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The Donkey Corner #6 - Rollout + Analysis

Posted By: Timothy Chow
Date: Friday, 4 April 2014, at 6:20 p.m.

In Response To: The Donkey Corner #6 - Rollout + Analysis (Robert Chow)

Robert Chow asked:

In my chess experience I have found that a difference in elo is a better indication of playing strength and thus a better predictor of performance at the higher levels than at the lower ones. As an extreme example, Magnus Carlsen, world chess champion and rated almost 2900 elo, hardly ever loses to a world-class grandmaster, 2700 elo. However, at the other end of the spectrum, a 1700 player will lose much more often to a 1500 player (or lower).

Is there a similar situation in backgammon regarding PR? Is 1 PR difference more significant for strong players who play at 4 PR and under than the same 1 PR for players at the lower levels?

There are a couple of different things being conflated here.

First, I'd expect that chess games between a 1700 and a 1500 are more likely to end with a decisive result (i.e., not a draw) than games between a 2900 and a 2700. But the overall score could be the same in the two cases, if we use the usual scoring system of win=1, draw=1/2, loss=0. My guess is that this difference in draws is the main explanation for the phenomenon you have observed. The other factor that I think is important is the one that Bob Koca mentioned, which is that high-rated players tend to have more accurate ratings because there is a lot of data and their playing ability remains relatively stable over time, compared to people who are still in an early stage of the learning curve.

Second, you ask if there is a similar situation in backgammon, but then you switch from Elo to PR in midstream. If we stick to Elo for a moment, then one significant difference is that matches are always decisive. So I would expect less of a discrepancy in backgammon than in chess.

Finally, there is a question of whether the linear relationship between Elo and PR holds universally. This is something that one would have to investigate empirically. I haven't heard any reports of anomalies from the people who have looked at the data. However, I'd guess that departure from linearity is more pronounced in the high-PR regime. Really, MWC is a better measure of performance than EMG, and my intuition is that the linear relationship between MWC and EMG may break down for high values.

By the way, if you're interested in this sort of thing, you might be interested in Sonas's alternative to Elo.

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