Well the first consideration, of course, would be the texture of the team in question's games.
To illustrate, imagine two hypothetical scenarios:
- The Bills had 10 games with opponents against whom they had exactly 0% probability of winning, and 6 games with opponents against whom they had a 100% probability of winning.
- The Bills had 16 games with opponents against all of whom they had exactly 6 16 = 37.5% probability of winning.
Now in both in cases expected win total is 6 games, but obviously the two distributions would be entirely different. In the first case you'd take the under 6.5 at ANY price as you would with the over 5.5. (While in the second scenario fair values on the overs would be o5 -267, o5.5 -146, o6 +104, o6.5 +156.)
Obviously this is a particularly pathological example, but I think you get the point.
An inextricably related issue is that of home versus away games. Even if you were to assume the Bills equally likely to win against all opponents on neutral ground, HFA would still come in to play.
With those caveats aside (and several others glossed over for the sake of brevity), were we to assume equal win probabilities for each game then the fair value for any given season win total can easily be calculated via the Binomial distribution.
Let S = Total games played = 16
Let W = Expected number of wins
Then for integer X:
The probability of Over X½ seasons wins would be given in Excel by:
=1-BINOMDIST(X, 16, W/S, 1)
And the
conditional probability of Over X seasons wins would be given in Excel by:
=(1-BINOMDIST(X, 16, W/S, 1)) / (1-BINOMDIST(X, 16, W/S, 0))
So for over 5.5, this would yield a probability of =1-BINOMDIST(5, 16, 6/16, 1) ≈ 59.3268%, which at a line of -136 would an expected edge of 2.95%.
Note, however, that this simple single-parameter analysis, while potentially valuable versus a rec-style bookmaker that sets its own lines, is most assuredly not going to beat Pinnacle.