# SOMS vs SOS [#1269]

82.203.162.177: SOMS vs SOS (2008-01-29 01:37) [#4228]

to velobici:

I see no reason to maintain a different term for "sum of opponents' scores in a swiss tournament" and a "sum of opponents' scores in a McMahon tournament". Clearly a "score" in any tournament system is the number by which the players are primarily ranked, so there is no difference between the two cases.

I would prefer having a term for "Sum of Opponents Scores", nevermind which tournament system is used. This is, as you say, the popular meaning of SOS.

Also, the term SOMS simply does not exist in Europe.

The number of wins in the "Pt" column of a MacMahon result sheet might be called a "score" by some. If this is very common (I haven't ever heard anybody calling it so), then there might be a reason to maintain the separate terms, with a note as to where each term is used. Otherwise, I suggest that the term SOMS is completely abolished as redundant, or reduced to "a clarifying name for SOS used in MacMahon tournaments".

``` -Bass, 2008-01-29
```
X
86.148.41.114: Re: SOMS vs SOS (2008-02-05 23:35) [#4258]

I agree with Bass. Sum of Scores is either your swiss score (wins) or McMahon Score (McMahon points) or some other fishy pointing device. The basic problem with having a page for SOMS is that nobody uses this. -Ian

velobici: difference between absolute and relative numeric values (2008-01-29 05:22) [#4229]

SOMS is analogous to degrees F and degress C. Is 40 hot or cold? SOS is analogous to degress K. 40 K is cold.

The sum of scores in a Swiss tournament is the sum of the opponents won games. The starting score is always zero. If SOS = 6, the player's opponents won six games. The number has an absolute meaning. It is not a relative number.

The numeric value of the McMahon Score in a McMahon tournament is meaningless without knowing the starting values. By convention, the top band is assigned an initial McMahon Score of 0. As a result the McMahon Score for the top band players, provided that they play each other only, is also their SOS. But often they do not player each other exclusively, so that doesn't hold most (nearly all) of the time. We could just as easily assign the weakest band an initial value of zero.

So, when I tell you my SOS and you know the number of rounds in the tournament (R) by comparing N to R you have an immediate assessment of my results in the tournament. Example: my SOS = R(R-1), you know that I played against a strong field in that each of my opponents suffered only one loss. We don't know which game they lost or if they won/lost against me. Combine this with my own win/loss record and you know a lot.

With McMahon Scores, if you know my SOMS and the number of rounds, you don't know anything...you may assume that the top band had a initial McMahon Score of 0, but you don't know. The situation is much worse if there is a super group (initial McMahon Score of +1 or super-super group). Then if my SOMS is R(R-1)...did I play against people in the super group? Did I win all my games? Which group had an initial McMahon Score of zero? How wide were the bands?

The numeric value of SOMS is relative, without being told the base you don't know the value. Even then the super groups deprive you of information.

Example: At the end of a 6 round tournament my SOMS is +1. How strong was the field that I played against? Answer this correctly and I will agree with you immediately.

82.203.162.177: SOS vs. SOW (2008-01-29 18:14) [#4232]

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.

X
82.203.162.177: Re: SOS vs. SOW (2008-01-29 23:34) [#4233]

If my previous comment made no sense to you, I apologize. I was trying to second-guess why you might want to use the term SOS the way you do, but could not make heads or tails of it, and it really shows in my comment.

Then I realized why I had such trouble. It is nicely condensed in these two sentences you added to the SOS page: "SOS is the generalization of SOMS. SOS is used in Swiss pairing tournaments."

You claim that SOS is a generalization of SOMS. In my dictionary, a generalization means that SOS applies wherever SOMS does and elsewhere. This is the popular meaning of SOS, and with this I wholeheartedly agree. The next sentence however seems to try to reverse this ("SOS is used in Swiss pairing tournaments"), and in your comment above you seem to base your argumentation on SOMS being the general case and SOS being the specialization for use in Swiss tournaments only.

Perhaps I can now make a more convincing argument.

In my opinion, it is better to think of SOS as the general case (sum of whichever scores are used to determine the winner), and SOMS as the special case, where the said scores happen to be McMahon points.

The reason for my opinion is that SOS (popular meaning) is a very good tie breaker no matter what the tournament system. If you invent a team tournament system where a 3-0 win scores 2 team points, and 2-1 win only one, you still can use SOS (popular meaning) to determine which team had the tougher opposition. Notice how there is very little sense in thinking of team points as a special case of McMahon points.

Bass, 2008-01-29

velobici: a little math (2008-01-30 13:16) [#4234]

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.

