Guest Post: Rethinking Late Game Defense in NCAA Play

In honor of the Sweet 16 games of the NCAA Men’s Basketball tournament tipping off later today, here’s a guest post from Kyle Schmitt on a radical reimagining of optimal strategy for late game defense. Kyle is a nuclear engineering consultant by day and aspiring sports data analyst in his spare time. He received his Masters in mechanical engineering from MIT in 2010.  Kyle, a born-and-raised Wisconsin sports fan, currently roots for his teams from across the border in Chicago, IL and can be found on Twitter @The_KyleSaurus.

Odds are at least one in this year’s Sweet Sixteen will come down to to a tie game with less than a minute left.  How each coach chooses to play this scenario could have an outsized effect on their team’s national championship hopes.

All basketball fans know the dismal experience of rooting for a team that finds itself tied, without possession, coming down the stretch.  They also know the universal strategy is to bunker down, come up with your best defensive effort, and play for overtime. It is basically unheard of to intentionally foul your opponent.  From an (albeit misleading) statistical perspective, the conventional strategy is bolstered by a roughly 1.0 point-per-possession average in the NCAA, relative to the 1.2-1.6 expected points you’d be handing your opponent if you sent them to the line.

But, have basketball coaches been getting away with crimes against middle-school math?  The answer may be yes, and it comes down to a simple fact: it is exceedingly difficult to win the game in regulation with the conventional strategy.

Let’s look at the closing seconds of a game.  Under the predictable strategy of allowing your opponent to run the clock before attempting a final shot, there are three basic outcomes we will consider: your opponent makes a field goal and you lose; your opponent is fouled as they attempt their field goal and you have to rely on them missing both free throws to go to overtime; or your opponent misses their field goal and you play extra time.[1. You can and should quibble with the lower likelihood events or correlations left out. For instance, the proposed decision tree neglects poor clock management by your opponent leading to an early shot and an opportunity for you to possess the ball before the end of the game; you getting a steal and an opportunity at a run out basket as the clock expires; an offensive rebound and a put back, or your opponent failing to get a shot off.  Under reasonable assumptions, these sequences of events have not been found to impact the conclusion of this article. The reader is encouraged to try to refute the conclusion with a more detailed model.]

Using the NCAA league-median for field-goal percentage (FG%=44%) and free-throw percentage (FT%=70%)—and an assumption that you foul your opponent as they attempt their final shot 10% of the time—the likelihood that you will lose in regulation is 53.1%; the likelihood that you will force overtime is 46.9%; and the likelihood you will win in regulation is 0%.

[2.

The reported values assume your opponent is in the double bonus. Under the assumption that they are in the bonus, the likelihood that you will lose in regulation is 51.0%; the likelihood that you will force overtime is 46.9%; and the likelihood you will win in regulation is 0%.] It is no wonder your heart sinks when that possession arrow points the other way.

So, what about the coach who throws convention to the wind? In a tied game, with the shot clock turned off, she boldly calls for a foul to send her opponent to the line.  Could this possibly be a good strategy?

The model becomes a little more complex.  There are different scenarios depending on whether your opponent makes zero, one, or two from the charity line.  If they make zero or one, you play your offense just as you would otherwise, effectively putting your team in the driver’s seat.

If your opponent makes both free throws, you might elect to run a play to win it regulation with a three-pointer; you are after all breaking with convention.  In this scenario, we somewhat arbitrarily[3. This ratio was determined as the ratio of league median field goal percentage (44%) to the sum of the league median field goal percentage and the league median three point percentage (34%). This is analogous to the concept of a current divider, where current is allocated between two parallel sources of resistance.  More current is allocated to the lower source of resistance (in this case, the higher percentage of tying or winning the game).] assume a 56% chance you draw up a play to tie and a 44% chance you draw up a play to win.

Assuming your opponent is in the double bonus, the likelihood that you will lose in regulation is 37.5%; the likelihood that you will force overtime is 29.7%; and the likelihood you will win in regulation is now 32.8%.  If your opponent is in the single bonus, the likelihood that you will lose in regulation is 47.7%; the likelihood that you will force overtime is 19.9%; and the likelihood you will win in regulation is now 32.4%.[4. Predictions are largely insensitive to whether you are in the bonus or the double bonus given that you being fouled during your shot attempt makes up only a small amount of the event space. The predictions reported in this article assume you are in the single bonus.]

Assuming a 50-50 shot in prevailing in overtime, you have given yourself a minimum likelihood of winning of 42% relative to the approximately 25% likelihood afforded by conventional strategy.  That is a difference that could turn an underdog into a Cinderella story.

So, what do you say to the coach who argues that, in late-game scenarios, the defense will be more engaged and active, resulting in a lower field goal percentage? Well, our analysis suggests the breakeven point would require the defense to hold the offense to a 24% field-goal shooting percentage if your opponent is in the single bonus or a 29% field-goal shooting percentage if your opponent is in the double bonus.[5. Ed. Worth noting this later percentage isn’t too far removed from what has been observed on last second game-winning shot attempts over several seasons of NBA play in the past.]  This may be asking too much of a defense.

As a useful analogy, we consider the even grimmer scenario in which your opponent is up by one with the ball. Of course, if your opponent is allowed to play the game out unfouled, they will win.  However, if you foul, you have roughly a 1 in 10 chance of winning the game in regulation and a roughly 1 in 5 chance of winning the game overall (assuming your opponent is in the double bonus). As demonstrated, however, the benefit of intentionally fouling your opponent down the stretch is not unique to scenarios in which you are playing from behind.

And so, we patiently await the coaching pioneer who will first implement this courageous new strategy.  Or, better yet, the strategic equilibrium that might follow—can you imagine, in a tied game, a procession of intentional fouls for the right to have possession as the game clock elapses?