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Tournament Operations » Post: Cumulative Tiebreaker?

Cumulative Tiebreaker?

July 31, 2013 08:59:48 PM

Sean Stackhouse
Judge (Uncertified)

USA - Northeast

Cumulative Tiebreaker?

So, I thought I knew what this was when I first started to explain it to someone, but… I don't. And it's being used at the World Championships according to the Standings posted in event coverage. How is it calculated?

Aug. 1, 2013 03:05:47 AM

Jordan Baker
Judge (Level 2 (Judge Foundry)), Scorekeeper

USA - Great Lakes

Cumulative Tiebreaker?

“Cumulative” tiebreakers in Swiss tournaments are designed so that a win early in a tournament has a higher weight than a win later in the tournament. The Wikipedia article makes more sense if you remember that Chess awards W-D-L as 1-.5-0 instead of Magic's 3-1-0.

It looks like the algorithm goes as follows:

The “tiebreaker bonus” starts 3 points. Each time you win a match, divide that number by four and add it to a “bonus pool”. Then, for the rest of the tournament, you will always get the number of points in your bonus pool, whether or not you win or lose.

So, lets say that you win first in Round 2. Then, whether or not you win in Round 3, you will get .75 (3/4) points for that round. If you won in Round 3, you gain 3.75 points for R3, but your bonus pool becomes .75 (3/4) + .1875 ((3/4) /4) = .9375 for each future round.

One effect of this method is that you will never gain more than one point per round, as the limit for the above equation for an infinite number of rounds is (I believe, it's been a while since calc) 1. Additionally, it fulfills the “goal” of a cumulative tiebreaker: it conclusively rewards wins early over wins late.