When I was younger, I used to walk around the ballpark after the game looking for stubs. I haven't done that for years but I do occasionally note the odd stub after a game.
My general gut feeling is that post-game discarded tickets are harder to find than they used to be - partially because there's more of an awareness of tickets as potential collectibles, and there's also the proliferation of print-at-home tickets, making "real" stubs (box office and season ticket style) scarcer.
Interestingly, I did find a discarded ticket stub after Game 4 of the 2015 World Series. This is how I found it:
(Photo taken October 31, 2015. © Gary Dunaier. Link to upload on Flickr.com: here.)
Unfortunately, once I picked it up I found it was soaked in beer, rendering it uncollectible... so I left it behind.
