Tuesday, November 07, 2006

Bernoulli and the 2006 Bengal Tigers:

Say what you will about Les Miles and his in-game coaching abilities, but his 2006 Tigers have garnered an advantage each week before the game even starts. In what seems fitting for Miles's high-stakes, riverboat gambler mentality, perhaps his team's most impressive yet unmentioned quality is winning the coin toss. And it's happened in all nine games this season.

Me: "I think it might be time to bring back the purple pants for a game."
Les: "I'll do one. I'll do one."

Coin toss probability follows a simple Bernoulli distribution, which is characterized by an event having two distinct outcome possibilities, usually labeled '0' for failure and '1' for success. A general Bernoulli distribution follows

P(n) = p for n = 1.
P(n) = 1-p for n = 0.

Jeff Sagarin is unzipping his pants right now.

In the case of a coin toss, p = 1/2. Probabilities are multiplicative for separate events (tosses), so the probability of a successful coin toss m times in a row is denoted by:

P(1) ^m = (1/2)^m

Obviously, we are discussing a successful coin toss in m = 9 games this season, leaving

P = (1/2)^9 = 1/512 ~ 0.00195.

The Bernoulli distribution is by far the easiest discrete distribution in Probability and Statistics, even to the point that JaMarcus, Dorsey, LaRon, et al. have seemed to master the concept.

Skimming the box scores:

Week 1: UL Lafayette at LSU:
LSU's game captains were 2 JaMarcus Russell, 30 LaRon Landry, 41 Chris Jackson.
LSU won the toss and deferred to the second half.

Week 2: Arizona at LSU:
LSU's game captains were 16 Craig Steltz, 18 Jacob Hester, 41 Chris Jackson, 72 Glenn Dorsey.
LSU won the toss and deferred to the second half.


Week 3: LSU at Auburn:
LSU's game captains were 2 JaMarcus Russell, 33 Jason Spadoni, 41 Chris Jackson, 94 Chase Pittman.
LSU won the toss and deferred to the second half.


Week 4: Tulane at LSU:
LSU's game captains were 25 Justin Vincent, 31 Jessie Daniels, 41 Chris Jackson, 80 Dwayne Bowe.
LSU won the toss and deferred to the second half.


Week 5: Mississippi State at LSU:
LSU's game captains were 3 Craig Davis, 18 Jacob Hester, 41 Chris Jackson, 52 Ryan Willis.
LSU won the toss and deferred to the second half.

Week 6: LSU at Florida:
LSU's game captains were 2 JaMarcus Russell, 16 Craig Steltz, 30 LaRon Landry, 41 Chris Jackson.
LSU won the toss and deferred to the second half.


Week 7: Kentucky at LSU:
LSU's game captains were 7 Ali Highsmith, 19 Jonathan Zenon, 41 Chris Jackson, 77 Peter Dyakowski.
LSU won the toss and deferred to the second half.


Week 8: Fresno State at LSU:
LSU's game captains were 3 Craig Davis, 41 Chris Jackson, 80 Dwayne Bowe, 93 Tyson Jackson.
LSU won the toss and deferred to the second half.


Week 9: LSU at Tennessee:
LSU's game captains were 41 Chris Jackson, 72 Glenn Dorsey, 75 Brian Johnson, 94 Chase Pittman.
LSU won the toss and deferred to the second half.

So Matthew Flynn and CJ do go clubbin' together! Tyson tags along since Ceej is the only one who knows how to play craps.

So, yeah, Chris Jackson apparently runs the thing. Dude probably does chi-square distributions on the sidelines during his free time. Couldn't seem to find anything on the record (at any level of football) for consecutive coin tosses in a row. Chili dog. This is the closest I could come:

"The record for consecutive toss wins by one country is also 12 - by Australia {1998-99 in Pak (2), v Eng (5) and in WI (4); 1999-2000 in SL (1)}. The captains were MA Taylor (7) and SR Waugh (5)."

And Chris Jackson. That was from a cricket website, by the way.

Why even write a caption for this? And to think, ten months ago I hated facebook.

Les Miles has notched an 18-4 record since moving to Baton Rouge. His captains are 17-5 in calling the coin toss correctly. Coincidence? No, those five belong to the Vanderbilt, North Texas, Appalachian State, Ole Miss, and Miami-- all convincing wins. There, you've got your first resource devoting an entire article to this somehow unmentioned phenomenon. I can't wait till Marty Mule' tries to go all Fibonacci on us tomorrow.

- P.T.

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