NCAA men’s basketball tournament…place your bets

I’m not much of a sports fan, but I enjoy reading “King Kaufman’s Sports Daily” at Salon.com. (I think Kaufman’s column may be only available to “Premium” (paid) subscribers). For the past few years, Kaufman has tracked the performance of self-styled sports “experts” in predicting the outcome of the National Collegiate Athletic Association’s (NCAA) men’s basketball tournament, which begins with 64 teams that are selected by committee and supposedly represent (more or less) the best teams in the country, and ends with a single champion via a single-elimination format. Many people wager on the outcome of the tournament — not just who will become champion, but the entire set of game outcomes — by entering their predictions into a “pool” from which the winner is rewarded.

Last year and this year, Kaufman included the “predictions” of his son Buster (now three years old). Last year Buster flipped a coin for every outcome, and did not perform well; this year, he followed a modified strategy that is essentially a way of sampling from a prior distribution derived from the official team rankings created by the NCAA selection committee.

The Pool o’ Experts features a roster of national typists and chatterers, plus you, the unwashed hordes as represented by the CBS.SportsLine.com users’ bracket, and my son, Buster, the coin-flippinest 3-year-old in the Milky Way. [Kaufmann later explains “Buster’s coin-flipping strategy was modified again this year. Essentially, he picked all huge favorites, flipped toss-up games, and needed to flip tails twice to pick the upsets in between. Write me for details if this interests you, but think really hard before you do that, and maybe call your therapist.”]

To answer the inevitable question: Yes, Buster really exists. When football season comes in five months and he’s still 3, I’ll get letters saying it seems like he’s been 3 for about two years, which says something about how we perceive the inexorable crawl of time. But I don’t know what.

Anyway, correct predictions earn 10 points in the first round, 20 in the second, and 40, 80, 120 and 160 for subsequent rounds.

Note that Buster’s strategy is to assign a win probability of 1 to a team that is a “huge favorite” based on pre-tournament seeding, a probability of 0.75 to a team that is a strong favorite, and a probability of 0.5 to a team that is playing another team of approximately equal seeding.

So, how did the experts do?

Because of [a particularly arrogant and ridiculous prediction several years ago] I’m always interested to see how Sports Illustrated does in the Pool o’ Experts. Generally, it doesn’t do well. And this year was no different — except, interestingly, in the case of Mandel. He won, and his co-workers lost.

Here are the final standings of the 2006 Pool o’ Experts, the winner of which is entitled to dinner at my house, home cooking not implied. The winner is also not notified, the better to avoid having to award the prize:

1. Stewart Mandel,Sports Illustrated, 920
2. Gregg Doyel, CBS.SportsLine, 880
3. King Kaufman, Salon, 780
4. Tony Kornheiser, Washington Post, 760
5. Buster, Coinflip Quarterly, 740 (2)
6. WhatIfSports.com simulation, 720
7. Yoni Cohen, FoxSports.com, 690
8. Luke Winn, Sports Illustrated, 680
9. NCAA Selection Committee, 630
10. Seth Davis, Sports Illustrated, CBS, 590
11. CBS.SportsLine.com users, 550 (1)
12. Tony Mejia, CBS.SportsLine.com, 530 (1)
13. Grant Wahl, Sports Illustrated, 490 (3)

Notes
1. Denotes past champion
2. Denotes 3-year-old
3. Just wanted to say hi

The “NCAA Selection Committee” did not make a formal prediction, but (as indicated in the list above) would implicitly have finished in 9th place if one assumes that they would pick their favorite in each game. Buster the coin-flipper, whose predictions were essentially one “realization” of the tournament using the NCAA rankings and a crude way of performing the simulation, beat the NCAA and indeed beat most of the competitors.

At first thought it seems that the best approach to trying to win a pool such as these is to pick the favorite in every game (as in the “NCAA Selection Committee” results): after all, if the seedings are correct then all-favorites-win is the single most likely outcome (with perhaps a one-in-a-million chance of occurring). But is this really the best strategy? Is there another strategy that would (1) beat pick-the-favorites more than half the time, or (2) would have a better chance of winning the pool?

A couple of other things: (3) Is the scoring system for evaluating the performance (described near the middle of this entry) reasonable?, and (4) as Andrew has previously pointed out, there’s no such thing as a “weighted coin”.

6 thoughts on “NCAA men’s basketball tournament…place your bets

  1. If the pool is shared between winners, the popularity of a given deterministic (or at least partially deterministic) strategy based on rankings may also be relevant. I am not sure how you would/could take this into consideration when making a decision, however.

  2. Some people have reasoned along the following lines. Suppose you pick the favorites in all or most of the games. You'll end up with favored teams in the final and semifinal games, which are worth a lot of points. Many other players in the pool will have also selected those teams. Thus, even if your selections for those games are correct, you haven't really "gotten anywhere": you're still up against many other players in the pool, and whether or not you win will depend on whether you got luckier than everybody else in picking the early-round games, many of which are essentially toss-ups.

    On the other hand, if you pick a less-than-favorite to make it all the way to the final, you are likely to be the only one, or one of the few, to have chosen that team. In this case you are likely to be the winner, even if the less-than-favorite that you picked is still a very good team.

    I am not sure the reasoning is exactly correct as given above, but I think the general idea has merit: you should take into account the betting pattern of the other players, not just try to maximize your chance of predicting your entire set of games — the entire "bracket" — correctly. Indeed, there is almost no chance that you will get the whole bracket right, nor is there a need to do so.

    I guess this is an extension of Matt's point: Matt suggests that if the pool is shared between winners (I suppose it's either that, or a tie-breaker of some kind), that might affect your strategy. I'm going beyond that and saying that even if it were not shared between winners, you still want to try to avoid picking brackets that "look like" those of a lot of other wagerers for the final few games. I think.

    I suppose the right thing to do here is to simply write down a simple model for both the games and the wagering, and work it out.

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