Hoping maybe a mathematical thinker or two can devise something that works here.
I have a list of provider groups, each being given a certain compliance percentage on a metric. So the data is basically a list with three columns: ID, numerator (N), denominator (D). I can calculate the compliance rate for any provider with N/D. I can calculate the compliance rate of the whole set by SUM(N)/SUM(D). Let's say for October this compliance rate is 72%.
I also have a completion factorthis is a way to estimate the final overall numerator based on a prediction what % of all the numerators for the year have accumulated. Let's say for October it's 80%. That means that we expect that our current numerators are only 80% of the final total, so we expect to end the year with 90% compliance on the whole set. (0.72/0.80)
So far so good. However, we are in need of a prediction that applies to individual groups. This seems fine for groups with a low performance, say 50%  their end of year forecast would be 0.50/0.80 = 62.5%.
The trouble comes in when an individual group is already performing better than the compliance factor. So say I've got a really good group that's at 85%. If I apply the factor that means I expect them at .85/.80 = 106.25%, which is ridiculous, as the numerator cannot exceed the denominator. There just aren't enough gaps (denominator minus numerator) to get that much of a boost. Even capping them at 100% doesn't make sense, as there's no reason to think they'll get full compliance just because their current results are that high.
Clearly the problem is that even if the overall set can be expected to get a certain percentage more by end of year, individual groups will not all get the same percentage, and some of them literally can't. I'm looking for a formula that gives larger boosts to lower percentages, and smaller boosts to higher percentages, so that no prediction exceeds 100%, but even high performers can expect to gain a little bit, and that still works out to 90% overall. So far the only one I found flattens the data too much, so that practically every group winds up at 90% or close to it. I'm thinking my problem is that I'm using a linear formula, and maybe something quadratic will be more balanced. But it's been a LOOOOOOOONG time for me for that sort of thing, and I'm coming up blank. Anyone got any ideas?
I need a formula!

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I need a formula!
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Re: I need a formula!
e=mc^{2}
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