X
194.111.136.197: Re: a little math (2008-01-30 15:28) [#4235]

Bass: Your definition of SOS is wrong. SOS is not the sum of opponents' wins. SOS is the sum of opponents' scores. In a McMahon tournament a player's score is his McMahon score, and thus SOS is the sum of McMahon Scores.

velobici: Re: a little math (2008-01-31 14:41) [#4238]

How is one opponent's score in a Swiss pairing tournament determined? I know how to do sums. Once I know how to determine a single opponent's score in a Swiss pairing tournament I can add up the scores for all opponent's played in that tournament.

194.111.136.197: Re: a little math (2008-01-31 16:28) [#4239]

In any tournament any player's score is determined by whichever method the tournament organizers decide is the best indicator of whatever it is they want to measure.

• In a Swiss tournament, the score is the number of wins.
• In a McMahon tournament, the score is the MMS.
• In a Hahn system tournament, the score is the sum of acquired bangneki-like points.
• In my Silly Team Tournament Format from an earlier comment, the score is the number of team points.
• In a future tournament system using whichever pairing the score is the number that is compared to find out which player should get the better place in the results.

In any of these cases, the sum of opponents' scores is a meaningful tie breaker, it tells the strength of the opposition as measured by that tournament system. You seem to argue that calling this sum "SOS" is a mistake, except in the first of the cases.

I cannot figure out any logical reason for doing so.

194.111.136.197: Velobici, please explain yourself. (2008-02-05 13:10) [#4252]

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
```
X
velobici: Explanation and response copied from [Bass] (2008-02-05 14:10) [#4253]

Velobici: Which IP address are we to track to know that you are the person writing? The post labelled 194.111.136.197: Re: a little math (2008-01-31 16:28) [#4239] of SOMS vs SOS is does not indicate that it was you. No reason to believe that it is not another person that does not sign in and use their account on this server.

Regarding SOS and SOW, a term that I have not seen till you started using it, please show me where the math included in the footnotes of SOMS is incorrect. Mathematical equalities are a very good reason upon which to base an assertion. If my math is wrong, I apologize and am quite ashamed.

In 194.111.136.197: Re: a little math (2008-01-30 15:28) [#4235] of SOMS vs SOS you assert: SOS is not the sum of opponents' wins. SOS is the sum of opponents' scores. How is SOS mathematically different from the number of wins in a tournament added to the initial score. Please show me the mathematical inequalities upon which you base your assertion that SOS is not the sum of opponents' wins. SOS is the sum of opponents' scores.

HermanHiddema: Re: Explanation and response copied from [Bass] (2008-02-05 14:46) [#4254]

I'm sorry, but your math is wrong:

In footnote 2 of SOMS you say:

```Score == initial score at the beginning of the tournament + number of wins.
```
```SOS == Sum of the scores by each opponent
== Sum of the number of wins by each opponent
```

Ok, so lets reduce this to single letters:

```S = Score
I = Initial score at the beginning of the tournament
W = number of wins
```

The math in the footnote goes:

```S == I + W
SOS == Sum of S == Sum of W
```

Incorrect, as you have defined S to be I+W, this should be

```SOS == Sum of S == Sum of (W + I)
```
velobici: I is zero for all players in Swiss paired tournaments. (2008-02-05 15:32) [#4255]

Using the single letter notation suggested by HermanHiddema:

```I is zero for all players in Swiss paired tournaments.
I is the players initial McMahon Score for McMahon tournaments.
```

For Swiss paired tournaments:

```SOS == Sum of S
== Sum of (W + I)
== Sum of (W + 0)
== Sum of W + Sum of 0
== Sum of W
```

For McMahon paired tournaments: Replace I in the above with the Sum of the players initial McMahon scores, a number that will most often not be zero, but may be zero. Example: 6 round tournament where a player's opponents score: -2, -1, -1, +3, +1, 0.

HermanHiddema: Re: I is zero for all players in Swiss paired tournaments. (2008-02-05 15:50) [#4256]

Exactly. So

```SOS = Sum of S = Sum of W
```

is only valid for Swiss tournaments. But

```SOS = Sum of S = Sum of (W+I) = Sum of W + Sum of I
```

is valid for both Swiss and McMahon tournaments.

The second is the correct definition of SOS. The first is flawed.

velobici: widening of usage for a term is not limited to SOS (2008-02-05 21:29) [#4257]

HermanHiddema: wrote ''Exactly. So

```SOS = Sum of S = Sum of W
```

is only valid for Swiss tournaments. ''

Velobici: This is a direct result of I == 0 for Swiss tournaments.

HermanHiddema: wrote ''But

