05/10/2014 AT 05:35 PM EDT
will be the first to admit that being a celebrity has its perks. For starters, a personalized booth at his favorite L.A. neighborhood eatery, where he's ordering a sopressata sandwich and a Diet Coke while bundled up in a scarf to ward off the remnants of a nasty spring cold.
And of course there are the legions of Don Draper fans desperate to buy a drink for their favorite antihero. "It's nice that people like what I do," Hamm says with a laugh. "But at a certain point, I can't drink that much Scotch!"
Now, with AMC's critical hit ending next year, Hamm, 43, is headed for the big screen as real-life sports agent J.B. Bernstein in the baseball movie Million Dollar Arm,
out May 16, while preparing to leave the role that launched him into the stratosphere.
"I've survived a lot in my life," says Hamm, reflecting on the sometimes heartbreaking road that led to fame. "I've had a lot of close calls with a lot of stuff. I think someone's watching out for me."