A lot of people ask me how much their CRE will decrease by if they don't play for a day. The answer is that your deviation changes (approximately) according to this formula:
new deviation ≈ sqrt((old deviation)^2 + 30178 * (volatility)^2)
Strictly speaking, your deviation increases by this much each day whether you play or not, but if you do play, the decrease from the games you play offsets it. However, after you play your first battle in a day, your CRE may sometimes decrease, and that's because you have not offset the daily deviation increase yet, which is applied in the rating window after your first battle in a rating period. After you play more in the same rating period, you will always experience a net increase in CRE.
Here is a fully worked out example. Suppose a user has these stats:
CRE: 1449
Rating: 1521-1569
Volatility: 0.051068226...
What will his CRE be if he doesn't play for a day? First work out his deviation and mean rating:
mean rating = (1521+1569)/2 = 1545
rating deviation = (1569-1521)/2 = 24
Now apply the formula above:
new deviation = sqrt(24^2 + 30178 * 0.051068226^2)
=> new deviation ≈ 25.587167266882
The mean rating is unaffected, so we use the formula for the CRE to find his new CRE.
new CRE = 1545 - 4 * 25.587167266882 ≈ 1443
So by not playing for a day, this user's CRE will decrease from 1449 to 1443. This should give you a tangible idea of what to expect with the daily deviation increases.
Last edited by Cathy; Jun 9th, 2009 at 11:10:53 AM.
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