NFL Fair Value vs Pythagorean ML

[uva3021]

In passing I made a rather intriguing observation about the asymmetry of NFL MLs. If one uses the pythagorean method to extract a win percentage given the spread and total, with an exponent of 2.37, the resultant win probability, compared to fair value probability (Pinnacle), is invariably under or over estimated. The designation of 2.37 as an understood exponent could certainly be an issue, and perhaps the bookies use an alternative measure or separate exponent for single game situations. Perhaps there is one or a multitude of other essential features that are being overlooked. I am inclined to believe in the former, that the discrepancy is merely an indicator of some other value of the exponent.


Here is a table showing the differences between the pythagorean probability and the fair value probability for the Week 4 home teams:





Teams that are favored (> 50%) on average have an upward market bias of about 1.5%, or in this case, ~ 11 cents. Fair value underdogs (<50%) have a seemingly innate downward pull of around 4.5%, or in other words, a glaring 52 cents. And the Standard Error is 2.75%. Obviously in this scenario the data is exposed to the limits of sample size. One week is hardly enough to come to any sort of conclusion on the matter. Though 87.5% of home underdogs combined with 57.14% of home favorites produce a contingency where just about 75% of the teams assessed in week 4 have a tendency to moneyline inflation. At length I’ll aggregate data to combat the limits of sample size. Yet I would contend there is a market bias in the outward direction of fair value moneylines, purely based on the nature of the commission based sports betting system.

The aforementioned and a brief survey of the table above should be enough to suggest such a tendency could possibly occur. But when displayed as a graph, it seems the pythagorean method, using an exponent of 2.37 (which I could obviously change and is largely based on preference along with some research), restricts any possible fluctuation to be optimized to an equilibrium central tendency, while the fair value odds procure the apogees at either extreme, and are free to flow to the most outer wall in either direction (upward for favorites, and downward for underdogs).



Using these two data sets, I can extract the best possible exponent where both the average fair value probability and the average pythagorean based probability are equal. Excel’s built in feature, Solver, found an exponent of 3.37. Perhaps this is a more ideal exponent for a one game situation.