He found that in 391 of the 443 instances, the leading team chose not to foul. Only 33 of those teams lost, yielding a win percentage of 91.6 -- about the same as Fenlon's estimate. Teams that fouled, in Ezekowitz's study, were actually worse off. Six of the 52 teams that fouled lost, yielding a win percentage of 88.5. Therefore, Ezekowitz concluded, "Both a two sample t-test of proportion and a Chi-squared test fail to reject the null hypothesis that there is a difference in winning percentage between the two strategies. ... [T]his means that there is no significant difference between the two strategies."

Ezekowitz's study was the first (or at least first known) of its kind for college basketball, and his "no significant difference" finding was quoted in places such as the Wall Street Journal's Web site and ESPN the Magazine. The recognition helped him earn a freelance gig doing statistical analysis for the Phoenix Suns. Some commenters on the Harvard Sports Analysis Collective's post remained unconvinced, raising qualms -- legitimate qualms -- over the fact the study didn't take into account how much time was left on the clock. Its data pool included all possessions that had potential to be a team's last, meaning that some of them might've been in the upper reaches of the 35-second shot clock. That part wasn't really Ezekowitz's fault; play-by-play data isn't available in sufficient detail at all levels of D-I. But it's difficult to make a definitive statement without a time factor. Coaches just aren't comfortable fouling with more than seven seconds left.

When I went to the Harvard Sports Analysis Collective's site in early September to re-read Ezekowitz's post, I noticed that the 19th (and most recent) commenter had volunteered a rebuttal. His comment, in full:

September 1, 2010 at 5:57 pm

Hi-

I wrote an article about the up 3 scenario a few years ago with the help of a math Professor here at DePauw University. I think there are too many things missing here for your findings to be accurate. If you'd like to read my findings send me an email and I'll pass it along.

Bill Fenlon
Head Basketball Coach
DePauw University

I was unaware of Fenlon's interest in the subject until then; curious, I called him in his office at DePauw and had a conversation about his article. "I can just e-mail it to you," he said, "and you can tell me what you think."

The next day, in my inbox, was a message with a Microsoft Word attachment and the subject, "You Gotta Foul!"

* * * * * * * * *

Is Brad Stevens a true believer in fouling? Fenlon can't answer that. "You never know with Brad," Fenlon said. "I'm not sure what he told you about it ... but he's one of those guys who plays everything close to the vest."

Here's what we know: Fenlon's paper was in Stevens' hands before he took over at Butler in 2008. His first encounter with the up-three, under-seven situation was at Valparaiso on Feb. 5 of that season. He ordered the Bulldogs to hunker. Valpo's Brandon McPherson, a 40.9 percent three-point shooter, missed a contested three at the buzzer, and Butler won, 71-68.

One week later -- and nine years to the day after the fateful DePauw-Trinity game -- Stevens was faced with the up-three situation again, this time against Wisconsin-Milwaukee. Again, he told the Bulldogs to play defense. The Panthers' star, Ricky Franklin, hit a three with 0.8 seconds left to send the game into overtime, in which Butler won 83-75. In the Indianapolis Star's game story, Stevens revealed that he had a "list" of scenarios that warranted fouling or not fouling. In the Milwaukee case, he told the Star he was worried Panthers power forward Marcus Skinner would rebound a missed free throw and score on a put-back.

But when discussing it 2 1/2 years later, Stevens suggests not fouling Franklin was a mistake. "It was just a bad move on my part," he said, mostly because his guards weren't tall enough to bother Franklin's shot. He is what amounts to a Situationalist -- "I think you have to take everything into account" -- but his lens is evolving. Coaches in this result-driven business tend to acquire their stance on fouling through experience. What they've been told is secondary to what's happened to them, or what they've seen happen to their peers.

Stevens and I were both in Salt Lake City on March 25 to witness the Kansas State-Xavier double-overtime epic, in which the Wildcats tried to foul, up three, in the final seconds of regulation, and accidentally fouled the Musketeers' Terrell Holloway in the act of shooting. Fenlon estimates this sort of accident will happen only 2 percent of the time. I asked Stevens whether he thought that number was low; it seemed low to me. "Offenses get more prepared for [the foul] the more they expect it," he said. "So that number is going to change over time."

Stevens was left on the sideline, on April 4, to consider all of those things: the odds, the personnel, and what Michigan State was expecting. His starting big man, Matt Howard, had already fouled out, and his two-guard, Shelvin Mack, was on the bench with an injury, so Butler's defense wasn't at full strength. The Spartans had three dangerous long-range shooters on the floor in Durrell Summers, Chris Allen and Korie Lucious. Gordon Hayward, Butler's best defensive rebounder -- with a vertical that allowed him to get up to 11 feet and clean the glass -- was also on the floor. The numbers in Stevens' head were tilting in favor of the foul.

And that's what Butler did. While Jukes and Veasley failed to draw a whistle with their double-team on Morgan, generating some undesired tension, Bulldogs guard Shawn Vanzant was able to corral Lucious deep on the left wing before he could get in the act of shooting. Only 2.1 seconds remained in the game, eliminating any chance of another Michigan State possession. Everything would come down to the free throws.

Lucious made the first. In the Fenlon model, this increased the chances of overtime from 4.9 percent to 7.5 percent, and the chances of Butler losing on a rebound-and-three combo from 0.16 percent to 0.19 percent.

As planned, Lucious missed the second. This only slightly increased the chances of overtime on the Fenlon tree, because his estimate was that a player could successfully miss 98 percent of the time. The key was the rebound: Given Butler's 4-to-2 man advantage in the lane, the odds of a Spartans offensive rebound were 20 percent or less. If they grabbed the ball, they'd have a 38.3 percent chance of sending the game to overtime.

The shot hit the back of the rim, bounced up and hung in the air ... and was snared and smothered by Hayward, just as Stevens had hoped. Jukes and Veasley, who were on the blocks, had created a perfect seal for Hayward to run in from the third position on the left side of the lane. He ran off the court making a "No. 1" sign. There was a 0.0 percent chance of overtime. Butler was in the national title game.

Fenlon took out his phone and texted to Stevens, "You finally listened!"

Stevens can't remember exactly what he wrote back. It might have been something about finally being coachable after 33 years, but it also likely included an admission of relief that the rebound bounced the way it did. It certainly did not include a guarantee that he'd always foul in the future. If Stevens ever makes that decision, he'll keep it to himself, anyway; he likes to play it close to the vest. I suspect, though, that he'll remain a Situationalist. He still has too vivid a memory of Summers, streaking in from the top of the key toward that final rebound.

"What he did there was illegal," Stevens said of Summers, who entered the key before the ball hit the rim. But there was no mistaking that with a Hayward-free path down the lane, and Summers' level of athleticism, he might have produced a highlight-reel play that set mainstream acceptance of the fouling strategy back decades. The odds of that happening -- escaping the eyes of three refs while also avoiding Hayward -- seem infinitesimally slim. Yet they provide no guarantee. "If Gordon's not there," Stevens said, "Summers could've tip-dunked it for the tie. And then, I made a bad decision."