We are 4 days before the new NFL season and everyone is getting their football mode on again (if they haven’t yet). Making any judgements on how the season will turn out using the pre-season game showings of the teams is rather useless. Equally bad is trying to transfer the ratings of last season to the current season (in the general case), since teams might have dramatically changed their roster during the offseason. So how can we get a first glimpse of what the teams will look like in the new season? Well “follow the money”, or else use the beliefs of Vegas to get some information. Vegas provides lines for the total wins of a team, and even though there are some headscratchers there (e.g., I cannot see how New York Jets can find more than 2 wins in their schedule — their line is 4.5) overall they are fairly good at setting the lines – as anyone who has tried to consistently “beat them” has come to realize. So I am going to use these lines to make preseason projections.
For every team T we want to find its rating r(T) that minimizes the prediction (squared) error between the Vegas line of the total wins and the projected expected wins based on the ratings r of the other teams. A rating r(T) = 0 represents an average team, while a rating r(T) = 2 represents a team that is 2 points better than an average NFL team. How do we calculate the expected wins based on the ratings though? If we have two teams H (home) and A (away) with ratings r(H) and r(A), then the projected score differential is 3+r(H)-r(A), where 3 points is the home edge traditionally used in NFL. From these ratings we can obtain a win probability by using the finding from Stern, that the final win margin follows a normal distribution with mean 3+r(H)-r(A) and standard deviation 13.86. Stern used the betting lines for his analysis, so I calculated the standard deviation for the rating scheme presented here to be around 14.5 and this is the value I am using. Summing up all the win probabilities for a team gives us the expected number of wins for this team for the season. For my projections I used the lines reported on an article at USA today. You can play with the code and the data here. The ratings I obtained are in the following table (along with the betting line used).
As we can see the teams with the 3 highest ratings are all AFC teams (Patriots, Raiders and Steelers). Using these ratings we can obtain win probabilities for all the regular season games (based on the normal distirbution mentioned above). You can find all the projections here. The following matrix presents the win probabilities for every possible mathcup based on this pre-season ratings.