Sherman is a ****ing beast.
Sherman is a ****ing beast.
Shouright,
My purpose is not to challenge your assertion that the Dolphins' rushing "success" rate is near the league average according to the Football Outsiders DVOA. I believe you, I promise!!
My goal is to see if I can identify another statistic involving a team's rushing performance that correlates highly with winning percentage and is easier to interpret than is rushing attempt differential.
Saying it another way, I am trying to define rushing "success" without relying on either rushing attempts differential or Football Outsiders DVOA. The challenge at arriving at an alternative definition of rushing success is how/whether to quantify the impact of outliers.
You have stated that the correlation between average YPC and winning percentage is low. My hypothesis is that the reason it is low is because a high YPC can be inflated by a couple of large gains. My thought is that if a high YPC is achieved via a larger degree of consistency, it would be more predictive of winning percentage. Rightly or wrongly, my thought was that a large positive skewness could quantify a team's lack of rushing consistency for a given level of mean YPC.
A "naive" definition of skewness is to calculate (mean - median) / standard deviation across a team's set of rushing yards per play in a given game. This provides a way to quantify the extent by which the average YPC was inflated by a few large rushing gains. I understand that such an analysis would be cumbersome.
With respect to today's game, the Dolphins rushing game appeared dominant using the "eyeball" test as compared with the Jets rushing game, despite the Dolphins lower mean YPC. What peaks my curiosity is whether the Dolphins lower (apparent) skewness of the distribution of rushing yards across all such attempts can explain the perceived relative rushing dominance by the Dolphins.
Last edited by nyashfan; 12-02-2013 at 01:29 AM.
I know you caveated the skewness measure but am curious if this formula is something commonly practiced. It's just interesting to see a "mean-median" calculation when one is used in parametric stats and the other in non-parametric stats. I'd be interested in any link to this use of the mean and median.
I'd also be interested if you guys have ever tried fitting any type of model to "winning/losing" outcome for the same data set that you are calculating the correlations from. Be interesting to see what a model "says" that gives you the optimal chance of winning. Good stuff here.
And all that makes sense, but I think the measure you're after, despite the fact that it's theoretically sound, would pale in comparison in sophistication to what's expounded on the Advanced NFL Stats website with regard to rushing success rate, in terms of how its defined by positive expected points added.
Sometimes other people have already done the work for us.
http:// http://en.m.wikipedia.org/wiki/Nonparametric_skew
I asked Shouright if there is a public database to download in order to do analyses and he didn't think there was. I think he gets pre-aggregated data from Football Outsiders and then does his own correlations.
The motivation behind using the (mean - median) / standard deviation definition of skewness is that its domain is from -1 to +1. It is thus interpretable in a similar manner to a correlation. See attached link.
I have never seen skewness used for anything. I have no idea if my hypothesis is correct. I was just "thinking outside the box" and skewness popped into my head as something potentially interesting to look at.
If Shouright had the data, he could do one of his partial correlation calculations between winning percentage and mean YPC, controlling for skewness.
Last edited by nyashfan; 12-02-2013 at 12:32 PM.
Sherman In A Nutshell - good place for him. Leave him there.
See what you think when you click on "Show All..." in the table entitled "Team Offense" at this link:
http://www.pro-football-reference.co...order_by=yards
Nerds!!!!!!
jk
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