```SOS = Sum of S = Sum of (W+I) = Sum of W + Sum of I
```

is valid for both Swiss and McMahon tournaments. The second is the correct definition of SOS. The first is flawed. ''

Velobici: The term SOS preceeds the work of Lee McMahon and Bob Ryder. The use of SOS to describe McMahon tournaments is a reuse of the existing term. SOMS is the exact term and is particular to McMahon tournaments. SOS has two definitions:

1. the exact: SOS = Sum of S = Sum of W + I; where I == 0
2. the common: SOS Sum of S = Sum of W + Sum of I; where I is not restricted to being zero and therefore encompasses both Swiss and McMahon.

This widening of usage for a term is not limited to SOS. We see it also in joseki...Nakayama has talked of following joseki in describing his morning routine...many folks talk of xeroxing a document when photocopying, or kleenex in place of facial tissue, etc.

So where is the math wrong ?

P.S. I have no objection to stating on both the SOS and SOMS pages or just one that SOS is commonly used and SOMS is rather exacting. There is a difference between SOS as used in Swiss and as used in McMahon. We should explain the difference and the common usage rather than insist that there is no difference.

HermanHiddema: Re: widening of usage for a term is not limited to SOS (2008-02-06 12:05) [#4259]

I do not think that the fact that SOS precedes McMahon is very relevant. If we look at a Swiss chess tournament, for example, then SOS is also Sum of Scores, not Sum of Wins. Te be exact, in chess it is:

```SOS = Sum of Scores = Sum of Wins + 0.5 * Sum of Draws
```

So the statement you made in your first post to this thread, "If SOS = 6, the player's opponents won six games" is not true. He might have score 5 wins and 2 draws, or 4 wins and 4 draws, etc.

In draughts on the other hand, where a win is 2 points and a draw is 1 point, it is:

```SOS = Sum of Scores = 2 * Sum of Wins + Sum of Draws
```

Now I'm not really up to date on draughts, but I understand that there have been proposals to introduce a "Winning Draw" for positions that are a draw, but where one player has a clear material advantage (as I understand it, they want this due to the high number of draws at the top level). In which case it would become something like:

