It's mostly to do with how powerful your units (champions and regular army) are.

Something bear in mind though is that (as I've said several times) your power rating has nothing to do with your actual ability to wage war.  Your mana stockpile isn't taken into account for one thing.  If your enemy has conveniently placed all of his military units in one place you can wipe them all out without firing a shot.

It also doesn't take into account just how quickly you are able to replace lost units.  When you get Arcane Forge enchantment going on a high-essence fortress you may practically be doubling its production capability.  Suddenly you go from struggling to crank the units out to woosh, there's your army.

I've asked repeatedly about this, without any response from the development team.  I guess they don't want us to know, which seems silly as it wouldn't make the game any easier to understand exactly what makes a faction rating higher, or lower.

All we know is: world achievements may help out.  Having more military, and earlier, definitely seems to help out.  More cities, and more heroes, helps.  Research and popuiation appear to help.  Probably none of this is simply a simple direct value, but who knows?

Early armies are not necessarily that much of an economic drain.  Only if you're trying to keep up with the Joneses will you run into financial trouble.

They have the benefit of providing experience for your champions and clearing out nearby lairs so that you can exploit resources.

When you don't need them any more you can disband them in cities that are still under their food cap for a small (but instant) population gain.

To be honest though I tend to move on to mid-game units quite quickly.  These are units designed with upgrading in mind, have their trait slots used up, have encumbrance calculated out in advance.  And they usually have mounts too.  You only need two such armies to lay waste to your enemy, or one and a half if you're really stingy.  The extra army provides relief for any units in the first army that have been injured, allowing them more time to heal back to full hitpoints.

Thanks to everyone who has replied so far, but no one seems to have the answer.  I was hoping that a modder who could read the code would know all the factors that go to make up Faction Power (FP) and their exact weighting, but perhaps that part of the code is not available or something like that, I don't know

If that is the case then we could get a good idea of what various things affect it by doing some tests on a known savegame position.  For instance I had a total of 1962 pop in my 9 cities and using the Death 5 spell Sacrifice I killed 1044 of them (gaining that much mana in the process).  You have to press end of turn for the FP to update. Next turn my FP dropped from 284 (without Sacrifice) to 242 a loss of 42 FP.  So population certainly does have some effect on FP and it seems to be about 4% of the pop.

Next I disbanded 3 units of level 8 Krax spearmen and the FP next turn dropped 5 FP so these units were contributing nearly 2 FP each.  By this process of elimination I should be able to get a fair idea of what the effects of things like unit level, total attack, total HP, defence, maintenance have on FP (if at all). I don't have a very good variety of units in my game at present so I stopped there. But this would be a tedious and error prone process anyway and that's why a code reader would do a much better job

JJ

I think city militia and archers count towards your FP.  It would make sense.

That 2000 jump is regarding gold supply. I accidentally found out when the tribute system bugged and gave me a million gildar one turn. I spiked to something like 200000 next turn, before going down to normal the next one. It kept spiking like that whenever I got more gold. I'm not sure exactly how it's calculated, but money fluctuations seems to be the key.