Player Score Distribution by Position

A tangent about player scores.

I mentioned yesterday that its theoretically odd that player scores do not line up closer to the median and discussed some justification for why that's not just a math error on my part.  Well here's a visualization of why that's true.

The following are charts of the distribution of scores by position.  (Click to see bigger.)







Just looking at the shapes you can see that very few look like normal, bell-curve distributions.  Kickers do.  QB to a degree as well.  RBs look like a bell curve where the low end has been sliced off.  WRs look more like a long-tail curve.  DBs and DFs... I don't know.  Some combination?

But in any event the median scores for most position are much closer to the low end of the range then the high end.  Mostly I think this is because most positions tend not to score much below zero so there is a bit of an artificial floor to the scoring distributions.

Something that I was not looking for but really jumped out at me was the secondary spike on the WR table around 7, 8, and 9.  I think what we are seeing here is that there is a primary spike around 2 points which is the most common score for a WR and is all yardage accumulated (anything between 40 and 59 yards receiving.)  Note that 8 points is essentially that same yardage with a touchdown thrown in.  And there is your second spike.