```SOS = Sum of Scores = 2 * Sum of Wins + 1.5 * Sum of Winning Draws + Sum of Draws + 0.5 * Sum of Losing Draws
```

The point is that in all these cases, there is an unambiguous definition of the term score. The score is the primary criterion to rank the contestants in a tournament. The score is defined in terms of wins, losses, draws, byes, forfaits, points, etc.

velobici: Re: widening of usage for a term is not limited to SOS (2008-02-06 12:41) [#4260]

Ah...Chess, draughts. My error, I thought we were talking about Go.

HermanHiddema: Re: widening of usage for a term is not limited to SOS (2008-02-06 13:09) [#4261]

Yes, we were. Although to be more specific, we were talking about a tie breaking system for go tournaments. And if you bring up the fact that SOS precedes McMahon, you must also acknowledge that the system is actually borrowed from chess, where it is know as Buchholz or Solkoff. Therefore chess and draughts are most certainly relevant to the current discussion.

Furthermore, although most Go tournaments us a komi with a fractional part to prevent draws, not all of them do. So in a Swiss go tournament, a SOS of 6 may also mean 5 wins and 2 draws. Also, many tournaments award 0.5 points for rounds not played. In such cases there is no way to determine from SOS alone how many of the SOS points were wins, how many were draws and how many were unplayed rounds.

velobici: Re: widening of usage for a term is not limited to SOS (2008-02-06 14:32) [#4263]
1. You still have not shown the error in the equations, once indicated that I is identical to zero for Swiss paired Go tournaments using fractional komi and not encumbered by the various draw rules.
2. Buchholz and Solkoff are not identical. Per Wikipedia, Buchholz is SOS. Solkoff is Buchholz modified by discarding either one or two outliers at both ends of the scale.
3. Go tournaments with komi, but not fractional komi? Can you cite an example of a nationally or internally sanctioned tournament (EGF, AGA, Nihon Kiin, etc) that allows draws provided that the game was counted (removing from consideration the Japanese rules "no result" and other items such as "draw by repetition"). Edit: forgot Ing Rules...whole number komi and equal score games are awarded to White...hence recorded as wins for White.
4. Have you seen/heard of a draw in such a tournment? (Unfortunately, it does not appear that I can query the European Go Database for number of draws recorded.)
5. Provided a player participated in every round, and in light of the above, how does a player's score differ from the player's number of wins?

It is strange to me that you are now arguing for exactitude (half points for draws (the rare), must play all rounds) but resist the exactitude of distinguishing between Swiss and McMahon (the common place) in which ther are two cases that of

1. Swiss: S = Sum of W + Sum of I (your equation from Re: I is zero for all players in Swiss paired tournaments. (2008-02-05 15:50) [4256], no provision for draws modified in Re: widening of usage for a term is not limited to SOS (2008-02-06 12:05) [4259] to allow for draws) where I is identically zero and
2. McMahon: where I is arbitrarily set ala initial McMahon Scores.

Shall we explain the full equation with the required conditions on the SOS page? Perhaps something like:

Swiss: Go: A player's score (S) is the sum of the player's wins (W). Chess: A player's score (S) is the sum of the player's wins (W) plus one half the sum of the player's draws (D). Draughts: A player's score (S) is the twice the sum of the player's wins (W) plus the sum of the player's draws (D).

Thus the player's score, provided they play in all rounds of the tournament and fractional komi is used, is equal to the number of wins.

Perhaps we can both agree that being exact is not easy :) Especially in words. Math is much easier.

HermanHiddema: Re: widening of usage for a term is not limited to SOS (2008-02-06 15:16) [#4264]
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)
2. They are, quote Wikipedia: (but this is really beside the point for the discussion)
Solkoff
Main article: Buchholz system
This system is the same as the Median system, except that no scores are discarded. [Emphasis added]
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.
4. See 3.
5. It does not. But you are specifying quite a number of additional conditions required for scores to be equal to wins.

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.

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.

194.111.136.197: Meaning of SOS (2008-02-06 15:20) [#4265]

Hi velobici, and sorry about not introducing myself in an earlier comment.

Because you stubbornly refuse to realise there is anything wrong with having a definition for SOS that is only meaningful in Swiss tournaments, I'll try these last attempt at pinpointing the source of your confusion.

These definitions are from onelook.com.

Sum
noun: a quantity obtained by addition
Opponent
noun: a contestant that you are matched against
Score
noun: a number that expresses the accomplishment of a team or an individual in a game or contest (Example: "The score was 7 to 0")

If you contest the meaning of one of these words, please say so.

The definition for "Sum of Opponents' Scores" is quite self-explanatory.

• The definition of SOS is "A quantity obtained by addition of numbers, belonging to contestants you are matched against, that express the accomplishment of a team or individual in a game or contest"

If you disagree with this definition, please say so.

• The validity of any mathematical formulation of SOS can be determined by checking whether the said mathematical results are always equal to this definition.

If you disagree with this step, please say so.

• In McMahon tournaments, "the number that expresses the accomplishment of a team or individual" is the McMahon Score.

If you disagree with this definition, please say so.

• In McMahon tournaments, "the quantity obtained by addition of numbers, belonging to contestants you are matched against, that express the accomplishment of a team or individual in a game or contest" is the sum of opponents' McMahon Scores.

If you disagree with this step, please say so.

• In McMahon tournaments, SOS is the sum of opponents' McMahon Scores.

If you disagree with this step, please say so.

• Any number which is not always equal to SOS is not SOS.

If you disagree with this, please say so.

• In McMahon tournaments, the sum of opponents' wins is not always equal to SOS.

If you disagree with this, please say so.

• In McMahon tournaments, sum of opponents' wins is not SOS.

If you disagree with this step, please say so.

After you have identified the step(s) you do not agree with, we can most likely have a more meaningful discussion.

