Wednesday, October 27, 2004

Dolan responds: Taranto's math right; 'Skins and Bush to lose; go, Irish!

Update: See bottom of post.

In piece on the Redskins in yesterday's "Best of the Web," James Taranto displayed his math skills. First he quoted Justin Taylor:

For the past 72 years, the fate of the Redskins in their last game before the election has predicted whether or not the incumbent party holds the White House. If the Redskins win, the incumbent party stays. If the Redskins lose or tie, the incumbent loses the White House. The rule has held for the last 18 elections....

David Dolan, an assistant professor of mathematics at the University of Wisconsin-Green Bay, calculated the odds of this happening for 1 in 263.5 million. (By the way, that's 2,600 times higher than the chance of getting killed by lightning!)
Taranto then quibbled with the analysis:

This number seems vastly out of line. If we assume that the Skins have a 50% chance of winning each game and the incumbent party has a 50% chance of winning each election, the odds of the two indicators matching up for 18 elections in a row are 1 in 262,144 (2 to the 18th power). The odds that they will match up for 19 elections in a row are 1 in 524,288. Does this mean you should bet against the pattern repeating? Of course not. The odds that it will are 50-50 (with Bush and the Skins both slightly favored).
In trying to stir up the nest a bit, I e-mailed Prof. Dolan inquiring if he'd answer some questions on the record about his analysis and Taranto's critique. He agreed.

Turns out Taranto was right; Dolan, who takes the whole thing in fun, says he was misquoted.

Onto more interesting topics, Dolan figures the pattern will continue with the Redskins and incumbent Bush both losing. Also, for the record, Dolan is a college football fan partial to alma mater Notre Dame, and he apparently follows the Packers enough to use their stats in his statistical coursework.

His answers to my e-mailed list of questions follow:

David M: Did the article convey your thoughts correctly? If so, do you stand by your statements?

Dolan: No. I was misquoted. I agree with the calculation noted in the WSJ.

David M: Please explain your methodology (in layman's terms if possible) for calculating the figure, 1 in 263.5 million.

Dolan: This is incorrect. It is off by a factor of about 1000.

David M: Please comment on Mr. Taranto's methodology for calculating the figure, 1 in 262,144 (2 to the 18th power).

Dolan: I believe this method is correct if you accept the chance of predicting an election correctly is 1/2. In order to refine the calculation, you would need to find the odds for all 18 elections and all 18 Redskins games. This would be difficult, especially for the early games. My sense is that the average for both would be around 0.5, so the calculation should be pretty good.

David M: How active a football fan are you? And what is your football team of choice?

Dolan: I am an active college football fan. I attend two or three games a year and follow all Division 1-A teams. My favorite team is Notre Dame.

David M: Whom do you pick in the Packers/'Skins game? Why?

Dolan: I am picking the Packers because since Sherman has been calling the offensive plays, they have been on a roll.

David M: Whom do you pick in the presidential election? Why?

Dolan: I am picking Kerry because more people will be voting in this election than in 2000 and that always favors the Democrats.

David M: Other comments?

Dolan: I use the Packers' season stats in my Applied Regression Analysis course. It's a good way to keep the students interested while they learn.

Update: Turns out the streak was broken in 1996, which that means the streak lasted 16 elections. On the surface, there was a 1-in-65,536 (2 to the power of 16) chance of that occuring.

However, it was actually considerably more likely than that. The new question is, "what are the chances that the Redskins pre-election fate corresponds with the incumbent party's fate 16 times in a row at some point in the last 18 elections? I calculate the answer to be 1 in 28,339. I leave it to the reader to check my numbers. I figure the 'Skins and incumbents have to share a fate for {elections three through 16}, and also for (either {elections 1 and 2} or {2 and 17} or {17 and 18} ).

(By the way, the Redskins have only been around for 18 elections.)