John,
Thanks for pointing out the mistakes I made! Pat stole 71 bases in 1916, which gave him 527 for his career, not 537. I suppose I just looked at it wrong.
I was also thinking for some reason that his AL record was 72 steals, not 82. So Cobb did only tie Pat's record.
Tillie Shafer came up in 1911, and has 460 steals in his career. His season totals are 41-66-82-102-91-78, so he's racking them up pretty fast. Shafer is an on-base machine; he's had OBPs of .508 and .486, and his career mark is .436. So he has lots of opportunities to steal.
Offense was down throughout baseball in 1916. As a league, the AL had a .689 OPS in 1915, and went down to .666 in 1916. That might explain some of Pat's decline. It took Pat a while to start hitting for power in 1916, which depressed his season's totals a little bit.
Hopefully Pat will bounce back in 1917 and enjoy a few more years of near-peak performance. The lively ball is coming, although, of course, Pat can't know that...