The analysis may be top rate, but the fundamental assumption that fumbles are randomly distributed needs to first be proven, including in the case of the Patriots.
BTW - I am no supporter of the Pats. I grew up a Jets fan. LOL
There is no such assumption, otherwise we would be looking at a chart that showed all the teams as almost a single horizontal line. The skills, techniques and cheating are inherent in the counts themselves. That is why the cheating Patriots stick out like a big sore thumb.