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. But there's a related question I'm curious about too: how does a given TrueSkill difference translate into win probability?
I can attempt to answer this by running TrueSkill on my copy of the CouncilRoom database, which might not be exactly the same as when DougZ runs it but should be close. And I'm not running through all the games, just letting it converge until I get bored.
Now, you can compare skill values, or you can compare levels (minimum proven skill values). There's a lot of uncertainty when you compare levels, because people who haven't "proven themselves" have levels far lower than their actual skill. I ran it, though, and to summarize the results:
If you're up by 5 levels, you have about a 60% chance of winning. At 10 levels up, you have about a 2/3 chance. And it hovers around a 2/3 chance as the difference gets higher, up until it gets lost in the noise.
From TrueSkill's point of view, it's more meaningful to compare the players' mean skills, not their levels. And these probabilities are interesting enough that I'll make a table of them.
diff win prob.
0 50.0%
1 54.2%
2 57.6%
3 60.0%
4 63.5%
5 68.6%
6 71.5%
7 75.5%
8 78.7%
9 82.2%
10 82.6%
11 87.7%
12 90.8%
13 93.9%
14 97.6%
15 97.3%
16 98.6%
>=17 100%-ish
