Undefeated seasons and aligning incentives

The Sports Guy has written recently about the relative probabilities of going undefeated in the NFL and in a given fantasy football league. Simmons skips the obvious historical approach--getting the a fantasy stats service to tell him how many teams go undefeated and comparing the incidence with the NFL's history--but he offers good reasons for thinking the undefeated fantasy season the rarer achievement. I'll add a couple of thoughts about the role of incentives in the comparison.

Many of Simmons's points boil down to the simple fact that fantasy results are hard to control due to misaligned incentives. If the Patriots are winning by three touchdowns and your fantasy team needs Tom Brady to through for two more, you're out of luck because Brady doesn't care what you need. His incentives are different from yours. Incidentally, this scenario demonstrates why I think fantasy baseball is a better pretend sport than fantasy football: in baseball, Manny Ramirez is going to try to hit well whenever he comes to the plate. His incentives are aligned with his fantasy owners' because there's no way to run out a clock.

(Side note: the latest Nobel prize in economics was awarded for work on mechanism designs that maximize incentive alignments. Here is one explanation of the work.)

OK, so the point is that misaligned incentives make fantasy football tougher to control. But there's also a contrary influence of incentives. In most fantasy football leagues, every team is trying to win a given year's championship. In the NFL, some teams are trying to win the Superbowl, but many of them are looking at least partly to the future, some are in full rebuilding mode, and a few are coasting along on low salaries to soak up guaranteed profits through revenue sharing. Therefore, the NFL is guaranteed to have unbalanced resources, with a handful of really good teams standing in the way of any undefeated season. It would be much easier to sweep a league that disbanded every team each year.

How do these variously misaligned incentives shake out to answer Simmons's question? I don't know. I'd love to see some data.

The Preakness: Odds and History

I was struck by the headline in The New York Times on the day of the Preakness Stakes: referring to Kentucky Derby winner Street Sense, it read, "Favored in Preakness by Odds, Less So by History."

The article, by Joe Drape, shows the opposite.

It opens with a reference to Street Sense's status as the 7-to-5 favorite in the Preakness. That means that the odds gave Street Sense just under a 42% chance of winning. Like other sports betting markets, that of horse races has a fantastic track record, so we can reasonably expect horses with 7-5 odds to win about 42% of the time.

The article then moves to this paragraph, quoting Street Sense trainer Carl Nafzger:

“What I know is that I have a 9-to-1 chance to win,” he said, referring to the number of starters in Saturday’s race. “And that’s a lot better than it was at Churchill Downs for the Derby when we were 19-1.”

Because I am a generous man and have a good dessert in my belly, I will assume that Nafzger likes to toy with reporters rather than that he is as silly as this comment. (By this logic, horse owners might as well toss any old entry into the Preakness; heck, but a bunny in the gate--it's a lot cheaper to feed than a horse, and it will still have the same chance of winning!) Even so, this is an inspired bit of nonsense. It combines obviously false egalitarianism with a classic confusion of probability and odds ("9-to-1 chance" rather than one in nine).

Drape makes more sense in the paragraph that follows:

History suggests that the odds are much better than that for Street Sense: 52 percent of Preakness winners were sent off as the post-time favorite, as Street Sense certainly will be. In the past 10 years, six Derby winners have won the mile-and-three-sixteenths race and headed to Belmont Park with a chance to sweep the Triple Crown.

And here the more interesting point arises: if pre-race favorites had won 52% of Preakness runs, and Derby winners have done even better in recent races, then Street Sense's 7-5 odds reveal a weaker favorite than one would expect, a horse given less of a chance to win by bettors than the performance of similar horses in the past would indicate.

"Favored in Preakness by Odds, Less So by History"? Nope--favored by history, a little less so by the odds.