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The ELO rating system and later improvements like Glicko are specifically designed, as far as I know, for mirror games. That is, we assume that no player has a systematic advantage over another. In chess, this is typically the case because a player will be black/white a roughly equal number of times.

But you can imagine that if in some variant of chess, the player who was white/black was not randomly determined that some players could gain a systematic advantage and this would be reflected in their ELO rating.

What about games like for example Starcraft, a computer game with 3 races (Terran, Zerg, Protoss)? The races are unlikely to be perfectly balanced. One is probably better than the others.

Would it be possible to calculate an ELO rating that took into account racial advantages and thus more closely measured the 'true skill' of a player? How would you do so and what is the best way? (References to existing, well-documented CS/Stat/Math/etc techniques are preferred in the response, but if you have your own unique way of tackling this problem, I'd like to know too.)

Note that you cannot assume that the player pools have the same 'true skill' distribution in real life. For example, in Starcraft 2, there are probably more pro-level players in the Terran pool than the rest, because many of the professionals grew up watching Starcraft 1, in which the most admired players were mostly Terran.

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    $\begingroup$ I think there are ratings systems that do work with non-mirror game. Maybe you should look at Go, since a stronger player often plays with a handicap and IIRC there are some ways to take these into account. Starcraft may be in some ways a bad example, since either you can pick your race (you could argue that picking a suboptimal worse is a bad strategy) or you play randoms only and then you it will even out. $\endgroup$ – Erik May 4 '12 at 9:40
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    $\begingroup$ I don't know the answer, but I was browsing in a bookstore the other day and saw a whole book on ratings. Despite the glossy cover, it's a serious book (both authors are math professors) $\endgroup$ – Peter Flom May 4 '12 at 11:45
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In our ranking system rankade you can build hybrid groups with both regular and ghost users. In your Starcraft example you should have as many actual players as in your playing group and three ghost (Terran, Zerg, Protoss). Then, you should record every match as a 2-on-2 match, building each faction with an actual player and his playing race, so doing something like 'Mike/Terran vs John/Protoss'.

There's obviously an issue that our algorithm can't manage (races have no capability to 'learn' over games, but their ree will change according to their performance), but it seems a good way to estimate what you called "'true skill' of a player" (warning: 'Trueskill' is a MS trade mark! :) ), cleaning it from races unbalancement effects.

If you're interested, check this link, where a rankade user worked this way (with a different goal - he was interested in races true ranking, cleaned from players unbalancement - and before 'ghost' feature was released) on '7 wonders' boardgame.

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