An even more cogent graphic. The Pats fumbled once per 42 touches in the period from 2000 - 2006. After the ball rules were changed, it went up to 1 fumble in 74 touches, a drastic outlier.
If you're statistically inclined, the P-Value on this 0.0001711874, meaning there is a 0.017% chance that this improvement in fumble rate was the result of chance, aka 'just the way the football bounces'.
This is a fairly widespread bell curve distribution but the Patriots are still up on the tail end by a mile.