For the first version of a Relative Activity statistic (https://voat.co/v/vocatalog/comments/982170)), I've settled on something like this:
M(PCX(1/4)) / S
M = a specific constant, I've been thinking of 100 000 or so.
P = posts made within the last month. if more than 250 posts (25 posts per page * 10 pages), then it is extrapolated according to the date of the oldest of those 250 posts. for example, if the oldest post was made around 9 days ago, then the extrapolation would be 250 * (30 / 9), or around 833 posts.
C = the sum of total comments in posts made within the last month. if P was extrapolated, then C is too in a similar fashion: so if the total is 584 comments and the oldest post was made around 9 days ago, then 584 * (30 / 9) or around 1947 comments. if C would be 0, then it is assumed to be 1 instead.
X = the amount of subscribers gained within the last month. if no subscribers were gained or some were lost, then X is assumed to be 1.
S = the new amount of subscribers in the subverse.
Then the 10s logarithm of the value is taken, which gives a decimal value. This decimal value is then displayed as 'Relative Activity'. Negative activity would therefore refer to low activity. If the original value was 0, then the activity would be rated as ---.
For example, let's take /v/askvoat.
After 10 pages, the oldest post is from 10 days ago, so we extrapolate AskVoat to have around 750 posts within the last month. The latest 250 posts have received a total of 5 081 comments, which extrapolates to 15 243 comments. Comparing to the last statistic of /v/askvoat subscribers, the new amount of subscribers is 51 550 while the old amount is 51 217.
So, M = 100 000, P = 750, C = 15 243, X = 333 (51 550 - 51 217), and S = 51 550.
M(PCX(1/4)) / S is around 94 735 794.523, the tens logarithm of is around 7.97, so the activity would be represented as +7.97.
If you want to I can give examples with any other subverse. Are there any recommendations for changes or such?