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1.
An abbreviation for Best Available Player According to Yahoo (or Best Available Player At Yahoo.)

Yahoo's fantasy sports include a list of players to aid owners in drafting, and their ranking is the "default" value for players in these leagues. BAPAY is the player currently at the top of the list.

For instance Albert Pujols is the 2010 "BAPAY" in fantasy baseball, the Best Available Player According to Yahoo in leagues just prior to their draft. When Albert Pujols is claimed Hanley Ramirez, listed at #2, becomes the new BAPAY.

When an owner is absent for part or all of his draft, his team may be built with BAPAY players by default. This is often perceived as being a significant disadvantage.
"Ah man, I just got BAPAY'd Manny Ramirez! Why didn't you guys wait for me?"
by Mojotronica February 17, 2010