When you play a multiplayer game, you have the total number of people in the game, say N.

All monsters get HP and exp multiplied by (N+1)/2. This is well known and also doesn't matter whether the players are partied, close by, whatever.

If you are playing off-realm you can also use /players X to raise the number of players to X > N. Then the HP and exp will scale up further to (X+1)/2 as you would expect.

Drops, however, are not the same. When you kill a monster in a multiplayer game, the game calculates a number to use as the nodrop exponent. This is not simply N.
It counts 1 for you, the killing player.
It counts 1 more for each player that is (a) partied with you and (b) within two screens of you.
It counts 0.5 for each other player, either unpartied or far away.
It rounds the final total down.

So, if you sneak into a full public game on the realms and don't party up but go MFing on your own, you actually only get a nodrop exponent of 4 (1 for you, 3 for the 7 unpartied players rounded down), while the other partied guys are getting an exponent of 7 (7 people in their party, and you rounded down to 0). Even though all of you are killing p8 monsters with their 4.5x HP. It is one of Blizzard's many measures to encourage party play.

You have your nodrop number (e.g. for Meph, this is 15) and your total of other drops (for Meph this is 65). This means the total ratio of nodrops in solo play is 15/(15+65) = 15/80 = ~19%.

You then apply your nodrop exponent (call it n) like this:
new nodrop rate = (base nodrop rate)^n
new nodrop number = new nodrop rate / (1 - new nodrop rate) * total drops, rounded down.

For example, Meph, nodrop exponent = 1
new nodrop rate = (15/80)^1 = 15/80
new nodrop number = 15/80 / (1 - 15/80) * 65 = 15/65 * 65 = 15 (just showing you that it works even for n=1)

Meph, nodrop exp = 2
new nodrop rate = (15/80)^2 = 0.03515625
new nodrop number = 0.03515625 / (1 - 0.03515625) * 65 = 0.036437 * 65 = 2 after rounding.
So with exponent = 2, Meph is already only missing drops 2/67 of the time.

Meph, nodrop exp = 3
new nodrop rate = (15/80)^3 = 0.00659
new nodrop number = 0.00659 / (1 - 0.00659) * 65 = 0.00664 * 65 = 0 after rounding.
So with exponent = 3, Meph is always dropping in full.

It is unfortunately extremely hard to test this empirically. Enough weird stuff happens that also seem to hide drops, plus Meph gets 7 drop chances and only 6 items can drop, that it is too hard to tell 2/67 apart from 0. So it could actually be that all this time we've been running Meph at players3 in SP to get full drops when really we are just getting exp=2 drops — you'd need to run him at players5 to get guaranteed full drops.

Extra players added using the /players command only count as unpartied players.

This makes no difference to what we already knew for monster HP and XP.

It does change what we thought was happening with drops. Unpartied players count as halves rounded down.

So, when using the Atma drop calculator, you need to translate your /players setting into the number you put into the Players field:

1 or 2 -> 1
3 or 4 -> 2
5 or 6 -> 3
7 or 8 -> 4

This affects all monsters, not just Mephisto, although for unique monsters like Pindle and random bosses that have fixed drops, it won't actually change any numbers.

It should also be noted that the things you "know" are still mostly true. You can keep running Meph on p3. In retrospect I always wondered why people ran him on p3 instead of p2, when the difference in drops is so tiny. Well, it turns out that running at p3 is actually what I thought was p2, and p2 is no different than p1, so now it makes sense. You may still see a 5 drop every now and then at p3, but not often enough that it is worth going higher.

Ultimately, if you are MFing, there is rarely a reason to use an even number setting. The only difference between an even number and the number one lower is slightly more exp, but only one-for-one with the increased HP. So your drops per HP are lower and exp per HP is the same.
For fast levelling, when all you care about is the most exp per monster you can get, p8 is still worthwhile.