Iso uses TrueSkill. (I think Goko uses something similar??? I am not sure, though.) There is tons of info on it via Microsoft (see
here and
here). I think of TrueSkill as Elo-like, but maybe that is not technically right.
I can also say that I have started to preserve my rating on Goko. It is not just a win against a 0 opponent that is a problem.... So, what I am getting at is because of the random factor, you can play a lower skilled opponent and losing against that player really hurts even if you played really well.
BA is correct.
Based on the Q&A a while back, the level is the mean minus two standard deviations (so it has an uncertainty factor), so you can win a game and have your rating go down. It seeds new players at mean 5500 (Iso seeded at 25) with starting level 1000 (Iso started at 0).
Via the
TrueSkill FAQ:
Q: Well there must be a bug in the system because I jumped into a 4 person race with 3 lower ranked individuals, won the race and my position in the league I was in dropped about 50 spots.
A: Surprisingly, this is not a bug and it happens when players with very small σ but widely varying μ get matched together (thanks to rugdivot for figuring this out). For example, try this link.
So, what is going on here? Between any two games of a gamer, the TrueSkill ranking system assumes that the true skill of a gamer, that is, μ, can have changed slightly either up or down; this property is what allows the ranking system to adapt to a change in the skill of a gamer. Technically, this is achieved by a small increase in the σ of each participating gamer before the game outcome is incorporated. Usually, a game outcome provides enough pieces of information to reduce this increased uncertainty. But, in a badly matched game (as the one described above) this is not the case; in this case, nothing can be learned about the winner from the game outcome (because it was already known before the game that the winner was significantly higher ranked than the other gamers he has beaten). So, conservatively speaking, the winner's skill might have slightly decreased! Note that this can only happen if the gamer is not matched correctly so that he can "prove" to the TrueSkill ranking system that his skill has not changed.
@DStu, I am not sure 0 is special based on the Q&A.
Regarding Elo, I think Watno is correct that a strict application of what the
Wikipedia article has would not result in rating declines after one game if you care about win/loss only. If you cared about points in a tournament (e.g. Chess), then you can have a decline in rating even if you have a winning record (in a Chess tournament). The article provides this example:
An example may help clarify. Suppose Player A has a rating of 1613, and plays in a five-round tournament. He loses to a player rated 1609, draws with a player rated 1477, defeats a player rated 1388, defeats a player rated 1586, and loses to a player rated 1720. His actual score is (0 + 0.5 + 1 + 1 + 0) = 2.5. His expected score, calculated according to the formula above, was (0.506 + 0.686 + 0.785 + 0.539 + 0.351) = 2.867. Therefore his new rating is (1613 + 32×(2.5 − 2.867)) = 1601, assuming that a K-factor of 32 is used.
Note that while two wins, two losses, and one draw may seem like a par score, it is worse than expected for Player A because his opponents were lower rated on average.
Online Scrabble systems sometimes care about the absolute difference in score, not just win/loss, so you can lose points, there, too if you don't do well enough. For instance,
in this implementation, you can lose points if one player is provisional.
I have no problem personally with systems that may result in rating declines for both not playing enough and not playing strong enough players, even after one game, as long as the rating does a decent job of resulting in ranking people well over time.
This is a bit piecemeal, but I hope it answers what people were asking me.