![]() StartingPoints No references
|
SODOS/ Discussion
Sub-page of SODOS
Defined as the Sum of Defeated opponent's McMahon Scores, SoDoS has the following property: SoDoS differences are NOT always invariant under change of origin of the McMahon scale. The origin of the McMahon scale does vary: it is zero at 20 kyu in many European tournaments, it is zero at shodan in the UK. To convert from the UK to the European value we need to apply the transformation: SoDoS(EU) = SoDoS(UK) + 20*D, where D is the number of defeated opponents. This transformation arises from the fact that any player's European McMahon score is 20 more than the UK score i.e. MMS(EU) = MMS(UK) + 20 Now when you sum the EU MMS scores over just D players, you get the sum of the UK MMS scores + 20*D. The implication of this is that two UK players may end up with the "same" SoDoS, but have done so by beating "different" numbers of opponents. In this case their position in the European version of the rank list may change, as the European SoDoS's will be different. Harleqin: I do not see any application of a comparison between SoDOS scores on different tournaments. After all, they are on different tournaments, aren't they? Geoff: No, we are comparing SoDoS for the same tournament, published under two different systems. I have to make this transformation whenever I send UK results to the EGF rating system. mgoetze: I fail to see how SODOS is relevant to anyone's rating. So does Geoff iirc, but it is still used as a tiebreaker anyway. Geoff: Here is an example of a 3 round tournament illustrating my concerns about using SoDoS as a tie breaker.
We have a shodan Alan winning 2 games playing: It is not necessary to show the entire tournament results table. Here is a summary of the key information for Alan's and Juliet's opponents' scores in UK and EU styles. Alan's opponents: UK MMS Euro MMS Name Wins initial final initial final Bob(1k) 2 -1 1 19 21 Cath(1d) 1 0 1 20 21 Dave(1k) 2 -1 1 19 21 Juliet's opponents: UK MMS Euro MMS Name Wins initial final initial final Karen(1d) 0 0 0 20 20 Lionel(1k) 2 -1 1 19 21 Martin(1k) 2 -1 1 19 21 Suppose we use SoDoS as the one and only tie breaker. Then we can construct the portion of the final ranklist showing both Alan's and Juliet's position. The column MMSi is the initial McMahon score, and MMSf is the final McMahon score. Then the final position of Alan and Juliet in the UK scale is: Wins MMSi MMSf SoDoS WHO CONTRIBUTES TO SODOS Alan(1d) 2 0 2 1+1=2 Cath+Dave Juliet(1k) 3 -1 2 0+1+1=2 Karen+Lionel+Martin Alan and Juliet are ranked equal, and they split a box of chocolate. However in the EU scale: Wins MMSi MMSf SoDoS WHO CONTRIBUTES TO SODOS Juliet(1k) 3 19 22 20+21+21=62 Karen+Lionel+Martin Alan(1d) 2 20 22 21+21=42 Cath+Dave Now Juliet is ahead of Alan and gets all the chocolate! I am not worrying here about which result is better!. All I care about is that they are different. Note that if you used SoS (Sum of all opponents McMahon scores) as the one and only tie breaker, then this effect does not happen because you are summing over all games, not just a selection. This is a copy of the living page "SODOS/ Discussion" at Sensei's Library. ![]() |