A real shootout. Everyone shoots each round. Scorers move up to fight for the top picks, misses play for the rest, until every pick is settled. Gameplay can be sped up or simulated to the end.
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 puck drops, and the shootout plays out that order.