Excellent analysis. I'd certainly have to agree with your conclusion.
Nevertheless, I do have one problem with the specifics of your methodology. Namely, you're implictly assuming that the transformation of win probability to point spread would be distributive over composite probabilities. This does not have to hold in the general case.
The way I might go about it would be as follows:
From Pinnacle:
Code:
Prob of Winning Super Bowl:
CHI 18.06%
IND 38.86%
NE 26.97%
NO 16.11%
Prob of Winning Championship Game:
CHI 55.23%
IND 61.50%
NE 38.50%
NO 44.77%
And after doing a bit of linear algebra one comes up with the following probabilities of winning a given Super Bowl matchup, along with the associated probability of that matchup occuring:
Code:
NO 30.70%
NE 69.30%
17.23% matchup probability
NO 39.29%
IND 60.71%
27.53% matchup probability
CHI 29.33%
NE 70.67%
21.26% matchup probability
CHI 34.82%
IND 65.18%
33.97% matchup probability
As a rough estimate we could pretty much stop here as by insepction it's readily apparent that the following associated approximate point spreads (and matchup probabilities) imply an expectation worth fewer than 6 points for the NFC.
Code:
NO +6 vs. NE (17.23%)
NO +3 vs. IND (27.53%)
CHI +6½ vs. NE (21.26%)
CHI +4½ vs. IND (33.97%)
However, if we really wanted to be strict about this we would first impute from each of the above four matchup probabilities the probability of covering a 6 point spread. Once this was accomplished determining the fair value for AFC -6 would become a simple excersise in expectations.
So for example, as a first-order approximation (through linear interpolation of a score frequency chart) we could say that given the above probabilities of winning the respective matchups, the probability of the AFC winning by more than 6 points (conditioned on not pushing) would in each case be:
Code:
NE -6 / NO: 49.57%
IND -6 / NO: 40.70%
NE -6 / CHI: 50.98%
IND -6 / CHI: 45.31%
Hence, the probability of winning AFC -6 would be 49.57%*17.23% + 40.70%*27.53% + 50.98%*21.26% + 45.31%*33.97% = 45.98%.
So by this analysis this means that AFC -6 would be a good bet at about +118 or better, and
at -110 the expectation of AFC -6 would be ~ -12.2%.