Tuesday, November 20, 2007

Week 12 - Why Finance Works, and Why I Hate You

Firstly, I hate that you had non-sack enough to stay a winner this week. Especially when the Box decided losing was fun.

More importantly, here's a rundown on why the financial rankings and scores work (in close spread games and otherwise).

As I've posted, the Alpha and Sharpe ratios are two different ways to measure the same thing: risk adjusted returns. By my figuring of each algorithm, Sharpe is a metric purely of ability to score and variance in that ability, while Alpha is composed of a ratio of a team's statistical score (adjusted for the league wide average) to the moving average of points scored. While it sounds like a mouthful, the most important thing to take away is this: Sharpe uses points, Alpha uses stats. In that way, they can both be useful in slightly different ways for small spread games.

When the spread is small (in this case, under 3 points), the game is essentially dictated by a team's ability to WIN rather than a team's ability to COVER, which is precisely what an Alpha or Sharpe comparison indicates. When you look at two teams' Sharpe ratios side by side, what you're looking at is their risk adjusted ability to score. If a team has scored inconsistently, or hasn't scored, it will be reflected in the Sharpe. Sharpe adjusts for risk by assessing whether a team can consistently score equal to or more than the league average. The league average points scored is roughly 20, so just by scanning score lines you can even estimate a Sharpe (a very rough approximation, anyway) by seeing how consistently a team has scored 20+ points. In crunch games, where Vegas estimates the margin for victory at under 3 points, this can be very useful. If JAC played TEN in Week 11, ranked 16th and 17th in Sharpe, and the spread were under 3, you could reasonably infer that JAC had the advantage since it has a proven ability to score slightly more consistently than TEN. Since the spread is so low, you don't care how MUCH more than average they score, just that they score more consistently.

For my new hybrid, I've combined the Sharpe and Alpha to get a fuller picture of the teams. Since the Alpha is statistically based ratios, Alpha indicates whether a team has consistently equaled or outperformed how the statistics said it should have performed rather than just how many points it scored. Alpha in a way is a window to say, "Well, DEN put up 34 points last night, but was that an anomaly, or is that in their nature against a team like TEN?". When you combine Alpha (stat based) with Sharpe (point based), you get a rounder view of a team. The rankings are often close for Sharpe and Alpha, but there's enough difference to draw some interesting conclusions.

For the sake of example, we'll use the NYG v. DET game, where the spread had the NYG giving 2.5. The Giants had a fair sized statistical advantage, but the Box predicted a 2.2 point victory, just failing to get over the 2.5 point margin needed for a statistically based NYG pick. The Box has not historically been strong in these low margin games, and it's unclear to me just yet why that may be. In my model, I am measuring approximately how much better than average a team is, and correlating it directly to how many points they should score against an average team. However, if the two teams are equally above an below average (for instance, in this case the Giants are slightly above where DET is slightly below), the point prediction the Box makes may not accurately reflect a team's real ability to score. This is my working theory, but it seems to bear out historically - the ability to generate points above and beyond the stats make the difference in low margin games.

I've talked a lot about Beta, too, which is a component of Alpha. Beta is important on a different level, though still very useful in making decisions. Where Alpha indicates how teams have done in the past, Beta attempts to measure, based on history, how likely a team is to repeat its performance. Those are the major differences and reasoning behind using the financial ranks right now.

I'm going to spend the next bit working on the stats that were just released, I'll have updated rankings today and tomorrow morning.

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