Trying To Explain The Error Bars

Continuing the discussion of expected wins, I think the two most interesting things you can find are the strength of a trend and then how to account for the outliers.

As I mentioned in the first post on the subject, there does not appear to be a direct linear relationship between passer rating differential and victories, but rather an exponential or logarithmic one. With an R-square (how stupid is blogger that I can't insert superscript?) of 0.65, passer rating differential may be the smokiest of guns.

It doesn't, however, meant that it can't be improved.

Considering the components of football that passer rating doesn't cover, we have the running game, special teams and fumble differential. I have a pet theory of a "superstar player" factor as well, but that is difficult to define or measure.

Anyhow, going back to passer rating differential some interesting things happen when the data is broken down to "positive" and "negative". Looking at a graph of teams that achieved positive differential over the last ten years:


we see a nice orderly progression. However, looking at teams that posted negative differentials:



we end up with a much different shape. The slope of the positive graph is about 60% greater than the slope of the negative graph (.26 v .16). I think I will need to extend the range by double or treble to determine whether this is accurate or simply a chicken-egg result. This decade New England and Indianapolis dominated both the total victory column as well as the passer differential column. This could be somewhat coincidental and the sole driver of the increased slope.

It gets very noisy when we look at seasonal results, but with a very surprising difference:
It is difficult to see from the two pasted graphs, but while the two slopes are similar, the intercepts are vastly different. Teams with negative passer rating differentials have an intercept at 7.8 victories while teams with a positive differential an intercept at 8.5 victories. With an R-squared of 0.26 for the latter, chance plays a significant factor in the latter result and in fact when other variables are factored in we may ultimately see the intercepts meet, but for now it is a startling outcome, and again suggests an exponential relationship.

Teams that achieve even a small positive in rating differential can expect an extra victory per year over expectation.


Winding down on this post I'm not sure what kind of progress we've made, but we'll forge on. Next up I think I'll take a look at some of the outliers to see what contributed to those seasons.