I automatch against any reg. But I generally only accept challenges from 25+. Of course, I'm not 40+, though I was a couple of days last week. The only way I do anything to "game" the system at all really though is to almost always make sure I "win-quit".
I actually haven't looked at the math that close - is there a way to see what % you need to score to maintain a certain level difference? Obviously +/-0 is 50%, but is +1 like 51%, 60%, 90%, where? and +2, +3, so on. Is this out there somewhere?
Well, it's not just about how many games you win, it's who you beat. Just like in chess or other games with a global ranking system.
This is exactly what I was asking about. And I meant to say level difference in the mean, not the levels as posted on the leaderboard. But you did what I was looking for anyway, but these numbers don't make sense with each other quite - easiest way to see that is by looking at difference ranges 13-16, but if you just look at the differences between consecutive numbers, you get a sequence that doesn't make a lot of sense:
1-0 4.2
2-1 3.4
3-2 2.4
4-3 3.5
5-4 5.1
6-5 2.9
7-6 4.0
8-7 3.2
9-8 3.5
10-9 0.4
11-10 5.1
12-11 3.1
13-12 3.1
14-13 3.7
15-14 -0.3
16-15 1.3
17-16 1.4ish
Don't know what exactly you mean that doesn't make sense, but if is the oszilating and even negative values in the table, I think that's mostly noise. You don't have so many games in the ~15-Differences, and often the has not "converged" in the sense that either the skill of the player really changes, or trueskill has not adjusted the skill yet correctly. So if a new player 25+-23 (Level 2) plays against and old player 9+-7 (Level 2), that seems like a fair game in the Lobby, but it that's as well a 16 diff as if a 51+-7 (Level 44) plays against a 35+-7 (Level 28). While in the second example the prob. is quite high that the "Skill-difference" is really ~15, in the firstone it might be significantly higher or lower. Don't know which one is more likely or which games happen more often on isotropic.
The Trueskill system is not designed to give you a "win probability" given the "mean", but to give you the win probability given "mean" AND "variance". As we integrate out the variance here the noise can be expected to be much higher, and bias can be introduced by effects like new players entering with 25,25 in the system espescially in the combination with the mechanism by which players choose against whome they play (which will mostly be influenced by the level, not by mean and variance directly). So if you look at the table and fit a line, I think you can say that with each additional difference in the level, your winchance de/increases by 3-4%, at least until somewhere in the 10-15th.
PS@offtopic: Thanks theory, reloading does help.
edit:
What did you do here? The player variance matters a lot in terms of pushing probabilities toward 50% regardless of mean difference. I don't see how you can reasonably ignore variance and still get output from trueskill.
I think if the database is high enough, the variance should just integrate out and you get the avarage win probability given the difference of the mean (integrated over the "variance distribution of isotropic"). That is some kind of output, question is how much this matters for one individual player.
I think you are right, the more interesting table would 3/4-dimensional and show win-probability given (mean difference, variance pl1, variance pl2). Or for the beginning just restrict to variance of both player ~$(typical value for $type player on isotropic).
