How often are you collecting?
I can do one for every hour, and another for every hour for 8 hours, 1 8 hour collection and 2 4 hour collections. (this its the part i need what numbers you want run)

In my mind the more AP the better no matter what. If you sit and try to hold a some rate you will loss out on a bunch of arti points in the long run even if you do a massive jump all at once I do not feel it is worth it. I think in the long run you would get more RP's with more AP then without. maybe not hour by hour but if you collect every two or three hours instead of every hour I think it will work out better that way. That is just my thoughts on this. You can agree or disagree and do what ever you want. It is your ship. lol

You also would also have to factor in the leftovers you had the hour before which can range from 0-3999 depending on the last artifact pulled the previous hour, so your value per aph would change when you're in this region. Off the top of my head I could see a minor benefit to keeping it at a certain break point, but it seems almost negligible when you have to factor in planet buffs, blockades, raids, etc which can movie this point around and the effort to hit this point would likely be more than it was worth in time spent on calculations as well as costs from rearranging structures every time you take a new planet.

I was thinking of the simple ideal case, collecting every hour. Your second scenario is more realistic, though for me it's more like collecting hourly for 12 hours, and then one 6 hour collection, and two 3 hour collections.

using collect all or individual pull and stopping at 4k?

20k intervals -after- exactly 20k/hr do not correlate with a higher chance for MSP anymore than 19k or 21k. While you can get more MSPs if you were to obtain multiple, you're not going to pull multiple (less than 1% chance to pull 2 MSPs in a row). The same goes for anything else, higher AP/hr does not alter the chance for pulling any artifact.

No, u can make it have less than 250 points by manually.collecting after the all button.

I'm inclined to agree with the OP. Pulling at 19999 will grant more 19999-4000 pulls than 20001, which would increase the number of MSP...

After 20k, however, the effect will dwindle and it'll go back to more AP=better.

20k intervals -after- exactly 20k/hr do not correlate with a higher chance for MSP anymore than 19k or 21k. While you can get more MSPs if you were to obtain multiple, you're not going to pull multiple (less than 1% chance to pull 2 MSPs in a row). The same goes for anything else, higher AP/hr does not alter the chance for pulling any artifact.