``` -Bass
```
194.111.136.197: Re: widening of usage for a term is not limited to SOS (2008-02-06 16:03) [#4266]

Bass: Hi velobici, you say "The term SOS preceeds the work of Lee McMahon and Bob Ryder."

This is exactly the same as saying "There used to be a time when you could calculate the SOS just by adding the opponents' wins".

Even though you could always do the calculation like that in the olden days, it was never the definition of SOS. It was a way to calculate SOS, which became obsolete at the arrival of the McMahon system.

velobici: Reply to 194.111.136.197: Meaning of SOS (2008-02-06 15:20) [#4265] (2008-02-06 22:49) [#4267]

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

Hi velobici, and sorry about not introducing myself in an earlier comment.

Because you stubbornly refuse to realise there is anything wrong with having a definition for SOS that is only meaningful in Swiss tournaments, I'll try these last attempt at pinpointing the source of your confusion.

These definitions are from onelook.com.

Sum
noun: a quantity obtained by addition
Opponent
noun: a contestant that you are matched against
Score
noun: a number that expresses the accomplishment of a team or an individual in a game or contest (Example: "The score was 7 to 0")

If you contest the meaning of one of these words, please say so.

The definition for "Sum of Opponents' Scores" is quite self-explanatory.

* The definition of SOS is "A quantity obtained by addition of numbers, belonging to contestants you are matched against, that express the accomplishment of a team or individual in a game or contest"

If you disagree with this definition, please say so.

I agree that is one possible rendition into English of the algorithm used to compute SOS. I would render it as: A numeric value computed for each player by summing the final scores of each player that the player in question competed against during the tournament. Dont like the repetition of the word player for two purposes, but cant find better wording at the moment. One reason why I prefer the algorithm. Please note that the study of algorithms is a branch of mathematics.

* The validity of any mathematical formulation of SOS can be determined by checking whether the said mathematical results are always equal to this definition.

If you disagree with this step, please say so.

Disagree. The algorithm is determinative. The rendition into English, any other natural language or into a computer language is not the definition. It is a translation. The algorithm is the definition, not the English. The primary reason is that we can specify clearly and completely via an algorithm what we mean by SOS or SOMS. In natural language that is much more difficult to do.

* In McMahon tournaments, "the number that expresses the accomplishment of a team or individual" is the McMahon Score.

If you disagree with this definition, please say so.

Disagree. The McMahon Score is the sum of the accomplishment in the tournament and the initial McMahon Score assigned by the tournament director. Because this assignment is arbitrary, McMahon Score can not be compared from tournament to tournament. Whereas accomplishment can be: I won 5 out of 6 games. The field of opponents faced may be different but at least the win/loss number can be compared.

* In McMahon tournaments, "the quantity obtained by addition of numbers, belonging to contestants you are matched against, that express the accomplishment of a team or individual in a game or contest" is the sum of opponents' McMahon Scores.

If you disagree with this step, please say so.

Disagree. The McMahon Score contains an element that is independent of accomplishment in the tournament. That independent element is the initial McMahon Score.

* In McMahon tournaments, SOS is the sum of opponents' McMahon Scores.

If you disagree with this step, please say so.

Agree and disagree. Agree that this is common usage akin to xerox a page in place of photocopy a page. Disagree in that the statement is inexact.

* Any number which is not always equal to SOS is not SOS.

If you disagree with this, please say so.

Don't know which definition of SOS you are using, the common parlance or the exact.

* In McMahon tournaments, the sum of opponents' wins is not always equal to SOS.

If you disagree with this, please say so.

Agreed assuming that we are using common parlance for SOS here. This follows directly from algorithm to compute SOS (SOMS to be exact).

* In McMahon tournaments, sum of opponents' wins is not SOS.

If you disagree with this step, please say so.

Agree in general, but disagree as an assertion. For any player that plays exclusively against those with an initial McMahon Score of zero, SOS is identical to SOMS is identical to sum of opponents' wins. Such players are often found in the top group, the group above the bar. But, not necessarily. After all, at the tournament director's discretion there may be no players with an initial McMahon Score of zero.

After you have identified the step(s) you do not agree with, we can most likely have a more meaningful discussion.

That would be wonderful. Couple thoughts:

• The initial McMahon score is arbitrary. The initial McMahon score differs from tournament to tournament . It has meaning only within a single tournament. I have heard that the BGA sets the initial McMahon score to zero for the shodans. The AGA sets the initial McMahon score to zero for the group above the bar. Super groups and super super groups have initial McMahon scores greater than one by convention.
• The assignment of players by rating/rank to McMahon bands is arbitrary. Each rank may receive a different initial McMahon score or two or more ranks may be grouped together into a single initial McMahon score. In the top section, several ranks are grouped together as a matter of course. Take a look at the results of the 2008 North American OZA in Baltimore. There we can see that both Feng Yun 9P and and Hong Suk Song, unrated, had initial McMahon scores of zero. In addition, I can make this assertion because I was there and can testify to such.
• Swiss SOS does not contain any arbitrary component.

-Bass

velobici: Reply to HermanHiddema: Re: widening of usage for a term is not limited to SOS (2008-02-06 (2008-02-06 23:48) [#4268]

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.

X
HermanHiddema: some actual research in reply to velobici. (2008-02-07 15:02) [#4280]

1. Sigh, instead of giving a single example to prove your point, how about doing some research? I have looked in the European Go Database at the results for four of the major european tournaments, variously (depending on sponsors) known as the "Pandanet", "Toyota Tour", "Fujitsu" or "Grand Prix d'Europe" tournament. For each tournament, I have listed the strongest player that did not play all rounds. The list gives a players final place in the tournament, his dan grade, how many rounds he Did Not Play (DNP) and whether or not he was in the top group (+ he was, - he wasn't).

Paris Panadanet/Toyota tour Grand Prix European Cup (200-250 players)

