organic chemistry - Migratory preference in a rearrangement involving carbocations

I just read about the Pinacol rearrangement and the following reaction was presented just after it. The book (Clayden) shows path 1 being taken.

My question is why is the second path not taken? I know that migratory aptitude of $\ce{Ph>H}$ but all we want is stability, so why can't the $\ce{H}$ migrate?