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Saturday, January 08, 2011

Handling tied ranks

The message below -- from a small online chess tournament -- reminds me of the different ways of handling tied ranks.


You have a message from
ChessWorld.net

A tournament you competed in - Tournament Number 159233 has officially finished

You can see this and other tournaments you are involved in or have finished from your My stuff..My tournaments page

The results table follows



Player Score Position
Salvatore 4 1
greenbook 4 1
ZBicyclist 4 1
TheGreenwoodbowler 0 2

Life is easy if all four players have different scores and the ranks (positions) can be 1,2,3,4.
But if there are ties there can be problems.

ChessWorld handles it by giving all 3 of us tied ranks 1,1,1 and giving the final player 2nd, even though TheGreenwoodbowler lost every game.  And all 3 of us got "first place" norms [meaningless for this small fun tournament, but nice anyway]

An alternative would be ranks of 1,1,1,4 -- the tied persons get the highest rank. This is the way sports leagues do it -- thus in the Big Ten Wisconsin, OSU and MSU all tied for first, and the next team was fourth.

Statisticians are fond of averaging the ranks which would ordinarily result, so you would end up with 2,2,2,4 -- statistically this has good properties (such as conserving the sum of the ranks, which is important for some statistical tests), but taken literally this would mean nobody finished first.  That seems un-American!

Tiebreaks might be used -- the NFL playoffs work this way, with a complicated set of tiebreak rules because there can only be one team that advances. 

In some statistical uses, it is inconvenient to have tied ranks and so the ranks are split randomly. So the ranks would end up 1,2,3 based on nothing but the roll of a die.