```Paris 2007 - #43 3d DNP 4 -
Paris 2006 - #54 3d DNP 1 -
Paris 2005 - #30 5d DNP 2 +
Paris 2004 - #35 5d DNP 1 +
Paris 2003 - #17 5d DNP 1 +
Paris 2002 - #34 5d DNP 3 +
Paris 2001 - #38 1d DNP 1 -
Paris 2000 - #17 3d DNP 1 +
Paris 1999 - #11 4d DNP 1 +
Paris 1998 - #41 3d DNP 2 -
Paris 1997 - #49 3d DNP 3 -
Paris 1996 - ??? 5d DNP 1 ?
Total 6/11
```

(Paris 1996 seems to be a swiss tournament, the data in the EGD is unsorted, so I went and found the strongest player with an unplayed round)

Amsterdam Pandanet/Toyota tour Grand Prix European Cup (100-200 players)

```Amsterdam 2007 - #45 3d DNP 1 +
Amsterdam 2006 - #19 4d DNP 1 +
Amsterdam 2005 - #26 2d DNP 1 -
Amsterdam 2004 - #20 4d DNP 2 +
Amsterdam 2003 - #40 3d DNP 5 -
Amsterdam 2002 - #19 5d DNP 2 +
Amsterdam 2001 - #43 4d DNP 1 +
Amsterdam 2000 - #20 6d DNP 3 +
Amsterdam 1999 - #47 3d DNP 1 -
Amsterdam 1998 - #19 4d DNP 1 +
Amsterdam 1997 - #23 3d DNP 5 -
Amsterdam 1996 - #10 5d DNP 5 +
Total 8/12
```

(Amsterdam 2004-2007 are listed under Amstelveen)

London Pandanet/Toyota tour Grand Prix European Cup (100-150 players)

```London 2008 - #18 6d DNP 3 +
London 2007 - #57 4d DNP 4 +
London 2006 - #29 7d DNP 5 +
London 2005 - #3  3d DNP 2 +
London 2004 - #15 5d DNP 4 +
London 2003 - ??? 3d DNP 2 +
London 2002 - ??? 4d DNP 2 +
London 2001 - #18 4d DNP 1 +
London 2000 - #14 3d DNP 1 -
London 1999 - #37 3d DNP 1 -
London 1998 - #23 5d DNP 1 +
London 1997 - #15 5d DNP 1 +
London 1996 - #25 5d DNP 2 +
Total: 11/13
```

London 2002 and 2003 are McMahon tournaments, but the data is unsorted.

Brno/Prague Pandanet/Toyota tour Grand Prix European Cup (110-160 players)

