How are the "on pace for" metrics on Area 51 generated and are they being done so correctly?

Question

Taking Biology as an example, Area 51 describes:

Every site needs a solid group of core users to assist in moderating the site. We recommend:

• 150 users with 200+ rep (on pace for 83 users at 90 days)
• 10 users with 2,000+ rep (on pace for 2 users at 90 days)
• 5 users with 3,000+ rep (on pace for 0 users at 90 days)

At the current time, there are

• 70 users with 200 rep or more
• 2 users with 2000 rep or more

_{See Biology User List (36 per page)}

So assuming that the projected extra thirteen 200 rep users are the next thirteen closest, the Area 51 projections say that the thirteenth user is expected get 44 reputation points, that is, 22% more than they have currently in the next 17 days.

Yet this doesn't seem to be the same logic as applied to the next category. Four users are within 170 reputation points (8.5% more) and some are only 22 reputation points (1.1%) away from crossing the threshold. Surely they are more likely to do this in the next seventeen days than the 200 reputation points users (I am sure their reputation per day is higher too) so why don't these users show up in the on pace stats?

Could the projections be broken for the middle category?

Similarly for the third category, a user is 66 reputation points (2.2%) away from the 3000 mark yet doesn't show up in that bracket. Surely they should be doing at this point?

I also think it's unlikely to be a caching problem as some of the 2k users haven't gained reputation points over the last couple of days but are still within striking distance.

Answer 1

I doubt very much that the algorithm checks the actual rep of any of the not-yet crowd at all. I think it goes like this:

• 70 users with 200+ rep in 74 days = 0.946 / day, so at 90 days there will be 85.1
• 2 users with 2000+ rep in 74 days = 0.027 / day so at 90 days there will be 2.43

This explains the numbers you see, once rounding is taken into account. In reality users gain rep faster as the site grows, since there are new users joining who can vote up their old answers and questions, but it's a simple enough metric to calculate. Heck, in reality it doesn't matter how many high-rep users you'll have at 90 days, it matters more how much longer till you have enough of them. But simple numbers have their uses.

Answer 2

Hmmm. This doesn't seem to be the way it is working at Genealogy & Family History.

As I write this, it is at 39 days in Beta, with 1 user with 3000+ rep, 4 users with 2000+ rep, and 42 users with 200+ rep.

Using the users/day calculation gives: 3000+ = 0.026, 2000+ = 0.103, 200+ = 1.077.

Using those users/day values and multiplying by 90, I get: 3000+ = 2, 2000+ = 9, 200+ = 97.

So Area 51 should be projecting 2, 9 and 97. However it is projecting 2, 6 and 66.

So if this is the way the calculations are being done, then they are being done wrong.

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My statistical background tells me that the proper way the calculations should be done is by using "not-yet crowd" method (Thank you @KateGregory for coining the term):

39 days out of 90 is this much through the beta: 0.433

People on pace for 3000+ are those who have 43.3% of that already = 1290 and there are 8.

People on pace for 2000+ should have 0.433 of that already = 860 and there are 10.

People on pace for 200+ should have 144 rep if they started at 101 (about 54 people) and 87 rep if they started at 1 rep (about 6 people). Note: This simply assumes that anyone with more than 101 started at 101, and using that assumption gives a conservative value.

So a better estimate of on pace would be: 8, 10 and 60.

None-the-less, whatever calculation is currently being used is not a good projection and should be modified to something better.

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Looking at the Robotics beta site. Day 33 of beta. 26 users with 200+ rep, yet the calculation says: "on pace for 42 users at 90 days".

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So can anyone at least tell us what the algorithm is???