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In Olympic combined climbing, the three scores are multiplied.

However I want to know what happens if there is a tie. Consider the following:

Climber A: 1st speed, 2nd Bouldering, 3rd lead Climber B: 2nd speed, 3rd Bouldering, 1st lead Climber C: 3rd speed, 1st Bouldering, 2nd lead

All three finish on 1x2x3=6 points. How is the winner decided in this case?

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Googling proved surprisingly useless, but finally I just went straight to the source: https://cdn.ifsc-climbing.org/images/World_Competitions/IFSC_Rules_2020_v151_PUBLIC_compressed.pdf

each relevant competitor will be ranked in ascending order of the Ranking Point Total (i.e. lower values are better), provided that where any competitors have the same Ranking Point Total, the relative ranking of the tied competitors shall be determined for any round:

  1. by comparing the head-to-head performance of such competitors within the round; and
  2. where following (1) any competitors remain tied, by comparing:
    1. where applicable, the Combined Ranking following the Qualification round; and/or
    2. if necessary, the Seeding of the relevant competitors.

It's not spelled out what a "head-to-head" comparison of the performance means. In your example, I feel that the competitors have the same head-to-head performance, because they had the exact same rankings, just in different stages of the event, and they're all supposed to be of equal importance.

So then in your example, they'd be compared based on their seeding.

I guess an example with head to head comparison could be something like:

Climber 1: 1st, 1st, 6th Climber 2: 2nd, 3rd, 1st.

According to my understanding, in this case, Climber 1 will win, because he beat the other climber twice and only lost to that other climber once.

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