Grad student H. sent me this fun Sports Illustrated link to a slew of photos of presidents throwing out the first pitch on opening day. Above are two related photos I found in the Library of Congress's Bain News Service collection. The top one is Taft at a Washington-Chicago game in August 1912 (never knew he had such a pronounced bald spot!). The bottom is Wilson from opening day just a few months later in 1913. If you're curious about what was happening politically between these two dates, James Chace's 1912 is a great popular treatment of that election.
In working through the slideshow, I was surprised to discover that the "first pitch" really did used to be just ceremonial in that it was delivered from the stands, not the pitcher's mound. If you're curious about who appears to have altered that tradition, be sure to click through all the images. Believe me, you won't be surprised!