Friday, September 14, 2012

Bad Beats: The Predictive Power of Past Years' ATS Record

Last week, I used this space to complain about losing money to my friend Dave by betting against Tulane football.

Faaascinating, I know. But it gives me a chance to make an Important Point about the predictive value of statistics.

My confidence in my bet was based on the fact that, from 2003 to 2011, Tulane covered just under 40% of their games against the spread. Winning 60 percent of your bets would make the average professional bettor salivate, so I was happy to bet based on this big trend.

There were two things I ignored: first, that one game is the smallest of sample sizes, and second, that past results are no guarantee of future performance. The second point is the interesting one, so let's focus on that: if a team has done better/worse than average against the spread in the past, does that tell us anything about its performance against the spread in the future?

First, a little experiment. Let's take the best teams against the spread from 2003-2010 (as again compiled from, and see how they fared in 2011:
Cover %
Best Teams ATS'03-'102011
Ohio State63.646.2
Boise State 60.838.5
Va. Tech60.630.8
Central Mich59.18.3

That's disappointing, but it does make sense. Imagine the following situation: bettors realize that certain teams keep covering the spread, and start backing them regardless of who they're playing. In response, the oddsmakers raise the lines these teams have to beat higher and higher, making it harder for them to cover.

But what if no one's paying attention to the teams at the bottom of the pile? Is there value in the perennial losers?
Cover %
Worst Teams ATS'03-'102011
Washington 37.653.8
Miss State 41.946.2
N Mex State 42.061.5

That's a little better. And yes, this bottom-six list looks a lot like the list of the worst teams against the spread I put in last Friday's post.

There is one other way to determine if this spread is simply random. In a perfectly efficient betting market, the odds of any team covering against any other team in any given game would be really close to 50%. Of course, we're assuming no pushes (ties) or public (popular) teams*.

* - In our case, these are schools like Notre Dame and LSU that people will back regardless of the spread because they root for them. Since there's more demand, oddsmakers can make the line a little "overpriced" for the public team, since they know people will want to bet them anyway. Examples of public teams in other sports include the Yankees, Packers, and Lakers.

Even in this "ideal" case, pure randomness dictates that you get a few schools with a cover percentage above 60% and a few below 40%. In fact, if you compare histograms of our ideal simulation and the actual results, they look really similar.
This suggests that the perpetually underperforming teams (like Tulane) and perpetually overperforming teams (like Boise State) are a function of luck* rather than some underlying market inefficiency. But don't go all Gambler's Fallacy on me yet: just because the Tulane coin has come up tails so often in the past is no indication that it will come up heads the next time the coin's tossed.

*-Well, at least as far as covering the spread is concerned.

1 comment:

  1. Had an email discussion with Dave over the weekend I thought was worth including for clarification purposes. Dave asked,

    I am confused by your graph. Are you basically saying if you flip a coin enough times it will converge to 50/50 odds and that's the same as betting ATS?

    Actually, I'm saying the exact opposite: that if you flip a coin with 50/50 odds enough times, eventually the percentage of times it comes up heads over a certain number of trials will converge to a particular normal distribution function* (thanks to the Central Limit Theorem), and that this bell curve looks an awful lot like the distribution of teams' ATS records.

    * - Namely, it converges to N(np,np(1-p)), where p = probability (0.5) and n = number of games per trial (12 games/season * 9 seasons = 108 games).

    The null hypothesis here is that all of the variation in the teams' ATS records can be explained by random chance, whereas my hypothesis was that Tulane's ATS record was a non-random outlier. The "ideal" curve is the result of an experiment I ran: I flipped a coin 108 times, representing the approximately 108 games each team played from 2003-2011, and counted the number of times it came up heads. I repeated this once for each of the approximately 120 teams in the FBS.

    Well, actually, I used a random number generator in an Excel spreadsheet and counted the number of times the random number was greater than 0.5. Same thing.

    Now, obviously, I made a lot of simplifying assumptions, and you can play a "Where's Waldo"-style game by finding all the things I swept under the rug. The point is that the random experiment produced extreme values as far away from the mean as real life, suggesting that the extreme values in real life can be explained as the product of random chance.