Baseball as we know it today was fairly new during Lincolns lifetime, perhaps he was a fan of this fledgling sport? Baseball in America gained popularity in the 1850's and was adapted from the English games of Rounders and Cricket.
Lincoln Park is primarily a baseball facility, more history about our country's greatest president and his interactions with Baseball can be found below.
http://www.thenationalpastimemuseum.com/article/base-balls-and-ballots-national-pastime-and-illinois-politics-during-abraham-lincolns-time