```Brno 2007   #23 4d DNP 1 +
Brno 2006   #27 3d DNP 2 -
Brno 2005   #24 3d DNP 1 -
Brno 2004   #20 4d DNP 1 +
Brno 2003   #43 2d DNP 1 -
Brno 2002   #29 3d DNP 1 -
Prague 2001 #13 4d DNP 1 +
Prague 2000 #32 1d DNP 1 -
Prague 1999 #43 2d DNP 1 -
Prague 1998 #43 2d DNP 1 -
Prague 1997 #16 5d DNP 1 +
Prague 1996 #33 3d DNP 1 -
Total 4/12
```
```            Grand Total 29/48
```

So on average 60% of tournaments had a player from the top group not playing all rounds

2. Ok

3. I've heard that roughly 1 out of every 50 games would be a draw with a round komi, so 1/40 sounds reasonable. Under New Zealand rules, if players have the same number of points, it's a draw.

4. Where did I claim that this was the majority? Such tournaments exist. As do those with draws do to unplayed rounds, or those with draws due to triple ko or other rules issues. Also, fractional komi is a 20th century invention. For most of the game's history jigo was a realistic option.

5. Common, yes, but seeing point 1, those conditions are a minority.

I will respons to the rest of your post separately.

194.111.136.197: Time to vote (2008-02-07 00:21) [#4269]

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".

X
86.146.173.203: Re: Time to vote (2008-02-07 19:33) [#4282]

yea

velobici: Re: Time to vote (2008-02-07 22:50) [#4283]

Only registered accounts get to vote. IP addresses are not allowed to vote.

tapir: Re: Time to vote (2008-02-08 01:22) [#4286]

Only registered accounts get to vote. IP addresses are not allowed to vote.

Please, do not reenact wikipedia experiences here. Votes, vote related account ranking etc. should all be unnecessary.

---

Instead of inventing new definitions I would be pleased if we just recognize current usage = meaning of SOS. While the meaning of score is different in each system, SOS is not ambivalent it is simply the sum of opponents scores. The meaning of score should be defined on the pages about McMahon score / Swiss pairing (as the most convenient way). Otherwise in a next step you have to consider such unchristian niceties as SODOSS and - beware - SODOMS.

Dieter: vote and comment (2008-02-07 01:11) [#4270]

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.

X
velobici: Dieter, which version are you referring to (can you give me the number?) (2008-02-07 23:43) [#4272]

Dieter, which version of the page are you in favor of? This list shows the versions. Current version is 37 (corrected: I mistakenly wrote 34), immediately previous on the list is version 29. Which version number is the abstract conceptual form version to which you are referring? Can you provide the number of the version?

If we go with the abstract conceptual form should we have a page(s) that describes the implementation(s) ?

Dieter: Re: velobici, on restoring pages (2008-02-07 13:57) [#4278]

Hi Velobici. I reread the pages. The SOS page is fine as it is and not misleading. My mistake. The SOMS page may be considered superfluous by some, but it is not problematic, except for footnote 2, where all of a sudden the until then general concept of SOS is set equal to SOW. This part is misleading.

SOS is a generalization of SOMS, obviously, but there is no mathematical "proof" of that. It is so by their very definitions.

You can indeed add some math to show the relationship between SOW and SOMS, which is what the footnote actually does.

xela: Vote? This is getting silly. (2008-02-07 04:09) [#4273]

I'm coming into this discussion at a rather late stage. It was only seeing the word "vote" at Recent Changes that caused me to glance at what should be a rather boring topic. Why is there a need for voting?

With each successive edit, the SOS and SOMS pages are getting more complicated and less readable. Can we please revert to earlier versions? Version 2 of SOMS is clear and unambiguous. Version 29 of SOS may provoke argument about "wins" versus "score", so we could revert and then add a footnote to mention that the disagreement exists.

It is not the role of SL to provide "official" definitions. If someone is using a particular term in a particular way, then it deserves to be mentioned. Let's try and keep this simple and readable.

X
82.203.162.177: Re: Vote? This is getting silly. (2008-02-07 09:49) [#4274]

Bass: Version 2 of the SOMS page may be unambiguous, but it is also extremely misleading. That version explicitly lists a very recent American tournament that has used the SOMS as a tiebreaker as if it were something very special.

But this ignores several hundreds of European McMahon tournaments that have used that exact same tie breaker, but have not felt the need for the redundant "M" in the tie breaker name.

The term SOMS was most likely invented by velobici himself after he had read this wiki's definition of SOS. (Which was mistaken from the beginning, and only very recently fixed, and then edited back to inaccuracy again by velobici). I would have invented SOMS too, had I not known that the definition of SOS on the SOS page was wrong.

Having a vote is admittedly silly, but I cannot think of another way to keep velobici from reverting the fixed version of the SOS page back into the mistaken one. Better suggestions are most welcome.

velobici: Re: Vote? This is getting silly. (2008-02-07 13:00) [#4275]

Dieter suggests that we have an abstract SOS page. I recommend that we add a page for implementation of SOS, this is a page that should define how SOS in calculated in full detail for each of the systems: Swiss, McMahon, Hahn, etc. That page should also show the mathematical relationship between the variants. This would allow us to delete the SOMS page without losing useful information.

Perhaps it is bothering you that I refer to initial McMahon scores as arbitrary. I mean arbitrary in the exact same way that the constant of integration that arises when a variable is integrated. Because the constant of integration is arbitrary, a single equation for velocity can be used for any initial velocity and therefore used for any time an acceleration is applied to an object. McMahon scores are completely arbitrary, in that the width of the bands, the location of the top bar and bottom bar, the location of the zero band if any, can all be set by the tournament director without reference to any past or future tournament.

What is driving me is that until recently we did not have a page on Sensei's Library that clearly and unambigiously stated how to calculate SOS (and its variants). How anyone maintain that we should not have such a page?

