adjust Glicko-2 to account for first move advantage

[niklasf]

http://www.glicko.net/glicko/glicko-boost.pdf suggests that this might be a straight-forward extension.

Primarily, this would improve the predictive accuracy of ratings.

cc @ddugovic, @cyanfish

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Second, this would allow removing or significantly simplifying the color balacing system, which is complex and may not be mathematically sound (#6783) because chosing black does not (and should not) allow accumulating a balance that can be cashed in for tournaments.

For example, consider the following simplification: Games with chosen colors no longer change the color balance. Colors in games with random colors (including tournament games) use and affect the balance counter, to prevent long streaks.

Currently this could be abused by picking White in rated games, slightly boosting the expected rating.

In a rating system that accounts for colors, doing so is no longer an advantage.

Edit: The same applies for completely removing the color balancing system, but this may be more controversial.

[cyanfish]

I haven't looked at data, but one concern I have is that some people may have different relative ability as black/white, e.g. someone that performs relatively well as black could now game this system by playing only as black to get the rating boost.

I wonder if the color balance system can be simplified? e.g. have a per-tournament color balance so no external factors can affect competitive play. And then the color balance can be used for lobby/pool games without needing special cases for black/ white.

[ddugovic]

I am curious how that concern would play out. Some players could specialize as White, and others as Black; and if enough players specialized (successfully gaining points), the rating system would pair them with each other or against opponents who could defeat them.

[niklasf]

someone that performs relatively well as black could now game this system

Good point, so this might be a tradeoff, not a pareto optimal improvement. I will try to get some actual data on this. (Intuitively, players performing better with black are rare, and more so at high ratings.)

This is also a flaw of the current color balancing system, which allows banking white games but not black games.

e.g. have a per-tournament color balance so no external factors can affect competitive play

That would be the most robust solution. Otherwise I guess with O(2^n) (?) collaborators you could still bank some color balance n, pretty much no matter what we do.

[niklasf]

My analysis so far: https://backscattering.de/chess/glicko2-first-move-adv.html. Summary:

• White scores 0.516 in the sample of 5 million rated standard games. This corresponds to the expected score with an 11 rating point advantage.

• 11 points advantage also minimizes Glickman's deviance metric (used to score rating systems), when modifying Glicko-2 as suggested.
  

• Looking at the maximum regression in average deviance for individual players, this quickly decreases as the number of games increases.

• Cosmetics: Comparing rating numbers of individual players between the two systems, the greatest change was -22.82. Histogram:
  

[ddugovic]

I created a PR, which I've only tested using sbt test. It does NOT address:

• Ultrabullet speeds across all variants have many unexpected outcomes (tuning tau seems a reasonable next step, but I'm overwhelmed trying to reason about it)
• Antichess is solved, and Atomic has a large first-move advantage
• Chess960 first move advantage differs by start position
• Horde first move advantage seems to be negative (assume 0.0 advantage)
• Racing Kings first move advantage is unknown (assume 0.0 advantage)