and this basically means that the only 2 point shot that is better than a bad 3 is a good shot right at the rim (a 70+% shot). This is the other mistake people make when saying “you don’t need a 3”, it’s really hard to get a 2 point shot that good.
These numbers are looking at when you are down 3 with 20-30 seconds remaining, so when you start to get down to 10 seconds and under remaining, the quick 2 looks even worse. Obviously each individual situation is different, things like how many timeouts do you have left (another thing I think teams get wrong is not saving their last timeout to advance the ball with under 10 seconds left) and the other team’s free throw shooting ability should impact the decisions you make, but if you use the numbers above as a starting point and adjust for whatever assumptions you have, you will probably find that teams aren’t aggressive enough at going for 3 in these end of game spots when they are down 3 with the ball. Unless you are getting a near guaranteed 2 point shot, you are better off taking a 3, even with as much as 30 seconds remaining.