Rating deterioration

[jeebus]

Every day the phi value increases, making your rating lower.

"φ is your deviation, which starts at 2 and will go down whenever results come in and go up when they don't."

Actually that doesn't seem to be accurate, as it actually goes up no matter what, right? In fact, it doesn't matter if you play, how many games you play, or what the results are - phi goes up the same amount, am I right?

I noticed when I was on vacation (not playing) that the level drop every day is pretty huge. I just wonder about the justification for this. Today I had 2 victories and 1 loss, and according to Dominion Scavenger, my mu is going up from 1.4758 to 1.4838. But since my phi is going up more, my rating will go down. The penalty for not playing a big number of games every day seems a bit steep.

I mean, I'm planning to limit my Dominion gaming to 3 times a day for a while now. Let's say I do this forever. Even if I were to win as much as the best player and get the highest mu, my phi will keep increasing every day. So of course assuming that my mu will level off (at the highest value of all players), I will actually steadily drop in rating. Or does the phi ever stop increasing?

[markus]

Phi goes up every day, but the increase depends on your current level. Similarly, the reduction of phi, when you play depends on its current level as well. In other words, depending on how many games you play per day, it will converge to a different value, and not go to infinity.

What that level is, depends also on the quality of your opponent (the better the match is, the more phi falls because a result against an equal opponent is more informative than an expected win/loss.)

I once calculated roughly
games/day   phi
1           0.39
3           0.30
6           0.25
10          0.22
So playing 1 game instead of 10 per day will cost you 2.5 levels but not more.

Having said that, my hunch is that sigma is a bit too large, i.e. the resulting phi (increase) is too large. I'd prefer to reduce that but add some slight mean reversion on mu (currently that remains constant if you don't play).

[jeebus]

Thanks for your reply.

Phi goes up every day, but the increase depends on your current level. Similarly, the reduction of phi, when you play depends on its current level as well.

So phi is increased depending on your current level? The higher your level, the faster it increases, I assume. I've noticed this before too, also on other platforms. But I don't really understand why it's implemented like that.

And phi is decreased depending on current phi value? Or did you mean something else?

What that level is, depends also on the quality of your opponent (the better the match is, the more phi falls because a result against an equal opponent is more informative than an expected win/loss.)

Interesting. You would then think that with an unequal opponent (poor match), if the result is the opposite of the expected, phi would fall more, because that is even more informative...?

I once calculated roughly
games/day   phi
1           0.39
3           0.30
6           0.25
10          0.22
So playing 1 game instead of 10 per day will cost you 2.5 levels but not more.

So these values are what phi will converge to eventually?

[markus]

So phi is increased depending on your current level?

Sorry, I was not clear: with "level" I meant the level of phi not the "level" that is calculated from (mu,phi) for the leaderboard. And it increases by more if it's currently low (not playing is more unusual when previously playing 10 games/day than when playing 1 game before.)

For example not playing increases phi from
0.2 --> 0.2088
0.5 --> 0.5036

And phi is decreased depending on current phi value? Or did you mean something else?

Exactly. If if's high, one game will decrease it more than when it's low. You can also see that from above numbers: going from 1 to 3 games/day does more than going from 3 to 10 games/day.

Interesting. You would then think that with an unequal opponent (poor match), if the result is the opposite of the expected, phi would fall more, because that is even more informative...?

The result doesn't directly matter for the updating of phi. This is a second order effect that would be captured by sigma (i.e. an usual result will increase sigma and that will actually increase phi over time. The intuition is the following: daily increase of phi captures that we're more uncertain about somebody's current skill if there's no recent evidence of their playing. If, however, unlikely results come in, we should become more uncertain about the current skill. But for practical purposes the algorithm can't capture that well and sigma is almost the same for everyone.)

I once calculated roughly
games/day   phi
1           0.39
3           0.30
6           0.25
10          0.22
So playing 1 game instead of 10 per day will cost you 2.5 levels but not more.

So these values are what phi will converge to eventually?

Yes, with the caution that it depends on your match quality. I think I calculated those numbers assuming that the win probability is 80%-20% back when that was more common. I'm setting narrower bounds for my opponents now.
Therefore, with on average 7.4 games/day over the last month (:o), my phi is only 0.20. So treat the numbers as rather upper bounds.

[jeebus]

Thanks!