Mathematics of Talent this year

As we in the "Triumvirate" (when collectively referring to Jason, Taylor, and Scott from now on, this address would be preferred) were discussing, the running back talent is sketchy relative to wide receivers this year.  We believe there are clear tiers for the running backs and there is a much more vague delineation between wide receivers.  In addition, due to the presence of RB committees, the production falls off rather sharply.  Finally, as we all know, you are less likely to be able to predict the performance of players which are chosen later in the draft, or not at all.  Barring very severe outliers such as Chris Johnson/Steve Slaton in '08 and Miles Austin in '09, I try to illustrate these points mathematically in the figure below.  You can see the RB ideal curve for this years draft has a discontinuous character more in line with a series of step functions convolved with a line.  For the WR ideal curve however, the function is more continuous and is represented by a classical sigmoid (modified logistic function) convolved with a line.  To make the prediction more realistic, I have included noise on top of these data.  The noise itself is also a monotonically increasing function of "Draft Order for Respective Position", although the RB data are noisier as is often the case.   Cheerio.  And please read the previous post by our esteemed commissioner.