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 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. 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 Pairing 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:
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

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 Pairing score, and MMSf is the final McMahon Pairing 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.


Start of entire text of main page at 2004-12-18


SODOS is Sum Of Defeated Opponents Scores.

This is sometimes used as a secondary tie breaker after SOS. It assumes that your strength is defined by the strength of the people that you beat.

Of course some would say that the strength of the people you lose to is equally important. :)

barry

SODOS (also sometimes abbreviated as SDOS) can be used in round robin tournaments, where SOS is of no use.

Matti


I have moved the example of the SODOS tiebreaker conversion from UK to EU scales posted by Steve Bailey to the Discussion page.

Geoff Kaniuk


(wms: In general, this example seems incredibly unclear to me. It is comparing SODOS under apparently UK standard McMahon Pairing and Euro standard McMahon Pairing, but yet it doesn't take all the differences and group them together in any one place; you have to pick apart the numbers to realize what starting score a shodan gets in England. And what the heck does a statement like "for rating = dan-1 or 0-kyu" mean? Then there is all this X and Y business, and X1 and Y2 and...well, I hope you see my point. Please, can somebody rewrite it so that it can be understood without spending 1/2 hour studying it? The point is quite simple, it should be possible to make the explanation simple also. Further, it shows that SODOS alone is a bad tiebreaker, but it isn't usually used that way, usually it is a secondary tiebreaker after SOS; when used this way, does the same problem exist?)

  • What on earth are you talking about? I see no example! DrStraw

Christoph Gerlach: Using SODOS as a tie breaker after SOS is also questionable. If SODOS will discriminate between two players, these two players have the same SOS. Let's say Player 1 has a higher SODOS, this means that he has won to stronger opponents compared with Player 2. But he also lost to weaker opponents compared with Player 2 (we know this because both have the same SOS). Would anyone really think it is more significant to win against stronger opponents than losing to weaker opponents?

Anonymous: So clearly then, never use a palindrome when an acronym will do.

Jens Baaran: Hi Christoph, I would say, if a player has more wins than losses, it's better to look at the wins than looking at the losses, simply because there is more data available to base a judgement upon. So when it comes to deciding the top places in a tournament using SODOS as a secondary tiebreaker seems reasonable to me (I haven't studied the above mentioned example though).

Christoph Gerlach: Since SODOS is a tie breaker usually used after the number of wins we can assume that everyone has the same number of wins if SODOS is used to break ties.

Jens Baaran: Hm, I don't quite see your point. Perhaps I haven't made my point clear enough. I'm not saying, that one should look at the number of wins/losses for a secondary tie-breaker. Of course this doesn't make sense. I am saying, that using SODOS (i.e. a number based on the defeated opponents' score) for a secondary tiebreaker as it is used today is better than using a similar number based on the scores of the opponents the players lost to, when one wants to decide the top places of the tournament.


Geoff Kaniuk:

Hi wms. I have moved the example to the discussion page as the SODOS page seemed to be getting unreadable. Please let me know if any further clarification is needed.

As to the question: does it happen when SODOS is used as a second tie-breaker? The answer is Yes in principle, players get different SODOS increments when converting between different McMahon Pairing origins. The difference may or may not be enough to change their actual rank position.

In my experience seeing an actual difference in this case is rare. The problem is that it can happen, and so probably does.


Jeff Boscole:

Readers are asked to review a discussion on rec.games.go which presents statistical analysis from tournament simulations. Minimal tournament entropy is obtained by summing SOS and SODOS for tiebreakers, even for end-of-round pairing methods.

        - jb

RobertJasiek: What you have analysed empirically is in the context of defining "fairness of a pairing method" as "minimal entropy". It does not conclude that SODOS is useful per se but that it has a useful meaning for this definition in the type of tournaments (Swiss?) for that you have done analysis. Your analysis does not clarify why your definition should be chosen or how and in which sense it might compare to other definitions. Broader definitions would be needed to enable us to also consider all earlier criticism of SODOS again (why won games are / should ever be emphasized more than lost games; the flaw of SODOS in McMahon) and compare both that criticism and your concept of minimal entropy to other tiebreakers (used for pairings and / or / either or used for ordering the final resuls) for a given tournament system.

