Draw value

[Daniel Shawul]

I think HGM is right. The existing ELO rating formula would simply not work when not scoring a draw with 0.5 - at least they won't work without changes.

From the FIDE Handbook:

Regarding the "3-1-0" system, what I understand is it would mean that a win gets scored 3 points, a draw 1 point and a loss 0 points. To easily transform this into the existing ELO system you would divide by 3 and thus keep wins and losses at 1 resp. 0 points, and draws would get 1/3 points. That is not 50% so I don't get your point in that part.

Yes you don't get that part indeed. HGM said based on the way you interpreted it, a side would be scoring 60% even if all they did is draw. I said calculating percentages that way don't make sense since the total points gained is different. Say you have 2W,4D,4L, the way you compare them would be by using directly the point system 3-1-0. So one side will have 2 * 3 + 4 * 1 + 4 * 0 = 10 points and the other one 2*0 + 4*1 + 4*3=16 points. So 10/26 vs 16/26 (38% - 52%) which you can use to get the elo differences directly from the logistic curve. Only this time draws are considered 1/3rd of a win. So for all the draws case both would score the same points ending in a 50%-50% i.e same elos.
I don't see much of a difference with the 2-1-0 system used. You just can not use percentages when you have different number of total points in each game as in the 3-1-0 system.

[Sven]

I think HGM is right. The existing ELO rating formula would simply not work when not scoring a draw with 0.5 - at least they won't work without changes.

From the FIDE Handbook:

Regarding the "3-1-0" system, what I understand is it would mean that a win gets scored 3 points, a draw 1 point and a loss 0 points. To easily transform this into the existing ELO system you would divide by 3 and thus keep wins and losses at 1 resp. 0 points, and draws would get 1/3 points. That is not 50% so I don't get your point in that part.

Yes you don't get that part indeed. HGM said based on the way you interpreted it, a side would be scoring 60% even if all they did is draw. I said calculating percentages that way don't make sense since the total points gained is different. Say you have 2W,4D,4L, the way you compare them would be by using directly the point system 3-1-0. So one side will have 2 * 3 + 4 * 1 + 4 * 0 = 10 points and the other one 2*0 + 4*1 + 4*3=16 points. So 10/26 vs 16/26 (38% - 52%) which you can use to get the elo differences directly from the logistic curve. Only this time draws are considered 1/3rd of a win. So for all the draws case both would score the same points ending in a 50%-50% i.e same elos.
I don't see much of a difference with the 2-1-0 system used. You just can not use percentages when you have different number of total points in each game as in the 3-1-0 system.

I understand your view. I also understand in the meantime why my initial interpretation would break completely, since changing the winning probability table for a draw score != 0.5 would work somehow for the case of 100% draws but not for a mix of W/D/L.

What I don't understand yet is why you focus on 3-1-0 while the original proposal of Fermin was just to try a draw score different from 0.5. Do you think it is possible to combine both proposals consistently? Instead of the ELO formula given in 8.55 (b) and (c) you would need a different formula, but which? What about a simple round-robin event with 10 rated players, how would you obtain the rating change based on your proposed calculation which is valid for a match between two players but I don't see whether it works for many players?

Actually I also fail to see why we even discuss this so deeply ... HGM does not like it ... you don't like it ... I don't like it ... so we are only discussing about the different reasons why we don't like it while desperately trying to find some way how nevertheless it could be made to work

Sven

[Kempelen]

Actually I also fail to see why we even discuss this so deeply ... HGM does not like it ... you don't like it ... I don't like it ... so we are only discussing about the different reasons why we don't like it while desperately trying to find some way how nevertheless it could be made to work

Sven

Well, my initial post had two question, and the thread has been about if a consistent elo system would be possible for draw values different that 0.5. But what I initially has in mind was the first question:

if someone test his engine in a framework that value draws at 0.4, be pay off in the long run for scoring in a system with 0.5???.

The main idea is given two identical result, we would prefer the one with less draws. As we are trying to improve we are trying to maximize victories. I though 0.4 would be a reasonable value (in fact elo doesn't matter !!! , what matter when testing is total score compored with other similar tourney).

My point is not based in a mathematical issue, but in a observation that promoting win-strategies will be worthy. Comparing to evolution, the lion need to run more than the deer, and the neer need to run more than the lion and also to seek grass to eat. The lion has better chances to survive as it need less conditions.

[hgm]

But if the overall result is equal, you would also be promoting loss strategies.

But there are indeed all kind of quality measures you could apply to an engine under test other than pure Elo. You could, for instance, award wins against higher-rated engines extra much, or penalize losses against lower-rated engines extra hard. That could have bigger effect on the 'optimum' you find than merely changing the draw award.

[Kempelen]

But if the overall result is equal, you would also be promoting loss strategies.

But there are indeed all kind of quality measures you could apply to an engine under test other than pure Elo. You could, for instance, award wins against higher-rated engines extra much, or penalize losses against lower-rated engines extra hard. That could have bigger effect on the 'optimum' you find than merely changing the draw award.

You purpose a system other that ELO that is completely the exact definition as ELO system. with Elo system, if you win a higher-rated you win more elo points (extra much ) Do you have in mind other different concept? (frai example is the best priacher )

[hgm]

That is not how static analysis programs work. You don't gain or lose Elo there after a single result, but the Elo is awarded based on your total performance. In EloStat a win vs a weaker opponent affects your Elo in exactly the same way as a win against a stronger.

[syzygy]

I have modified my tool to take into account white elo advantage. During the course of programming it, I started to debate with myself if draws should value other than 0.5. I have done experiment downloading all games from CCRL 40/40 and run my tool with different draw values, and standing classification changed noticeable. I have tested different draw values even progressive according to opponent elo.

If you value draws higher for black than for white in an attempt to take into account the inherent advantage of white, it seems to me you should also want to value black wins higher for black than white wins for white.

So instead of (1, 0) / (0.5, 0.5) / (0, 1) for white win / draw / black win, you would use e.g. (0.95, 0.05) / (0.45, 0.55) / (-0.05, 1.05). What this boils down to is always subtracting 0.05 from white and adding 0.05 to black.

However, in the (not even very) long run each player plays white as many times as black, so this all cancels out, which means you can as well use the regular values.