020: Darts Tournament

To find just the best thrower, a ladder tournament is optimal. However, as Lewis Carrol pointed out, a ladder may not find the second best thrower (since they may be beaten by the best thrower in an early match). I solicit solutions to the problem of identifying the $k$ best throwers where $k > 1$ (and especially for $k=4$ as this was the original question to comp.theory).