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Mathematical tie-breakers for round-robin tournaments

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You're right, but from the tabroom's perspective, it's easier to say to a coach "your team got fewer points" than to explain the methodology of the more accurate system.


Is there a way you can incorporate this easily into standard tab software?

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Two other methods, from chess, are head to head and Sonneborn-Berger--and I prefer them mainly because I see speaker points as a deeply flawed, arbitrary scoring system compared to ones that focus on wins and losses.


Head to head is simple: In a 2 way tie, the team that won the matchup between the tied teams wins the tiebreak; in an n-way tie, compare the records of the teams in the tie against the other teams in the tie. In your scenario, compare B, C, and Ds wins within their subgroup to get:


D: 2-0

B: 1-1

C: 0-2


Sonneborn-Berger is a strength of beaten opposition tiebreak--add up the records of all the teams beaten. Here, that comes out as


D: 6 (beat 3-2, 3-2, and 0-5 teams)

B: 5 (beat 3-2, 2-3, and 0-5 teams)

C: 6 (beat 4-1. 2-3, and 0-5 teams)


So of course that doesn't completely break the tie here, but it gives C credit for beating the top team that C wouldn't get as much credit for in the other systems.


Both are reasonable, very easy to understand, and ignore speaker points entirely.

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Sorry I didn't respond earlier. Vacation.


Head-to-head is equivalent to Kemeny-Young, I think. (K-Y tries to minimize upsets, but by putting the tied teams in order against each other, you've done the same thing.) It's so straightforward and easy to understand that it wouldn't be difficult to convince people it's a fair tie-breaker.


Sonneborn-Berger is equivalent to my weighted wins system, except without "minus points" for weighted losses. Again, I think it'd be pretty easy to convince people that it's fair.


Both methods could be easily done by hand or easily added to a program. (So could ranked pairs, but people might find that more confusing; Schulze needs to be done by computer.)

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