Quote:
Originally Posted by Rei Ayanami
Well, I mean part of what Das Boot said is correct (it's not quite reasonable to just manipulate draw rates as your variable, and that draw rates are already incorporated into ELO calculations in the first place), but I think he might have missed the point of the analysis.
The idea *isn't* to demonstrate that a higher draw rate benefits Carlsen per se, and certainly not to suggest that Carlsen should actively play in a manner that seeks draws.
Rather, the idea is that there exists a "natural" draw rate between these two players, that is already factored into their ELO ratings, and if they play in a "normal" manner, and draws occur at that expected natural rate, then Carlsen should score 60% of the total points.
The problem is that we don't necessarily know what this natural draw rate is, and without it we can't calculate precise odds of each player winning the match, even if we were 100% confident that their long term results would converge towards a 60/40 split of the points.
Therefore we are forced to guess the "natural" draw rate. As a poster on a message board, or as the author of a column on 538, the most reasonable thing to do* is provide a series of different estimates of the match probability, for different draw rates, and allow the reader to pick whichever draw rate they think is most realistic, and use it to estimate the odds. Now wlrs used a smaller range of draw rates than the 538 article (which for some reason charted draw rates under 25%, which we know is absurd). The 538 analysis does show, though, that the odds offered by Ladbrokes would be accurate to ELO *if* the draw rate was truly zero, but underestimate Carlsen's hopes for any draw rate higher than zero.
One possible conclusion would be that Ladbrokes was lazy in their analysis, forgot that draws are a thing in chess, and posted a bad line. The other possible conclusion is that they are accounting for other factors besides pure ELO. I'll leave the choice of conclusions as an exercise to the reader.
Das Boot is right when he points out that continuing the trend described in the article, if the draw rate were 90% it would "mean" Carlsen was "expected" to win 150% of the decisive games. This isn't a criticism of the method of simulating match results though, this is just proof that 90% is clearly not the correct "natural draw rate" to use in a realistic simulation of the match.
*For a simple post/article; what I'd prefer to see out of 538 is a more detailed analysis of what the natural draw rate most likely is, using a large sample of games between players at a similar level with similar rating differences (you could define "similar level" as any game where both players are >2700 if you wanted to avoid limiting yourself entirely to games involving Carlsen).