So, I've just been looking at my garrisoned forces and their police strength, after reading Meowth's comment:
The idea is that a tank is better than a grunt for suppression, but not linearly so (hence the sqrt). Between an equivalent tonnage of tanks and smaller units, the smaller units are more effective because they can be in more than once place. This gives an extra purpose to light personal weapon infantry too (cheap, small units for occupation).
I have a 2500 ton Infantry brigade on one world made up mostly of infantry with light armour and improved personal weapons at size 6 per unit, plus some specialist infantry.
On the second neigbouring world I have some garrison batallions totalling 2500 tons. They are mostly made up of my "military police", infantry just carrying light personal weapons at size 3 per unit.
The first world has 236 total ground units providing 8 police strength, the second has 566 total ground units providing 14 police strength. So more, cheaper units provide almost double the police strength for the same tonnage.
I thought this might be useful to know, if you didn't already. It could make it a lot quicker and cheaper for you to field a pacifying force for that alien homeworld, rather than sending all your high tech ground units there which will be a lot less efficient at adding police strength. Of course my "military police" are really just cannon fodder if anyone decides to invade a world with them as the garrison.
Yes cheaper units would be better for policing but that was not the only problem. I found this world approximately 25-30 years in. Having gone through a couple of mineral and wealth crises I had only just begun to expand my navy having found a precursor system with a fleet that was at least double or triple my existing fleet. I then ran across the aliens only two jumps out and after a couple of months squabbling over possession of that system they blew away my diplomatic ship.
I had only 10 troop transports and 8 armoured brigades each of 1 x HQ unit plus 4 x Armoured battalions plus about 4 infantry brigades and 8 garrison battalions, about half the armoured battalions were the then new heavy units. once the initial slaughter of the landing was over it was the heavy units which vanquished the aliens as they found it very difficult to penetrate their armour. I did pillage my mining companies and gained another 13 garrison battalions.
If I had double that total amount of "police units" they would have evaporated. I was facing at least 45,000 to 50,000 enemy units, most were infantry although there were quite a lot of STO units which I took out by orbital bombardment (rods from God). I defeated the aliens with a force which at the finish had an occupation strength of less than 700. To force a surrender I required an occupation strength of 85,244 but once that was achieved as it reduced to 10,250 and SMing a lot of basic infantry the police strength required was only 44, the population down to 73 million.
I found it difficult to work out what an alien battalion consisted of as in pacifying their home system all their mining bases have 4-5,000 infantry, 20 each of AA & AT teams 10 AA vehicles and 16-20 STO units plus HQ units. I don't know about you but building STO units takes me forever. I have just found a new alien planet with a ground force of 41,500, they took out my survey ship with STOs. The nukes are on their way!
As an aside I would have been better off nuking the planet as the ground combat went on so long the planet had been wiped clean anyway, might have been a few installations left.