I see your point, and I'll take your word for it that it is useful to have such absolute values. I also agree that a tournament system with everybody in the starting band of zero points is indeed a more important special case of the McMahon system than, say, the British system (zero at shodan) or the everybody-positive system (zero at the lower bar). However, I really do not agree to having a term defined ambiguously.

Would you not be satisfied with calling the sum of opponents' wins SOW instead? This would make every term unambiguous, and allow "SOS" to have its popular meaning. And still, in a swiss system, SOS would have all the desirable properties you mentioned.

Perhaps I could have worded my comments regarding SOS and SOMS better.

Swiss pairing is the general case, with McMahon pairing as a more specific case in which different bands are assigned different starting scores. SOS is the general case, with SOMS as a more specific case in which the starting McMahon Score is taken into account.

Math:

For each player:

SOS = Sum of the number of wins by each opponent
Final McMahon Score == initial McMahon Score + number of wins.
SOMS == Final McMahon Score of each opponent \
     == (inital McMahon Score of opponent A + number of wins by opponent A)
        + ...
        + (inital McMahon Score of opponent Z + number of wins by opponent Z)
     == Sum of inital McMahon Score of each opponent + number of wins of each opponent
     == Sum of inital McMahon Score of each opponent + SOS

SOMS - SOS == Sum of inital McMahon Score of each opponent.

But the inital McMahon Score of each opponent is arbitrary. We can set the bands to contain one single rank/rating or several. We can set the zero point to shodan, top band, bottom band or anywhere else we wish. Therefore SOMS of 65, 5, and -65 can not be compared from tournament to tournament unless we are provided the boundaries of each band in each tournament and the initial McMahon Score of each band in each tournament (there are times when the McMahon Scores increment by more than one between adjacent bands!).

So Sensei's Library should contain the popular usage and explain the laxity of popular usage. Perhaps its like the use of "car" in the United States. A "car" in popular usage is a automobile, a motorcar. Actually a "car" is a generalization of "railroad car", "motorcar", "streetcar", etc. We speak of cars and assume that everyone will understand we mean motorcar. Here we speak of SOS when we mean SOMS and assume that everyone will understand.

Velobici, please give a very good reason why you keep propagating your flawed definition of SOS without so much as a comment in this thread.

So far, not a single one of the tournament organizers and rules experts I have asked has ever even heard of your definition of the term SOS. Using the abbreviation of "SOW" for "sum of opponents' wins" was a common suggestion.

However, SOW (which is the way you use the term SOS) is a meaningless number outside the Swiss system. In the Swiss system, by chance, SOW happens to coincide with the common, correct and meaningful sense of SOS, and that is the only reason it makes sense there.

All this makes your edits seem a lot like vandalism, and a very good explanation would be in place to prevent them from getting treated as such.

Thanks,

 -Bass

There is a lot of text here. Hermann Hiddema's comments are in italic typeface. My responses are in roman typeface.

1. True with those prerequisites. But in my opinion I have shown the math to be in error except only in this very narrow case (I=0, fractional komi, all players play all rounds, no other draws possible)

Not at all convinced that this is a very narrow case. Those very conditions (I=0, fractional komi, all players play all rounds, no other draws possible) apply to the top band of a McMahon tournament quite often. Since only the players in the top band can win the tournament, I maintain that the constitute an important population of players. Example: http://www.usgo.org/media/File/2008_01_20_OzaEastFINALRESULTS.pdf The top 34 players played all games.

2. They are, quote ext Wikipedia: (but this is really beside the point for the discussion)
Solkoff
Main article: ext Buchholz system
This system is the same as the Median system, except that no scores are discarded. Emphasis added?

My error. Read the article too fast.

3. German Korean Ambassadors Cup 2007 http://dgob.de/tourn/tourn.cgi?f=07debbcp.txt&mode=cml (qualifier for the KPMC amateur world championship). Also New zealand rules specify komi in even games as 7.

Well. I am surpised. Appears that 32 players played each round for 16 games per round or 80 games. Of these 80 games, there appear to have been two draws or 2.5% (1/40th). New Zealand Rules do not define the outcome of a game in which both players have the same number of points. Per the rules, such a game does not have a winner, but neither is such a game defined as a draw or as a no result. It is simply undefined. Neither NewZealandRules/Explanation nor NewZealandRules/Discussion take up the matter. I will pose the question on the latter page.

4. See 3.

Do you maintain that such tournaments are the majority? 10% of all tournaments? 1% ?

5. It does not. But you are specifying quite a number of additional conditions required for scores to be equal to wins.

Those conditions seem to be quite common among the top players in both amateur and professional tournaments.

I'm sorry if it is strange to you, but it is strange to me that' you will accept no other definition of score than number of wins. If you want that exactitude, why not create a page SOSS (Sum of Opponents Swiss Scores). Then you can define SOS as

* SOS == SOSS in Swiss tournaments
* SOS == SOMS in McMahon tournaments.

The matter of how to calculate SOS and McMahon scores is poorly documented in a large number of places. Reading the docs of the FIDE, what is written in Sensei's and other places is more fustrating than enlightening. We can have a quick definition available and presented first. Taking the time to explain the matter clearly and exactly will save others the trouble that I have had in determining the information needed to understand.

