When being bad is good

As you know if you've followed me for a while, I'm a bit of a sports stat nerd, and I'm a sucker for anything that highlights the intersection between math/statistics and sports. In that vein, this item from Nate Silver's FiveThirtyEight blog was one of the most well-done statistical pieces about sports and strategy that I've ever read.

In short, Silver wonders if--and proves that--it's in fact significantly better to draw an 11 seed in the NCAA Men's Basketball Tournament (hello, Gonzaga) than to draw an 8 or a 9 seed. In fact, an 8 or a 9 is pretty much the worst seed you could possibly draw--only the lowly 16 seeds (you know, the directional schools that you've never heard of unless you happen to be an alum) are in a worse competitive position.

The reason, as Silver points out, is that the winner of the 8 vs. 9 game earns the dubious privilege of playing their region's #1 seed in their next game. This matters a good deal, because the #1 seeds tend to be dramatically better than the 2, 3, and 4 seeds in their bracket--in other words, you want to avoid playing the #1 at all costs. Silver explains:

The root of the problem is that the relationship between team strength and seeds is not linear. Instead, the No. 1 seeds (and to some extent the No. 2 seeds) are often quite a lot better than anyone else in the field. They are also especially dangerous in the first two rounds because, under the “pod” system the N.C.A.A. adopted in 2002, these teams will almost always play within a few hundred miles of their campuses in what may amount to a de facto home game. It is worth going to some length to avoid facing one of these teams as long as possible, hoping that you get lucky and that someone else knocks them off.

The graphic that follows shows the average computer power rating, by seed, for teams playing in the tournament since 2003. These ratings also include a geographic adjustment. In the first two rounds, as we’ve mentioned, the No. 1 and No. 2 seeds (and sometimes the No. 3 seed) are generally placed at tournament sites that are close to their campuses, which further increases their advantage...

That little "S" curve in the chart (but most notably, the steepness between the 1 and the 4 seed) turns out to cause a good deal of havoc in seeding strategy. Without boring you too much with the mathematical details (you can read the whole thing if you're really interested), here's what your actual probability is of making it to the Sweet 16, Elite 8, and Final 4, based only on your seed (the Final 4 chart has been truncated to eliminate the high-probability top 4 seeds and focus only on the differences in the mid-range):

As you can see, even the 15 seed (this year: Long Island University, Northern Colorado, Akron, and UC-Santa Barbara) has a better shot of making it to the promised land than does the 8 seed (George Mason, Michigan, UNLV, and last year's runner-up, Butler). That's counter-intuitive, but the math doesn't lie.

As Silver points out, this is quite the problem, because it creates a bit of an incentive to lose--as long as you know you're likely to make the tournament field (which is common for a big-conference team), you're better off juuuuust sneaking in than you are fighting for every last win down the stretch. It's a similar problem to the "tanking to get a better draft pick" dynamic that the NFL and NBA have battled with over the years, and that has led the NBA to institute--and then constantly tweak--a "Draft Lottery" system.

So while it may be fun to watch that 8 vs. 9 game (yup), and we do every once in a while see an 8 or a 9 topple a #1, it's definitely not a good spot to find yourself on Selection Sunday. And, yes, Villanova, we know that you were an 8 seed back in the first year of the 64-team field. But George Mason (2006) and LSU (1986) were 11 seeds. So shhhhhhhhhh.

[FiveThirtyEight]