Round Robin: SODOS or Direct comparison?

[HermanHiddema]

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]

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]

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]

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: Select all

    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]

By the discussions elsewhere, you have not convinced me.

Why is convincing you a worthy goal?

[RobertJasiek]

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

[HermanHiddema]

By the discussions elsewhere, you have not convinced me.

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

[RobertJasiek]

Code: Select all

    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]

Code: Select all

    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.

... 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]

Code: Select all

    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.

[RobertJasiek]

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

This applies at moment after such rules have been set. During moments before, there is rather the question first whether and possibly why ties shall be brokwn.

[topazg]

This applies at moment after such rules have been set. During moments before, there is rather the question first whether and possibly why ties shall be broken.

I agree, but is there honestly an argument for why the reasoning for one is more appropriate than the reasoning for another? The validity of the advantages against the disadvantages of each are in the eye of the beholder only - fairness with regards to awarding the most appropriate result is entirely subjective, dependent on what people feel individually is "fair".

[Matti]

Let's assume, as done in many rating systems:
rA is a scalar measuring player A's strength
rB is a scalar measuring player B's strength

p(A beats B) = 1/(1 + exp(rA - rB))

NA number of wins of Player A in round robin
NB number of wins of Player B in round robin

I believe that the following conjecture holds:

In a round robin if NA = NB, then rA = rB.

I have not constructed a proof, but any maximumlikelihood computation on Round robin results I have done has supported it.

[pwaldron]

I believe that the following conjecture holds:

In a round robin if NA = NB, then rA = rB.

I have not constructed a proof, but any maximumlikelihood computation on Round robin results I have done has supported it.

If it is true, it depends on the functional form of the probability function. The AGA system uses a cumulative normal model and the assertion doesn't hold in that case.

[EricBackus]

Code: Select all

    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 D should be 4th. When DC is possible, I think it should be used before SODOS, at least for the round-robin type tournaments we are discussing here.

When I think about SODOS, it seems to me that any argument for it can be reversed into an equally valid argument for SOLOS. So the choice between SODOS and SOLOS seems arbitrary. (For example, the SODOS rewards E for winning against stronger opponents. But why not instead penalize E for losing against weaker opponents?) By comparison, the argument for DC can't be reversed into an equally valid argument for the other player. SODOS can still be useful, and I think it can be used when DC is not possible, when some method of tie breaking must be found. But in the case where DC is possible, I think it makes a better tie breaker.

I think this all becomes a little less clear when dealing with a typical McMahan tournament, because of the issue of one player possibly facing easier opponents overall than another player. But even in this case, any argument for SODOS can be reversed in to an argument for SOLOS, so even in this case I think DC is a better tie breaker.

In addition, I suspect that there may be complications in applying DC when there are cycles (A beats B, B beats C, C beats A) where each player in the cycle has the same number of wins. If we can't use DC due to the cycle, and then we use some other tie breaker to eliminate one player, do we then go back and use DC to decide between the remaining two?
--
Eric