What the discussion keeps coming back to, in my opinion, is the definition of score. In my vocabulary, score is not the same as number of wins. It is the score according to the rules of the tournament, which may be a McMahon score, a Swiss score, a Hahn point system score, or whatever. The main thing is that score indicates a players ranking and ranking indicates a players skill. The important thing about SOS is that is gives an indication of how strong were your opponents. This is skill. In McMahon, the McMahon score is the main indicator of how strong a player is, not his number of wins.

Score does not equate to skill. Score is determined by performance in a particular event/tournament. Performance depends, in part, on the pairings assigned. In performing the pairings for a tournament (now there is a can of worms!), I have seen tournament directors manually pair in an attempt to force at least one loss on each player, even if it means that the pairings are quite a stretch. In doing so, the tournament director is deliberately creating players with equal scores so that he may answer all questions regarding placement on the results sheet with well, you should have won all your games. In doing so, the tiebreakers used become more important. But which tiebreakers are to be used (another can of worms!). There are those that maintain that SOS and SOSOS should be used in that order. There are others that prefer SOS and SODOS in that order. The FIDE specifies a different method of tiebreaks.

It gets worse. Score is also assigned in tournaments that involve both skill and luck such as poker tournaments. Scores for running events are effected by the weather and the terrain. Score gives us a obscured glimpse of skill even when there is no luck involved due to the effects of emotion and immediate (time wise) health on the competitor.

Repeat: In McMahon, the McMahon score is the main indicator of how strong a player is, not his number of wins.

The McMahon Score is not a indicator of skill, that is not an indicator of how strong a player is. Its not even and indicator of performance. Who is more highly skilled (stronger): the 6k that wins 6 games in a McMahon tournament and ends with a score of 0 or the shodan that loses 6 games and ends with a score of zero. (number of assumptions here. among them: shodans are assigned an initial McMahon score of zero; the 6 kyu was assigned -6; there were 6 rounds; etc.) I don't know who is more highly skilled. I do know who performed better based upon number of wins. This is quite realistic and not uncommon as children from Feng Yun's Go School are chronically underrated and so have initial McMahon scores that are inappropriate but are based upon their prior performance. A problem there is that they improve faster than the rating system allows.

Lee McMahon in an attempt to fix a problem with Swiss tournaments hit upon the idea of assigning a number of losses (wins if you prefer) to players before the tournament begins. In doing so the initial slaughter rounds are not played, and people get more evenly matched games (assuming that the ratings are not out of whack). The cost of doing so was to inject past performance information (the initial McMahon score) into the results of the tournament. Its a cost/benefit decision. We should make it clear to readers of Sensei's Library, what Lee McMahon was trying to achieve and at what cost.

All this ignores the problems with rating systems which is not a small field of study in Statistics called Paired Comparison Experiments (Google it). But please realize that ratings are numeric assignments based upon a model applied to a selection of A in preference B (the winner over the loser). The quality of the model is quite important. In the model there are assumptions regarding the distribution of skills; among the distributions used are the Normal Distribution, because the mathematics is well understood, and the Logistic Distribution. The canonical introductory text to this subject is The Method of Paired Comparisons by H. A. David.

Bass: Ok, this is getting rather lengthy. The matter is purely that of reaching an agreement and I see velobici is digging his positions too deep ever to change his mind again, and the same goes for me. Also, I do not like the idea of pulling authority over him, as he is clearly a quite knowledgeable person.

So the only civilized weapon I have left is democracy.

The following are to be the official definitions for "Score" and "SOS" used from now on at Sensei's Library.

Score

In a tournament, a "score" is the number assigned to each player for the purpose of finding out which player should be placed higher in the results. Examples of "scores" include the MMS in McMahon tournaments, Hahn points in the Hahn system, and the number of wins in the Swiss system.

SOS

Sum of Opponents' Scores. (See "score", above.)

Those in favour, say "yea". Those against say "nay".

I think anybody with a desire for conceptual elegance will feel attracted to a "sum of scores" concept that is independent of the implementation of "score".

A specific page on SOMS mixes both the concept "sum of score" and the implementation of "score", which is inelegant and leads to redundancy. It can exist, but it will probably decay.

However, the current explanation of "sum of scores" is also and tacitly dependent of the implementation of score, namely "score = number of wins". This is not only inelegant, it is also confusing, some may even say wrong.

If we accept SOS to equal SOW and SOMS to be what it is described to be here, then we also need separate pages describing the mixture of the SOS idea in its abstract form with the actual implementation, for each such implementation. That is not a very attractive idea.

I vote to restore the SOS page to its abstract conceptual form and to have a SOMS page exist next to it, because we must respect a contributor's apparent need for its existence, even when meeting strong resistance.

Ok, I'm really tired of this by now. I propose that SOMS be deleted or be made an alias to SOS. I am not about to have a vote over this. I have refuted every argument that velobici has brought to bear, and I see no reason to continue the discussion.

SOMS as a term is redundant and can only confuse people. Everybody knows what SOS is, and I have never met anyone who was confused by the term. SOMS seems to have been introduced by PyTD, and immediately caused confusion: http://www.godiscussions.com/forum/archive/index.php/t-3836.html

I suggest Bass edits the SOS and SOMS articles, his suggested definitions above are clear and to the point.