Round Robin: SODOS or Direct comparison?

RobertJasiek · **#21**

The Order of Finishing tiebreaker is a bad joke. Even worse, it contradicts the aim of the game to win every single game.

willemien · **#22**

Did some more investigation into the "433221" graph
selecting all tournaments games where

A has 4 wins
B has 3 wins and won from C
C has 3 wins
D has 2 wins and won from E
E has 2 wins
F has 1 win
Then there are 12 different tournaments (8640 / 6!)

Of these 12
7 have C winning only against D E and F ( and thus having a sodos score lower than B)

The 5 others are:

Code:

 1   a  b  c  d  e  f  | sc | sodos   
 A:  =  W  L  W  W  W  |  4 
 B:  L  =  W  L  W  W  |  3     6 
 C:  W  L  =  W  L  W  |  3     7
 D:  L  W  L  =  W  L  |  2     5
 E:  L  L  W  L  =  W  |  2     4
 F:  L  L  L  W  L  =  |  1 

 
 2   a  b  c  d  e  f  | sc | sodos   
 A:  =  W  L  W  W  W  |  4 
 B:  L  =  W  W  L  W  |  3     6 
 C:  W  L  =  L  W  W  |  3     7
 D:  L  L  W  =  W  L  |  2     5
 E:  L  W  L  L  =  W  |  2     4
 F:  L  L  L  W  L  =  |  1 


 3   a  b  c  d  e  f  | sc | sodos   
 A:  =  W  L  W  W  W  |  4 
 B:  L  =  W  W  L  W  |  3     6
 C:  W  L  =  W  L  W  |  3     7
 D:  L  L  L  =  W  W  |  2     3 
 E:  L  W  W  L  =  L  |  2     6
 F:  L  L  L  L  W  =  |  1 

 
 4   a  b  c  d  e  f  | sc | sodos   
 A:  =  W  L  W  W  W  |  4 
 B:  L  =  W  W  L  W  |  3     6
 C:  W  L  =  W  W  L  |  3     8
 D:  L  L  L  =  W  W  |  2     3
 E:  L  W  L  L  =  W  |  2     4
 F:  L  L  W  L  L  =  |  1 


 5   a  b  c  d  e  f  | sc | sodos   
 A:  =  W  L  W  W  W  |  4  
 B:  L  =  W  W  W  L  |  3     7
 C:  W  L  =  W  L  W  |  3     7
 D:  L  L  L  =  W  W  |  2     3
 E:  L  L  W  L  =  W  |  2     4
 F:  L  W  L  L  L  =  |  1 

All taking it together I find Sodos a fairer tie breaker than Direct comparison
(especialy seeing the 3rd example)

Sodos doesn't break the tie in the 5th example and i think that only then Direct comparison should be used.

RobertJasiek · **#23**

"fairer" in which sense?

willemien · **#24**

Hi Robert

Quote:

"fairer" in which sense?
"fairer" in which sense?

Meaning that (for example in tournament 3 C is a better player than B

FRom an earlier post of you:

Quote:

I have become thirsty of numbers:)

There are more interesting questions: What are the tie frequencies (esp. for place 1) after application of either of these tiebreakers?

- MutualGameScore iff 2 players are tied on a place
- Non-iterativeDirectComparison
- IterativeDirectComparison

What do you (exactly) mean by these tiebreakers

(Where does mutual gamescore differ from [non- iterative] Direct comparison , do give examples)

(Then i can build these tiebreakers into my program and give results

RobertJasiek · **#25**

I understand that you prefer SODOS. I do not understand why you prefer it. Is, for you, "preference" the same as "fairness"?!

"MutualGameScore iff 2 players are tied on a place": It is applied if and only if exactly 2 players are tied on a place. For each of them, the MutualGameScore is 1, if he wins their game, 0 if loses their game, 0.5 if he ties their game.

"Non-iterativeDirectComparison / IterativeDirectComparison":
http://home.snafu.de/jasiek/DCqual.html
And if you don't understand that, read my more detailed explanations on RGG or SL.

willemien · **#26**

The main reason why i prefer SODOS above DC is that SODOS makes a difference between winning against relatively stronger players and against relativly weaker players.
(what is defined by their number of wins)

as in example 3

Code:

3   a  b  c  d  e  f  | sc | sodos   
A:  =  W  L  W  W  W  |  4 
B:  L  =  W  W  L  W  |  3     6
C:  W  L  =  W  L  W  |  3     7
D:  L  L  L  =  W  W  |  2     3 
E:  L  W  W  L  =  L  |  2     6
F:  L  L  L  L  W  =  |  1 

C won from A (the stronger player)
But lost against B

While B and C played the same against the other players.

In my view C deserves the 2nd prize trophy and B only the 3rd

But if you look to the game between them (or MutualGameScore, what is exactly the same)

B deserves the 2nd place and C the 3rd

The problem is that MutualGameScore only looks at the mutual game.

look also at the tie between D and E for the 4th and 5th place

D only won against E and F
While E won against B and C (stronger players measured by their number of wins)

Who should get the 4th place trophy?

HermanHiddema · **#27**

RobertJasiek wrote:

http://home.snafu.de/jasiek/DCqual.html

Warning: the above linked document contains several falsehoods, the most glaring of which is: "Direct Comparison values do not contain any noise."

Harleqin · **#28**

Quote:

The main reason why I prefer SODOS over DC is that SODOS makes a difference between winning against stronger players and against weaker players.

