mid-15c., from tadde "toad" (see toad) + pol "head" (see poll (n.)). Also pol-head (mid 13c.).

"children's game," 1738 (in reference to "Queen Mary's reign"), perhaps a variation of Scottish tig "touch, tap" (1721), probably an alteration of Middle English tek "touch, tap" (see tick (n.2)). Baseball sense is from 1912. It's not an acronym and doesn't stand for anything.