Jeff Boscole:

My tournament simulation runs "adjacency pairing" with no pairing avoidance for multiple matches. Justification for the "fairness" definition is not required because neither Robert nor anyone else has proposed any alternatives. Minimal entropy just means minimum complaints and minimum arguments about the tournament. Because SOS = SODOS + SOLOS there is a simple choice which to use in combination with SOS (but not both). I invite Mr. Jasiek to propose any tiebreaking methods he wishes to test and we will test them. A number of them have been tested already.

           - jb

RobertJasiek: I hope to find time some time to offer other definitions of fairness so that they are useful for tiebreaker study. - What you might study: Evaluating usage of not using any tiebreaker at all. Explain the nature of additional or lost information gained from using (particular) tiebreakers. How is that information related to the particular player's playing skill and responsibility and why is it or is it not just playing with numbers for its own sake or information on that the player does not have influence? If part of the information is asssociated with either type, then which percentage, what does that mean for the player's skill, and how should it be interpreted?

Jeff Boscole:

In each case additional rounds are usually the better method of obtaining skill results. Tiebreakers are topical only for the context of limited tournament time, or for awarding prizes. Direct skill is not being measured: only the likelihood of having more skill. Robert is correct that initial round pairing has some influence, yet if he posits no knowledge of player skill from the outset then we have no idea whether initial rounds matter. The "information difference" among choice of tiebreakers is rather small even as tiebreakers may be compared. Along with tiebreakers used for pairing midway through a tournament we need also to consider various pairing strategies.

           - jb

RobertJasiek: Thanks. - If you should have time, I would also like to see the following being tested: SOS-1. SOS-2. Direct comparison provided a) it is applied iteratively (if meaningfully possible) and b) it is applied only if the tied players have played an implicit round-robin (or multiple thereof) within the Swiss tournament's pairings, i.e., each tied player has played equally many games against each other of the tied players.

Jeff Boscole:

I am guessing that SOS-1, SOS-2, refers to SOSOS & SOSOSOS. These were investigated and appear to drift away from being tied more directly to the informative player statistics. Robert's request to examine tiebreak first from SOS and then SODOS turns out to be inconclusive (see 15 Mar '07 post to rec.games.go). For later Rounds, and in smaller tournaments, successive tiebreaks may offer some slight advantage yet for tournaments of 48 or more players a simple sum of SOS+SODOS appears to be less entropic. Tiebreaking first by SOS and then SODOS seems to work well for tournaments having player numbers some power of 2, yet does not otherwise perform as well as SOS+SODOS.

           - jb

RobertJasiek: SOS-x means to modify SOS: for every player and for x rounds, throw away his worst (smallest) values as noise.

Jeff Boscole:

You have described several ways to interpret SOS-1 (SOS-2) so I am first trying the approach of applying a rule to ignore one (or two) minimum opponent McMahon Score(s) from each player's SOS (but not SODOS). Using that idea, my tournament simulator does not detect any appreciable improvement for this tiebreaking context: MMS, then SOS, then SODOS. Since sidebar data is slightly useful, any impairment to collecting SOS (and SODOS) data results in marginally deleterious effects upon entropy minimization. The arguments which stem from examination of "defeat chains" among near-equally ranked players are not particularly strong because there is also remains the marginal likelihood of some "unrepresentative" game result. On rec.games.go I also detailed a means whereby the tournament end-result can be evaluated for fairness. Because initial entropy for an n-player tournament (by the way I am measuring it) also corresponds to tetrahedral numbers (n-1)*n*(n+1)/6 we may obtain a precise estimate for expected initial entropy - `ent' - and then invoke the level of signicance p>=0,05 for identifying a tournament entropy value which must be less than "ent^((1-p)/(1+p))" for a fair tournament result (where pairing methods were being uniformly applied).

           - jb

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