Should Michigan State Have Fouled at the End of Regulation?

Leading by 3 with 12 seconds left, Michigan State elected to play honest defense against Maryland's final possession, and Dez Wells hit from long range with about 3 seconds left to force overtime. Naturally, this led to plenty of criticism. But was it the wrong decision?

The case for fouling seems obvious. Players make three-point shots several times a game, and the obvious way for a non-shooting foul to backfire - make the first free throw, miss the second on purpose, get the rebound and put it back - seems much harder. But a study two years ago by Ken Pomeroy suggests that, although the difference isn't large enough to be sure it isn't an artifact of small sample size, playing straight defense in the situation the Spartans were in has actually been slightly more successful in recent history.

If the case for fouling seems that clear-cut, why does the data not bear it out?

1) Desperation 3s don't go in at nearly the same rate as "normal" 3s.

Implicit in the usual analysis is the expectation that a last-second 3-pointer is as likely to make as a 3-pointer in any other circumstance - about a 1-in-3 chance. But the data says otherwise. In the sample Pomeroy used (from the start of the 2009-10 season to February 2013, teams trailing by 3 and gaining possession with between 5 and 12 seconds left in the game), the trailing team was just 16% on 3-point attempts (98 for 608). That's a large enough sample size and a large enough difference to be clearly significant - a whopping nine standard deviations* below what you would expect if the circumstances didn't matter.

There's a perfectly logical reason for this discrepancy: Most three-pointers over the course of a game are attempted by good shooters in rhythm with open, or at least moderately open, looks. Most three-pointers in the final 10 seconds when the shooting team is down 3 are rushed, often attempted by weaker shooters who don't have time to pass, and are more likely to be covered closely when the defense doesn't care about giving up an easy dunk. If the shooter is wide open, then almost by definition you can't foul him before he gets into the act of shooting; if he isn't, it's a low-percentage shot.

(* For the non-statistically-inclined, a good rule of thumb: a difference of one standard deviation is insignificant, in that it will happen frequently in a random sample even if there is no real difference. Two standard deviations is interesting but could be coincidence. Three, and you can start being cautiously confident that there is some real effect going on. Five standard deviations is very unlikely to happen just by chance. Nine standard deviations? For that to happen by chance, if every person in the world tried it a million times each, maybe two of them will see it happen once.)

2) Offensive rebounds on intentionally missed free throws are far more common than on "normal" free throws.

Typical offensive rebound rates on missed free throws are in the 15-20% range. On intentional misses in the situations Pomeroy's study covered, that jumped to 40% - not just more than the usual FT OR%, but more than the usual overall OR%! This is over a somewhat smaller sample (only just under 100 attempts instead of 600), but it's still about five standard deviations above expected if there is no difference between the two situations.

Again, there's a perfectly logical reason for the difference: Missed free throws normally don't miss badly, and therefore have soft, short rebounds, with two defenders given ideal rebounding position by virtue of the lane setup. If you're trying to miss and get a rebound, you can skew your shot to bias the bounce of the rebound toward the areas that your team controls.

Combine the two effects, and it's easy to see why fouling sounds so much more effective than it really is. Instead of a 33% chance of tying versus about 8% (assuming an 80% free throw shooter, 20% OR, and 50% on the putback), it's 16% either way. The main reason we see so many more failures defending is simply because most teams defend, so there are more chances to see it fail.

3) There are lots of ways for fouling to go wrong.

The obvious disaster scenario for fouling is if you foul in the act of shooting. Now instead of a rushed three-pointer, your opponent has a 34-51% chance (assuming 70-80% FT shooter) of tying. But there are more subtle types of problems that can occur. One that I've seen at least twice (including a Minnesota game last year, though I don't remember the opponent) is that in scrambling to foul, you are more likely to get yourself out of position and leave a shooter wide open. If that happens, you are now facing a far better shot than you would have if you had played straight defense. Another is to foul again while trying to prevent the tip-in or offensive rebound (I've seen at least one team lose by giving up a three-point play on the rebound after the intentional miss).

4) More possessions is the last thing you want when you're ahead.

Foul too early, and the opponent won't try for the desperation backward 3-point play. They'll just shoot to make both and foul you and hope you miss. It's much easier to make up three points in two (or three) possessions than it is to do in one. This, in particular, is why it's an especially bad idea for this Michigan State team to foul in these situations - a free throw contest is all sorts of bad news if it's anyone besides Trice at the line.

5) Fouling is awful aesthetically.

This isn't a statistical reason to avoid it, but it has some impact. I'll admit to being biased against fouling simply because it's bad enough to have it benefit the trailing team to intentionally break the rules and get caught; having both teams do it would make the endgame descend into farce. This could easily work against you from the referee's perspective as well. It's well known that subconcious even-it-up biases exist among referees; when there is a large foul disparity, the team with fewer fouls is disproportionately likely to get called for the next one, and the phenomenon grows even more pronounced when that team is ahead. Thus, it's plausible that a referee in doubt as to whether it should be a 3-shot foul or not would err on the side of calling it a shooting foul, without even considering the possibility of an unconscious bias against the practice of fouling in that situation leading them to want it to fail. If I were a referee, I'm not certain I could avoid an intentional bias in that direction, much less an unintentional one (which is one reason why I'm not a referee).

In summary, the obvious arguments for fouling don't hold up under numerical scrutiny, and the sheer number of ways fouling can go wrong make up any gap that does exist. And it's just ugly and makes a mockery of the game.

#TeamDefend forever.