I have done a 2 dimensional fit to the pTrel and signed impact parameter distributions for soft muons.  The fitting function is a simple product of template pdfs obtained from the heavy flavor W+bb and W+cc MC for the bottom and charm, and W+jets for the light flavor.  The data selection here is standard W(met>25, mT>20, pT(lep)>20) + soft muon ID (soft muon likelihood < 3.5).  The fits are shown below for the electron and muon triggered W events separately.

Two interesting things to note:

1. The bottom and charm fractions are inconsistent between the different triggers.
2. The muon triggered sample has an excess of soft muons at high pTrel.  This needs further examinations – emTiming, pSum, event displays, etc.