Did the Patriots RB depth win Sunday's game?

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It's been noted all year long just how many running backs have been placed on the depth chart for the Patriots this season. That number declined a bit after the Patriots cut Leon Washington, however the Patriots still had four solid backs in their backfield.

This normally means nothing, but after a Ridley fumble (big surprise there) and then a Blount fumble. Bill Belichick turned to Shane Vereen and Brandon Bolden to carry the running game the remainder of the way. Together, the two backs carried the ball 23 times and gained 89 yards on the ground with Bolden getting the only rushing touchdown.

If it wasn't for the depth at RB, who knows what could have happened? The threat of running the football still existed with Ridley and Blount out, which turned out to be a great positive for the Patriots comeback. So among all the factors in Sunday nights comeback win, was the depth at running back one of those reasons?