In Re: Nerds in the Springtime

It's the best gambling weekend of the year: March Madness, Rounds 1 & 2! I just had an incredibly interesting email exchange with a friend about vagaries of various brackets - one common (crappy) bracket structure is the "get bonus points equaling the difference between seeds for upsets" meme. Basically, if a 5 beats a 12, you get 1 point - if the 12 beats the 5, you get 7 points. This encourages wild first-round picks, but is it really worth it? Let's look at the math (note: this math relies on a somewhat-odd 1/2/4/16/32/64(!) structure - most are 1/2/4/8/16/32, which does change the Final Four math slightly, but only by a few percentage points):

Here's the odds breakdown for the big seeds (how often you need the lower seed to win to "break even" on rd 1):

15/2: about 8%
14/3: about 9%
13/4: 11%
12/5: 14%
11/6: 20%

If you assume that the higher seed would win the next round, too (so we're 'guaranteeing' the higher seed 3 points):

15/2: 20%
14/3: 23%
13/4: 27%
12/5: 33%
11/6: 60%

Here's the real problem, though: the massive jump between rd 3 and rd 4 makes this just ridiculous. If we assume each #2 seed has a 15% chance of making the Final Four (which would earn you 1+2+4+16=23 points), that means that the #2 seed is "worth" 3.4 points, which is why I used the numbers above. If we assume the breakdown is more like:

1-seed: 40%
2-seed: 25%
3-seed: 15%
4-seed: 8%
5-seed: 7%
6- and below: 5%

Then it's more like:
16-seed has to win 61% of the time
15-seed: 44%
14-seed: 31%
13-seed: 20%
12-seed: 23%
11-seed: something like 14% depending on how you assign that last 5%

Hilariously, if we look at historical data our WAG assumption isn't that far off - over the last 30 years, the chances for a particular seed to reach the Final Four:
1-seed: 42.5%
2-seed: 21.7%
3-seed: 11.7%
4-seed: 8.3%
5-seed: 4.2%
6-seed and higher: 11.7%

So we under-estimated the chances of Cinderella making a run, but past that, we're pretty close. Since it looks like with the notable exception of George Mason and the 2000 FF the seedings have become a pretty efficient market (NOTE: strong chance of confirmation bias after last season), we don't even really need to re-run the numbers. It looks like the best strategy for your "upset pool" at work or with friends is to pick every single 10/11/12/13 to win outright unless you think that the 4 or 5 has a big-time chance to make a deep run.

Oh, and the other big key: correctly pick the championship game. That's about half of your realistically-possible points right there, and it would be nearly impossible to lose under any scenario. Make money make money.

Also, my current first-round picks before the public money rapes the pooch:
Alabama State (+3.5) - very iffy one here, it's right at the Sagarin line but I trusted someone else who loves this line.
Butler +2.5 (it's probably closer to PK)
BYU -2 (LOVE this line)
Oklahoma State +2 (looks iffy with the latest efficiency ratings, but meh)
Cal -1
Utah +1 (should DEFINITELY be favored; money-line play if you can find one)

For reference, the lines for rds 1 and 2 are usually so bad that you don't need a "system" - just use kenpom.com and Jeff Sagarin's Predictatron point spreads, accounting in your mind for travel or probably home-court, and get there. That's the key: Get there.