194.111.136.197: Re: Vote? This is getting silly. (2008-02-07 14:54) [#4279]

Bass: The SOS calculation page is a good idea.

It does not bother me in the least that you refer to the McMahon Scores as arbitrary. They are. So are any other scores. But this is beside the point.

If I got you correctly, you would be okay with this kind of arrangement:

1: have a page that has the SOS implementations for different tournament systems listed 2: revert the SOS page to version 34 in meaning, clarify the text and add a link to the implementations page 3: delete the SOMS page altogether

If this was what you were saying, I'll get to work right away.

velobici: Let's let Dieter, xela and others weigh in. Please do not get to work right away. (2008-02-07 23:53) [#4285]

Dieter states that the current version (version 37 not version 34...I mistakenly wrote version 34...I have corrected the error and placed a note there indicating my error.) if fine. So revision to version 34 is not warranted at this moment. Perhaps it will be, just not at this moment.

Bass said: It does not bother me in the least that you refer to the McMahon Scores as arbitrary. They are. So are any other scores. But this is beside the point.

Well, what you are saying makes me believe that you do not understand the meaning of arbitrary. Number of wins is not arbitrary. It is a direct result of the performance of the two players. Let's say three wins out of six games for player A. Three as the score for player is not arbitrary. Now let's add in the final McMahon score for player A. It is 3 + player A's initial McMahon score. What is player A's initial McMahon score? It is an arbitrary value assigned by the tournament director.

This is the difference between arbitrary and non-arbitrary. Do you agree? I believe the difference is an important one.

Please do not get to work right away.

Let's let Dieter, xela and others weigh in. Lord knows you and I done so!

82.203.162.177: Re: Let's let Dieter, xela and others weigh in. Please do not get to work right away. (2008-02-08 02:27) [#4287]

Bass: Awarding 1 point for every win is completely arbitrary. You could award ten points for a ten point victory just as well, or you could even award another point for a team victory if it was a 3-0 win.

Also, instead of running a 7 round tournament, you could just as well award some of the prizes after the first 2 rounds, and then discard the scores and run another 5 round tournament. You could also start the 5 round tournament at the previous tournament's final score, since you might feel you do not want to discard that information. Or if everybody was not present at that 2 round tournament, you could approximate their score, say, by assigning these people some initial scores using, for example, the McMahon system. Or you could even skip the 2 round tournament altogether, and approximate every players' score by their performance in earlier tournaments, say, by the McMahon system, thus saving a whole day of valuable tournament time for better use.

Some of these things will feel more natural than others, but the one thing these have in common is that they are all "arbitrarily assigned by the tournament director".

However, this is largely irrelevant. Let's not have this evolve into another useless sidetrack.

xela: Re: Let's let Dieter, xela and others weigh in. Please do not get to work right away. (2008-02-08 03:38) [#4288]

Thanks, but I've said my piece. I'm not going to read the whole of this discussion in detail and think about it--I can think of much more constructive ways to spend my time!

The important thing is to remember that this is a library. The goal is provide a clear and useful public reference. It's not about proving who has the biggest ego or who can score the most debating points.

The pages in their current state give a long-winded description of concepts that should be simple. I'm sure they can be greatly improved. I hope that people can calm down and do this in a constructive way. That's all I have to say.

HermanHiddema: Propose deletion (2008-02-08 12:15) [#4290]

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.

X
xela: Re: Propose deletion (2008-02-09 00:42) [#4293]

Um, this seems the wrong way round to me. You have a link there which shows that SOMS is actually used in real life (not just a made-up term on this site) and that people want to find out what it means. So it makes sense to have a page here saying what it means. It can be a very short page: "SOMS is sometimes used to refer to SOS in the context of a MacMahon tournament: see discussion at..." or whatever people can manage to agree on.

82.210.116.85: Re: Propose deletion (2008-02-09 08:50) [#4294]

Yes, that is also fine. I was thinking about making it an alias, then starting the SOS page with something like "SOS means Sum of Opponent Scores". In McMahon tournaments, it is also sporadically referred to as SOMS (Sum of Opponent McMahon Scores). But keeping a short explanation ofthe term here, then referring to SOS for the actual meaning migjht be even better. --Herman Hiddema

Dieter suggests that we have an abstract SOS page. Agreed.

Herman Hiddema suggests that either making SOMS an alias for SOS or keeping a short explanation of the term here (the SOMS page), then referring to SOS for the actual meaning migjht (sic) be even better. I would prefer Herman's second suggestion.

I recommend that we add a page for implementation of SOS, this is a page that should define how SOS in calculated in full detail for each of the systems: Swiss, McMahon, Hahn, etc. That page should also show the mathematical relationship between the variants. This would allow us to delete the SOMS page without losing useful information.

1. Create an abstract SOS page removing implemenation and scoring system specifics. Strive to keep it to one paragraph. Refer the reader to the implementation page for details.
2. Truncate SOMS to a short explanation and refer the reader to SOS. Perhaps we should mention PyTD and its role regarding the term SOMS.
3. Create a SOS implemenation page that provides the details for each system of interest: Swiss, McMahon, Hahn, etc. That page should also show the mathematical relationship between the variants.
X

Sounds good. Perhaps we can create several SOS implementation pages as subpages for SOS? So SOS/McMahon, SOS/Swiss, SOS/HahnSystem, etc

Useful details on these page would include:

• What is the Score in this system?
• What score do you add to SOS for unplayed rounds (no opponent).
• What score do you add to SOS for default wins (byes) or forfaits