Sudden death, one batter at a time. Keep going deep and you stay in the box. The first one to come up empty takes the last pick, the next one out takes the pick before that, and so on up the board. Last one standing takes pick 1.
How weighted odds work. Give each manager ping-pong balls, from 1 up to the number of teams in the league (16 max). Every ball is one entry in the draw. Pick 1 is drawn first, then pick 2 from the balls that are left, and so on down the board. More balls means better odds at every pick, never a guarantee. The draw happens the moment the first pitch is thrown, and the Derby plays out that order.