Dominion Strategy Forum
Dominion => Dominion Online at Shuffle iT => Dominion General Discussion => Dominion Isotropic => Topic started by: Quadell on April 19, 2012, 08:27:10 am
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1. If I win a game 41-40, or if I win a game 62-10, do these both affect my "skill range" on the leaderboard the same? (In other words, are all wins equal for the purpose of TrueSkill evaluation?)
2. If I come in second in a 3-player game, or if I come in third, to these both affect my "skill range" the same?
Thanks!
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1. If I win a game 41-40, or if I win a game 62-10, do these both affect my "skill range" on the leaderboard the same? (In other words, are all wins equal for the purpose of TrueSkill evaluation?)
Yes
2. If I come in second in a 3-player game, or if I come in third, to these both affect my "skill range" the same?
Every n player game is splitted into 1/2*n*(n-1) 2-player games for isotropics TS, so it's the same as if you played each one 2player game against the winner and the loser, and lose/win this game.
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The thing about 3p games is not quite right. That's how my crappy prototype version worked, but DougZ implemented the more probabilistically correct version that takes the entire ordering into account.
TrueSkill assumes that there is an un-observable "actual rating" that comes from playing a game, and that players finish in order of their actual rating. The actual rating is in a fuzzy range around your mean skill rating (the 99% margin of error for that range is shown on the leaderboard), but nobody can actually tell where it is in the range because you might be lucky or unlucky, or having an on or off day.
But if A beats B, that says that A's actual rating (whatever it is) was higher than B's (whatever it is) for that game. TrueSkill takes that into account and updates their skill ranges to make that more probable.
In a three-player game where A > B > C, it actually gets a lot of information about the actual rating of B, because it's in a narrow window between A and C. I'm not entirely clear what the practical difference is between this and doing the pairwise comparisons, except that your variance decreases more when you rank in the middle.
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If I tie someone ranked better/worse than me, does my ranking go up/down?
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TrueSkill assumes that there is an un-observable "actual rating" that comes from playing a game, and that players finish in order of their actual rating. The actual rating is in a fuzzy range around your mean skill rating (the 99% margin of error for that range is shown on the leaderboard), but nobody can actually tell where it is in the range because you might be lucky or unlucky, or having an on or off day.
I think this might be a little misleading. The 99% uncertainty range on the leaderboard is uncertainty about the true skills of the players. But within a game, the standard deviation of performance is assumed to be the same for every player, since it comes from the parameter beta=25 (http://dominion.isotropic.org/faq/#leaderboard).
The implication is that the rating system doesn't distinguish between consistent players (about the same performance every game) and inconsistent players (wildly different performance every game).