Up Three, Under Seven (cont.)
At Trinity in '99, Fenlon was faced with the up-three situation for a third time ... and he hunkered for a third time. He was hung up on the nightmare scenario of creating a four-point possession -- and losing -- as a result of fouling. And so he watched Trinity's Ryan Hyslop come off a staggered screen and hit a falling-down three at the buzzer. DePauw lost in overtime. Fenlon had no good excuse.
One of Fenlon's backup guards, senior Brad Stevens, played seven minutes and scored zero points in that game, the fifth-to-last of his career. After graduation he'd leave basketball and take a job analyzing marketing data at pharmaceutical giant Eli Lilly in Indianapolis. Stevens was so savvy with numbers, that a former coaching colleague once called him a "math savant," but he had forgotten his stats from the Trinity game -- perhaps because they were unremarkable, well under his season averages of 5.4 points in 15.2 minutes. He said he remembered one thing: "That was the road trip that started to change [Fenlon's] philosophy."
DePauw men's basketball had no traveling beat writer, so the only recap in the school's online archives is a one-paragraph summary calling the loss a "heartbreaker." A Lexis-Nexis search for "Trinity" and "DePauw" during that week of 1999 yields only two articles. One is from the San Antonio Express-News, which briefly previews the game in a local-college roundup. The other hit is more peculiar, and unrelated to basketball: the New York Times' "Genius or Gibberish? The Strange World of the Math Crank".
The Trinity referenced is the college at Cambridge, England, not San Antonio. But the DePauw is the correct DePauw, from Greencastle, Ind. The article states that a DePauw professor, Underwood Dudley, is the world's foremost expert on Math Cranks -- amateurs who send absurd letters and theories to mathematicians purporting to have discovered "important new truths" in the world of numbers. Dudley acknowledged to the Times that it's hard to pin down exactly what makes a crank a crank, but said, "It's like obscenity -- you can tell a crank when you see one."
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Fenlon left the '98-99 season determined to conduct a mathematical investigation. He wanted to discover the actual odds of hunkering versus fouling when your team is up three and on defense, with seven seconds or fewer left in the game. (Any more time on the clock, and most coaches believe the danger of allowing an extra possession is too great.)
A crank might have conducted the investigation on his own. Fenlon asked for help from one of his team's season-ticket holders, DePauw math professor Mark Kannowski. He created a series of decision trees using probability data Fenlon provided on average three-point and free-throw percentages, as well as estimates for rebounding and turnover percentages, and accidental-foul rates. Fenlon seeing the finished decision trees, Kannowski said, "was what made everything click."
Fenlon included the trees as supporting material for a 2,728-word paper he titled, "Up Three: To Foul Or Not To Foul," at the bottom of which Kannowski is credited for the math and Esquire writer-at-large Tom Chiarella, a visiting professor at DePauw, is thanked for the editing. The paper's conclusion is that coaches should always foul, trusting the aforementioned odds (4.9 percent chance of overtime by fouling, 19 percent chance of overtime by hunkering) and ignoring any other factors.
Fenlon wrote: "It's about the probabilities over the long haul. It's not about the chances in this moment. It's about the chances in this situation every time it occurs. You can't be like the guy at the roulette table who has his money on red, watches black come up six times, changes his bet, and then it comes up red. You can't win that way. You have to be consistent, and you have to know the numbers. A lot in coaching is dictated by your feel, by your gut. This situation is not, it is dictated by the numbers. Take a look at these numbers and I think you will find it very difficult to make a case for not fouling in this situation."
At DePauw, the fouling strategy gains new converts every time Kannowski teaches Computational Discrete Mathematics, or Math 123 in the school's course catalog. The Tigers (according to Fenlon) are 6-0 when fouling up-three, and Kannowski figured the basketball decision-making trees he created would be better teaching material than standard textbook problems. "I've gotten a lot of mileage out of being able to use that example in class," Kannowski said. "Kids will sit up a little bit and say, 'Really?' "
Although Fenlon's may have been the first, other examinations of the college fouling strategy exist in academia. A 2006 study, "Optimal End-Game Strategy in Basketball" by David Annis, then an assistant professor at the Naval Postgraduate School, was inspired by the Michigan State-Gonzaga epic from the 2005 Maui Invitational. The game is mostly remembered as Vintage Adam Morrison; he scored 43 points and the Zags won in triple overtime. But it went to overtime in the first place because the Spartans' Maurice Ager was allowed to sink a 3-pointer at the end of regulation.
The central character in Annis' paper is Gonzaga coach Mark Few, who responded to a question about the hunkering strategy with this postgame quote in the Seattle Times:
"It's not a debate for me ... If the guy [fouled] hits the free throw, they can tip it out and hit a three and you can lose the game. They can score four on you ... I've never, ever fouled, and I've been in that situation a lot of times. I think you've got to make somebody hit a real tough shot. And they did."
Few -- who's hardly alone among D-I coaches in his beliefs -- is the anti-Fenlon. Annis, in his equation-heavy analysis, wryly labels the hunkering strategies "Few" and the fouling strategies "Non-Few." He concludes that while the "Few" approach gives a team an 86.6 percent chance of winning, the "Non-Few" approach has win odds of 95.9 percent, with the chance of losing on a tip-out and a 3-pointer just 0.6 percent -- so remote as to be a non-factor. Annis' study, therefore, thinks fouling offers even more of an advantage than Fenlon's; assuming that each team enters overtime with an equal chance of winning, Fenlon's decision trees would yield win odds of 97.6 percent for the "Non-Few" approach and 90.5 percent for "Few." That's a 7.1 percent split compared to 9.3 in Annis.
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