OK, so what do these numbers mean, anyway? How do you assign a percentage to a game’s importance? Let’s assume that we already have a) a way to estimate the probability of either side winning a given game on the NFL schedule, and b) what effect that will have on the final playoff picture in every possible scenario (or at least a significant sample of possible scenarios). The next question is to decide what outcomes we want to link the games’ importance to. Just making the post-season? Winning the Super Bowl? These posts use a sort of compromise between the two: success is determined by the post-season picture, but the different seeds are weighted by the theoretical chance they afford a team of making the Super Bowl, taking byes and homefields but NOT team ability into account. This is different from actually simulating the season all the way to the Super Bowl.
The next question is how to express a game’s relationship to a given outcome. There are two ways you might view this. One is to answer the question “in what percentage of possible scenarios would the final outcome be dependent on this particular game?” That gives you what you might call the “absolute importance” of the game (which is exactly half of what Mike Beuoy calls “swing”). It doesn’t take into account, however, our expectations for the game itself. If we are 95% sure that Denver will beat Oakland, for example, it may be true that that game has a 100% importance to the top seed, but it isn’t likely to tell us much about the final result that we hadn’t already predicted.
To take this into account, we look at what I call the “expected importance” of a game, which essentially answers the question “By how much, on average, do we expect our expectations of the final result to change after this game?” This is the figure used in these rankings. It should be noted that it can never be more than the absolute importance; it is the same as the absolute importance if the game is a coin-flip, to us, and becomes less and less the surer we are of the game’s result.