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The reasoning behind this scheme

Posted By: Roland Scheicher
Date: Monday, 4 May 2026, at 7:02 a.m.

In Response To: Swiss tournament payouts (Roland Scheicher)

What's the reasoning behind this payout scheme?

If we look at a single elimination tournament first, we often find a payout scheme, such that

- The runner up is worth half of the winner,

- a loser in the round of four (i.e. semifinal) is worth 1/4 of the winner,

- a loser in the round of eight of is worth 1/8 of the winner, a.s.o.

This payout scheme reflects the fact that the probability to reach the round of eight is eight times the probability of winning the tournament (at least, if all players were of equal strength); the probability to reach the round of four is four times the probability of winning the tournament, the probability to reach the final is two times the probability of winning the tournament.

Thus it seems a justifiable (maybe not necessarily the only possible) generalization to state that the player who finishes n-th place, i.e. reaches the group of the n best players, is worth 1/n of the winner.

This scheme can be used for Round Robin and Swiss tournaments.

Yours, Roland

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