Psychout: that actually sounds pretty fun! Like only using the characters you'll actually bother levelling up? (like in FE6, would it be like not using Marcus, Zealot, Toreck, or Lance, and only using Alan as your Cavalier/Paladin?)
A draft play is when you compete against other FE players to complete the game in the lowest amount of turns possible, with the twist that the characters are chosen by turns, or "drafted" for use just like in sports. For example, let's say four guys are playing in a draft. Eric, Bob, Jim, Michael. They draft in that order.
Eric picks Alan, then Bob picks Lance, then Jim picks Clarine, then Michael picks Dieck, and then Eric gets to pick again, and it continues until all the characters are picked. So it could end up like this:
Eric: Alan, Lugh, Saul, Dorothy, Chad, Ray, Wendy, Zeiss, Dayan, Karel, Cath, Juno.
Bob: Lance, Thany, Miledy, Ellen, Echidna, Klein, Niime, Zealot, Wolt, Douglas, Hugh, Yodel.
Jim: Clarine, Rutger, Tate, Sue, Lilina, Treck, Lot, Noah, Igrene, Geese, Bors, Ward.
Michael: Dieck, Shin, Fir, Percival, Cecilia, Oujay, Gonzales, Sophia, Astol, Bartre, Garret, Barth.
You can only use the characters which you picked, along with Roy, Marcus, Merlinus, Lalum, Elphin, and Fa, who are available to everyone.
The person who manages to beat the game in the lowest number of turns with his allowed characters wins.