Gameplay.constants may yield some clues:
pirateRaidData
starArrivalDelayTime 10.0
initialSpawnTime 1200
minSpawnTime 300
maxSpawnTimeAtMinTotalSupply 600
maxSpawnTimeAtMaxTotalSupply 360
minTotalSupplyPerPlanet 0
maxTotalSupplyPerPlanet 20
raidChanceIncPerPlanet 1.0
raidChanceIncPerCargoShip .25
raidChanceIncPerBounty 0.002
supplyPerPlanet 8
supplyPerCargoShip 0.75
supplyPerBounty .004
maxSupply 200
raidStrengthThreshold:EarlyGame 75
raidStrengthThreshold:MidGame 150
raidStrengthThreshold:LateGame 250
pirateRaidComposition:EarlyGame
requiredShipCount 0
randomShipCount 5
randomShip
type "FrigatePirateScout"
weight 10
randomShip
type "FrigatePirateMedium"
weight 2
randomShip
type "FrigatePirateHeavy"
weight 1
randomShip
type "FrigatePirateAntiFighter"
weight 3
randomShip
type "FrigatePirateSiege"
weight 3
pirateRaidComposition:MidGame
requiredShipCount 0
randomShipCount 5
randomShip
type "FrigatePirateScout"
weight 4
randomShip
type "FrigatePirateMedium"
weight 10
randomShip
type "FrigatePirateHeavy"
weight 3
randomShip
type "FrigatePirateAntiFighter"
weight 3
randomShip
type "FrigatePirateSiege"
weight 3
pirateRaidComposition:LateGame
requiredShipCount 0
randomShipCount 5
randomShip
type "FrigatePirateScout"
weight 2
randomShip
type "FrigatePirateMedium"
weight 6
randomShip
type "FrigatePirateHeavy"
weight 8
randomShip
type "FrigatePirateAntiFighter"
weight 3
randomShip
type "FrigatePirateSiege"
weight 3
Judging from this, it looks like pirates don't start raiding until 1200. This could be 1200 ticks, which would be faster than you can blink - and thus I find unlikely. It's more likely to be 1,200 seconds - 20 minutes into the game. These first lines in particular seem to be the most relavent, with the rest being details of the composition of the pirate fleet at early, mid and late games.
pirateRaidData
starArrivalDelayTime 10.0
initialSpawnTime 1200
minSpawnTime 300
maxSpawnTimeAtMinTotalSupply 600
maxSpawnTimeAtMaxTotalSupply 360
minTotalSupplyPerPlanet 0
maxTotalSupplyPerPlanet 20
raidChanceIncPerPlanet 1.0
raidChanceIncPerCargoShip .25
raidChanceIncPerBounty 0.002
supplyPerPlanet 8
supplyPerCargoShip 0.75
supplyPerBounty .004
maxSupply 200
raidStrengthThreshold:EarlyGame 75
raidStrengthThreshold:MidGame 150
raidStrengthThreshold:LateGame 250
Presumably, the MinSpawnTime is 300 - a minimum of five minutes between raids. Not sure what Min and Max Total Supply means, but I think it means the resources of the planet in question are taken into consideratino, and means that the latest the pirates will raid is from six minutes for a heavily-stocked planet, to 10 minutes for an exhausted one.
The raidchance per cargo ship is pretty self-explainatory - every four cargo ships are worth a +1% to the chance the pirates will choose to raid - I'm not sure if that is to choose to raid a given planet, or to raid an empire. The raidChanceIncPerBounty is pretty clear - every credit adds 0.002 to the chance of a raid. Every time you press the button to add bounty, you're adding a half a percent, so if you hit it 200 times - IE, jack the bounty to 50,000 or more - you've basically garunteed a pirate raid.
Although I don't understand supply per planet and per cargo ship - I suspect they add to the supply total the pirates bring to the fight, though whether it means the pirates' cargo ships/planets, or yours, is unclear, the supplyPerBounty pretty clearly adds .004 to the supply the pirates bring to the fight - IE, the more ships they can sustain in their fleet. Every 250 credits is worth a point, so 25,000 credits maxes the pirate fleets out at 200 supply.
Which makes no sense, since we've seen pirate fleets much larger than 200 points. I've had to wax so many pirate fleets that I've taken stationing fleets of four carriers around my sun, ready to bomb incoming pirate fleets to snot.
So perhaps RaidStrengthThreshold has something to do with it - maybe it's in addition to the pirate strength from other factors, leading to a maximum lategame pirate strength of 450 - more in line with the fleets I've had to bomb to dust.