basically, i'm wondering how the active runner number is determined

Want the specifics?

Min(Max((1-(((100-(Now-Max([Most Recent Run Date])))/30))^2)/(1-((100/30))^2),0),1) for each player, then totaled up for the game. (1 = 1 day)

If that makes no sense: When a player submits a new PB, that player's 'activity' is valued at 1.0. Over the course of 100 days, that number gradually drops, faster in the beginning and slower later on. After 100, the player is considered to no longer to be 'actively' running the game. Of course, there's no objective measure to this, we honestly don't know if they're still playing, but 100 days helps to compensate for that.

That all is then added and rounded up into the active player number you see. You can see the number to 4 digits by hovering over it in gamestats.

I know I'm late, but...
This is the function you've described (where R = number of days since last run). It hits 0 after only 70 days, and actually starts to rise again after 130. Even with input clamping, it doesn't do quite what you described.

This is a nice alternative. Gives you the quadratic falloff you were going for...but it's secretly just half a parabola. You can do away with the min/max wrapper if you just clamp the input to [0,100].

Is what you posted the officially used formula?

@warmCabin
you forget that it disregards any person after 100d, so even if it rises up after 130d, that doesn't matter since at that point the data is already disregarded.
what ROMaster2 posted was most likely part of the calculation, not the full code.

Yeah, that's what "input clamping" means: disregard any runs older than 100 days. I only brought it up because the max(...,0) thing becomes totally unnecessary if you clamp the input properly (actually, so does min(...,1)), so I thought maybe they weren't.

The real issue here is that this function hits 0 at 70 days, when it's meant to be 100.