Quote:

The main reason why I prefer SOLOS over DC is that SOLOS makes a difference between losing against weaker players and against stronger players.

RobertJasiek · **#29**

Herman, discussion of the various statements on my page, elsewhere and by others elsewhere can go on for some more years, I guess. It is not necessary to discuss that now though. I have linked to the page here just to point at the definitions.

topazg · **#30**

willemien wrote:

C won from A (the stronger player)
But lost against B

While B and C played the same against the other players.

In my view C deserves the 2nd prize trophy and B only the 3rd

Of course, the flip side of this argument is that C only deserves 3rd because his loss was against a weaker player

I think the coin flips equally well both ways though, it's preference rather than intrinsic fairness to me

HermanHiddema · **#31**

RobertJasiek wrote:

Herman, discussion of the various statements on my page, elsewhere and by others elsewhere can go on for some more years, I guess. It is not necessary to discuss that now though. I have linked to the page here just to point at the definitions.

Then just link to the definitions in the EGF rules, or the Sensei's Library pages with examples, not to irrelevant personal opinion documents.

topazg · **#32**

HermanHiddema wrote:

Then just link to the definitions in the EGF rules, or the Sensei's Library pages with examples, not to irrelevant personal opinion documents.

Agreed. The commentary section is very flawed, particularly points 2 and 5 which are simply wrong.

RobertJasiek · **#33**

By the discussions elsewhere, you have not convinced me. Before next year I might have too little time to proceed much with the SOS versus DC discussion though. Your chance to publish well worked out research with good reasoning on it!:)

Anyway, the real battle should rather be between lightning games instead of whichever tiebreakers.

willemien · **#34**

I started this treat to discuss the point so do blame me if you like.

But lets concentrate on D and E in the last example:
(just by coincedence this is a good example between these two, I first wanted to concentrate on B and C but waybe it is more fruitfuul to concentrate on D and E

Code:

    a  b  c  d  e  f  | sc | sodos   
A:  =  W  L  W  W  W  |  4 
B:  L  =  W  W  L  W  |  3     6
C:  W  L  =  W  L  W  |  3     7
D:  L  L  L  =  W  W  |  2     3 
E:  L  W  W  L  =  L  |  2     6
F:  L  L  L  L  W  =  |  1 

Who thinks that E should be 4th
and who thinks D should be 4th?

(and why)

topazg · **#35**

RobertJasiek wrote:

By the discussions elsewhere, you have not convinced me.

Why is convincing you a worthy goal?

RobertJasiek · **#36**

Like the SOS-DC discussion itself, I prefer to resume meta-discussion on it also only later.

HermanHiddema · **#37**

RobertJasiek wrote:

By the discussions elsewhere, you have not convinced me.

True, I have not convinced you, I have just proven you wrong.

RobertJasiek · **#38**

willemien wrote:

Code:

    a  b  c  d  e  f  | sc | sodos   
A:  =  W  L  W  W  W  |  4 
B:  L  =  W  W  L  W  |  3     6
C:  W  L  =  W  L  W  |  3     7
D:  L  L  L  =  W  W  |  2     3 
E:  L  W  W  L  =  L  |  2     6
F:  L  L  L  L  W  =  |  1 

Who thinks that E should be 4th
and who thinks D should be 4th?

(and why)

I think that D and E should be equal on place 4 because they have the same number of wins and that is all that matters. Tiebreakers don't matter because the aim of the tournament was to achieve one's greatest possible number of wins - it was not to achieve wins, losses or ties against specific opponents, to win a tiebreaker lottery or to win a retrospect battle about which tiebreaker possibly might be preferable to other tiebreakers.

topazg · **#39**

willemien wrote:

Code:

    a  b  c  d  e  f  | sc | sodos   
A:  =  W  L  W  W  W  |  4 
B:  L  =  W  W  L  W  |  3     6
C:  W  L  =  W  L  W  |  3     7
D:  L  L  L  =  W  W  |  2     3 
E:  L  W  W  L  =  L  |  2     6
F:  L  L  L  L  W  =  |  1 

Who thinks that E should be 4th
and who thinks D should be 4th?

(and why)

The answer is always "it depends". Whoever is responsible for deciding on the rules of the tournament (normally the organiser or TD) is responsible for deciding on the ranking system, including what tiebreak is used. If the TD says "SODOS will be used to tiebreak", then E should beat D, if he says "DC should be used", then D should beat E. There is no inherently fair system, other than making sure all tournament participants understood the system at the beginning of the tournament.

RJ wrote:

... because they have the same number of wins and that is all that matters ...

What matters is anything the tournament rules state that matter. If that includes a tiebreaker, then wins is not all that matters.

Bill Spight · **#40**

willemien wrote:

Code:

    a  b  c  d  e  f  | sc | sodos   
A:  =  W  L  W  W  W  |  4 
B:  L  =  W  W  L  W  |  3     6
C:  W  L  =  W  L  W  |  3     7
D:  L  L  L  =  W  W  |  2     3 
E:  L  W  W  L  =  L  |  2     6
F:  L  L  L  L  W  =  |  1 

Who thinks that E should be 4th
and who thinks D should be 4th?

(and why)

I do not think that the idea of a tie-breaker is applicable to round robin tournaments. Every possible comparison is made, with equal weight.

With Swiss-style tournaments it is different, because there is some luck of the draw. Two players may have the same score, but one may have faced stronger opponents, or opponents who were more in form during the tournament. Then it makes sense to break the tie in favor of the player who had less luck.

Round Robin: SODOS or Direct comparison?

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