Syracuse lost a game to Villanova this weekend when they were up three points, and allowed a tying three pointer to send it to overtime. It’s not the first time that has happened this year, as Iowa State having a chance to beat Kansas in Allen Fieldhouse but allowing the banked shot by Ben McLemore comes to mind.

It again has spawned the question about whether coaches should foul when they are up 3 very late, prevent a team from tying it, and make the opponent (1) not get a shot off before the foul, (2) hit the first free throw, (3) miss the second, and hit the rim, (4) get the offensive rebound, and (5) make a shot to either tie, or kick out for a winning three pointer.

I tried to do some general calculations on the two strategies, though coming up with some of the estimates are better served by real examples. How likely is a team to accidentally foul on a shot when trying to intentionally foul before, giving three free throws? How likely is someone to miss the rim entirely on an intentional missed free throw?  I guessed at those.

Others, we can use data. For example, here is an old Ken Pomeroy post on rebound rates on 2′s vs. 3′s vs. free throws. The offensive rebound rate on missed free throws was 20%, and we can use average results. Free throw rates, and three point rates can be considered.

Throwing all that together, my theoretical estimate was about 5-10% chance of getting tied by employing the foul strategy, depending on how much of a chance you want to attribute to a player getting a legitimate shot off while being fouled. It was about 20% of going to overtime, by playing defense straight up, depending on just how much you think the normal 3-pt rate is affected by being rushed, and the defense knowing you need a 3.

Obviously, based on my theoretical estimate, teams should be employing a foul strategy more often than not. How does that compare with actual results? Mike DeCourcy had a piece last weekend in which he cites high school coach Steve Finamore. According to Finamore, there had been 279 situations with a team up 3 in the final 7 seconds. 259 times, the team played defense, and gave up a tying three 46 times (17.7%). 20 times, the team fouled intentionally, and once, the opponent tied by getting the rebound/put back (5%).

A few years ago, Harvard Sports Analysis wrote about it, concluding the results between the two strategies were not statistically significant. For the 2010 season, foulers allowed a tie 7 of 48 times (14.6%), while the straight up defenders allowed a tie 93 of 395 (23.5%). The conversion rate there might be higher because there was no time limit (only final possession), so that teams with more time to set up could get a better shot at three pointers by setting screens, or passing on one shot for another when the defense got out of position. It was noted that over half of the times the “foul” strategy did not work, it was due to committing an intentional foul while the opponent got a shot off.

Bill Fenlon of DePauw University wrote about the issue, and is one of its biggest proponents. My general estimates were close to his. Why is this important? Fenlon was Butler coach Brad Steven’s college coach, and Stevens notably employed the strategy in the Final Four win over Michigan State, covered by Luke Winn here.

I think if you read all of those things, you should be fairly up to date on the state of the “foul” versus “defend” strategy up by 3 points. I will say that the optimal strategy should be to foul more often than not. Factors can swing that in an individual game, including having to foul a great free throw shooter (which improves the opponent’s chances of making the first/getting a quality miss on the second), and the matchups when it comes to rebounding. As Brad Stevens alludes in the Winn piece, if the opponent knows what you are going to do, they can counteract it better. The optimal strategy would be to foul more often than not, but vary it for maximum effect over time.

That said, I am surprised that coaches are currently opting to play defense over 90% of the time in 2012-2013. One of the main issues with football decision making is a reactionary and generally conservative traditional media in covering the game, from broadcast announcers to columnists. I do not get the sense that is the case in college basketball. I have read plenty of columnists who mention the concept, and have heard game announcers discuss it. Intentionally fouling is an accepted and normal strategic part of the game–albeit usually when trailing–and is not anathema like letting an opponent score in football.

In an environment where coaches are not scalded as hotly and others in the mainstream discuss the idea, you would think it would be a more commonly used practice. It should be.

[photo via USA Today Sports Images]