Betting on the Super Bowl? Read this report on “NFL Alphas” first.

CAPM / Alpha Theory 13 Jan 2008

Although it’s usually obfuscated by complex mathematics and applied only to world of investment management, “alpha” is a remarkably ubiquitous concept with applications that go well beyond the Capital Asset Pricing Model.   Steven Sapra, co-author of a recent paper on 130/30 (see related posting) provides us with proof of this.  Regular readers may recall his article about “NFL Alphas” posted on the Analytic Investors website last winter (see related posting).  Sapra has continued to research this topic and his latest conclusions are contained in an article to be published in the upcoming edition of the Journal of Sports Economics (a very cool-looking publication that AllAboutAlpha readers may find interesting).  The study is also available here.

The article goes by the unwieldy title “Evidence of Betting Market Intra-Season Efficiency and Inter-Season Over-reaction to Unexpected NFL Team Performance”, but can probably be summarized as simply “Don’t Fall for the Darlings”. Sapra compares the expected results of over 4,000 regular season NFL games (based on the point spread) with the actual results of each match-up.  If the NFL wager market is perfectly efficient, the actual results should be randomly distributed around the predicted results.  In other words, a “fair” point spread means that the marginal bettor is ambivalent between taking either side of a bet – in the same way that the marginal investor should be ambivalent about paying the “fair” price for a security.

The comparison of predicted and actual results yields a table consisting of annual alphas for each team (click thumbnail image at right to view table).  As you can see, all teams exceed expectations in some years and underwhelm in others.

(As an aside, sports match-ups provide a really interesting allegory for financial markets.  As Sapra points out, investors never really know the “fair” price for a security.  The myriad of factors that go into pricing a security are in a state of constant flux.  As a result, they never really know how good the market actually was at predicting the future.  But sports match-ups come to a finite conclusion – a winner, a loser, and a score.  So, unlike in financial markets, you can actually measure the ability of the markets to predict sports outcomes.)

In any case, if actual results consistently differ from the point spread, then it might be possible for a bettor to consistently win.  For example, if the universe of bettors consistently underestimated the New England Patriots, then a passive bettor could just take the Patriots’ side of the wager every game and generate consistent (arbitrage) profits.  Of course, this opportunity would be arbitraged away as other gamblers eventually clued-in that the point spreads were always wrong. They too would pursue this strategy – pushing the point spreads back to where there was no consistent and exploitable pattern in the long run.

Unfortunately for any budding “quant” NFL gamblers out there, Sapra finds that the betting market provides no such easy money.  In other words, the “no arbitrage” rule seems to apply.  However, he finds that teams that, on average, exceed expectations one season, are slightly more prone to underperform expectations the next season.  Sapra calls this phenomenon “mean reversion in NFL alphas”.  In his words:

“Mean reversion in Alphas is evidence of market over-reaction in response to the prior season’s excess performance…Teams with high Alphas tend to be NFL darlings, which bettors appear to overprice in the following season. Likewise, teams which under-perform expectations make adjustments in the off-season which the market may not completely anticipate.”

“13 out of the 18 seasons (72%) were characterized by mean reversion, as measured by negative season-over-season Alpha correlation.  The year 1989 was characterized by the largest mean reversion, with a rank correlation of -0.407 with the prior season. In 1998 the rank correlation was +0.241 and the worst year for the mean reversion effect.”

So, basically the “market” got it wrong in 1989 and there were a lot of upsets that season.  In particular, Dallas, Atlanta and Arizona were upset a lot, and Green Bay, San Francisco, Pittsburg and Denver rode to several surprise victories.  Interestingly, it was two such Cinderella teams – San Francisco and Denver – who challenged for the Super Bowl.  The 49ers won.

Sapra doesn’t go into the mechanism that leads to the love affairs with the “darlings” or the distain for the dogs (although we hypothesize that it has something to do with the self-reinforcing nature of media coverage).  But he does propose a passive betting strategy to exploit this behavioral anomaly (at least, in the absence of bookmakers’ commissions).

He finds that the propensity for gamblers to overrate last years darlings is far greater than their propensity to underrate last year’s dogs.  So he suggests that the best strategy is to bet against the darlings:

“A very simple mean-reversion betting strategy which commits a $100 wager on match-ups where the prior year alpha spread is at least 10%, would have resulted in total profits before bookmakers commissions of $10,522 over the past 18 seasons.”

While Sapra acknowledges that it’s not clear if this strategy would be profitable after commissions, this exercise clearly illustrates how a little creative thinking about financial theory can be applied far beyond capital markets.  It also has some interesting parallels to the burgeoning field of behavioral finance and, of course, much to contribute to “Bill Swerski’s Super Fans” of Saturday Night Live fame (right).

Sunday Evening Addendum: While this analysis doesn’t include this year’s games (and does not count playoff match-ups in any season), the following observation about this season’s conference finalists provides some food for thought.  Recall Sapra’s “mean reversion in NFL Alphas”…

  • San Diego, New England and Green Bay all exceeded expectations in 2006 (i.e., had postive alphas)
  • The Giants under-performed expectations in 2006 (i.e., had negative alphas)
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