SODOS

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Table of contents

Definition

SODOS is a tie-breaking method sometimes used in small (often round-robin) tournaments. It should not be used in McMahon tournaments.

SODOS stands for Sum Of Defeated Opponents' Scores.

It is defined as the Sum of Defeated opponents' McMahon scores, which is equivalent to "sum of defeated opponents' wins", when used properly.

As the name SODOS suggests, its value depends upon how many opponents you have defeated. If you lose all your games then your SODOS is zero. If you beat two others then it is the sum of two scores. If you beat 10 others then it is the sum of 10 scores.

The intent behind using it is to discover how strong your opponents were. The theory being that if you have defeated a stronger set of opponents than another player on the same final score, then you are slightly stronger / better than they are.

SODOS is also sometimes abbreviated as SDOS. Chess players dub it Sonneborn-Berger.

It is sometimes used in round robin tournaments, where SOS is of no use. However it still suffers as described below.

However the use of SODOS as a tie breaker is flawed:

SODOS differences are NOT always invariant under change of origin of the McMahon Pairing scale.

The origin of the McMahon Pairing scale does vary: it is zero at 20 kyu in many European tournaments, it is zero at shodan in the UK.

Here is an example of a 3-round tournament illustrating concerns about using SoDoS as a tie breaker.

We have a shodan Alan winning 2 games playing:
Bob(1k)-, Cath(1d)+ Dave(1k)+

We have a 1kyu Juliet winning 3 games playing:
Karen(1d)+ Lionel(1k)+ Martin(1k)+

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

If 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 Pairing score, and MMSf is the final McMahon Pairing score.

Using the UK scale, we have Alan and Juliet ranked equal and sharing any prize:

            Wins MMSi MMSf   SoDoS   WHO CONTRIBUTES TO SODOS
 Juliet(1k) 3    -1   2    0+1+1=2   Karen+Lionel+Martin
 Alan(1d)   2     0   2      1+1=2   Cath+Dave

Using the EU scale Juliet is ahead of Alan, Juliet gets the prize:

            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

It does not matter here which result is better. It demonstrates that SODOS is flawed and should not be used.

Note that if you use SOS (Sum of all opponents McMahon scores) as the tie breaker, then this effect does not happen because you are summing over all games, not just a selection.

Read the example above again comparing either scheme with one where a shodan scores -100. In that case a player with no wins scores 0 whilst one with several wins will be far worse off with a score of minus several hundred!

wms: I find this argument to be totally bogus. If I understand correctly, the argument is: SODOS changes based on your origin, therefor it is a lousy tiebreaker in MM tournaments. My answer: Each tournament has only one origin, so within the context of the tournament the SODOS is reliable, therefore the "problem" doesn't exist.

Harleqin: For SODOS, losing a game is worth the same as winning against a player with 0 MacMahon points. Obviously, below the origin, you will get behaviour inverse to that over the origin. This means that for getting the desired direction of your tiebreaker, you have to make sure the origin is lower than the last player. Also, the effect of losing a game is directly proportional to the distance from the origin. This means that also with swiss pairing, the top players (whose opponents have points close to the number of rounds) will see a big effect of winning or losing on their SODOS, while the last players (whose opponents have points close to 0) will not see any big effect.

wms: Yes, that is what I alluded to in the next paragraph. For high ranked players, when the weakest players started with 0 MM points, SODOS will place players with more wins above those with fewer wins, and when both players have the same number of wins, it will behave the same as Swiss-style SODOS. I find this behavior good, so therefore, I would call SODOS a good tiebreaker (if you set up your tournament properly).

Further, I find SODOS to be a better first tiebreaker than SOS if the bars and MM points are set up so that people only have positive initial scores. My reasoning is that in a tournament, the only thing a player has control over is when they win and when they lose. If the stronger players have positive starting scores, then the SODOS will prioritize the player with more wins over the player with fewer wins, so a player starting with 19 points who gets 3 wins will usually have a higher SODOS than a player starting with 20 points who gets only 2 wins. Meanwhile, using SOS as the first tiebreaker will usually give proritize the player who started with 20 points and won fewer games, because they started at a higher point, and thus probably played opponents with more points.

On KGS, originally I did use SOS then SODOS as the MM tiebreakers (same as used in Swiss tournaments), but found that the "tiebreaker" would always just hand the win to the player who started with more points, instead of the player who actually won more games. This struck me as a terrible tiebreaker since it would use something utterly beyond the control of the players to break the ties, instead of using actual tournament performance. I switched to SODOS first, and since then I can't find a single tournament where comparing wins vs. tiebreaker results "feels" wrong.

Chris Hayashida: Having just run the Cotsen Go Tournament, I find myself thrust in the middle of all of these tie-breaker problems. I think example above uses SODOS incorrectly. If I understand SODOS correctly, it should only be applied after the win-loss record is taking into account.

The example above is flawed in that Juliet, with 3 wins, is being compared against 2 wins. Juliet should always win because of a better record, regardless of SODOS. SODOS only comes into play when comparing two players with an equal number of wins.

wms: Chris, I think that usually in MM tournaments, the winner is not the player with the most wins. The winner is the player with the most MM points. Since you can gain (at most) one point on the current leader per round, that means that if you start more than 5 points below the top player in a 5 round tournaments, you have zero chance of being the overall winner. This sounds unfair, but the reason for it is that MM is a system that lets you have one tournament with people of all different ranks in it, and have the games be "close." In a Swiss tournament, the weaker players don't play each other, so you get a lot of badly lopsided games. But if MM gave the win to the player with the most wins, then the tournament wouldn't be won by the best player, it would instead be won by the biggest sandbagger, which wouldn't seem very satisfying either.

So MM gives the win to the most points at the end, and the best overall player wins, and the weaker players enter the tournament for the fun of it and have good games.

There's nothing stopping a TD from handing out prizes for "most wins", etc., which can give weaker players something to try for, but the tournament winner should be the best player in the tournament, which (if the tournament is set up properly) will be the player with the highest MM score at the end.

I thought that Cotsen was a Swiss tournament. Is it MM?

Proper uses of SODOS

You can only use SODOS as a tie breaker if your tournament is so small that you only have one McMahon group. (So that you are basically just doing swiss pairing) Even then, you should consider using SOS first.

Some acceptable reasons for considering SODOS are

  • SOS would not break any ties. (In a round-robin tournament all players at the same score have identical SOS)
  • You want to award some tie breaker points according to how close the game was. (In a team tournament? you may want to award more tie breaker points for a 3-0 win than a 2-1 win, and maybe even something for a 1-2 loss)

However, you are probably better off using another tie breaking method, as SODOS tells nothing about the strength of the opponents the player lost to, and can therefore sometimes be considered unfair. (or more fair, depending on your point of view, of course)


This page was WMEd by SGBailey on 2004-12-18. The entire old contents of the page was appended to the discussion page. Original input from me, Geoff Kaniuk, Matti, barry, Christopher Gerlach, Jens Baaran, DrStraw, wms.


This is a copy of the living page "SODOS" at Sensei's Library.
(OC) 2007 the Authors, published under the OpenContent License V1.0.
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