Like he said, the higher the level, the bigger the fleet.
Also, the higher the threat level, the bigger perecentage of that fleet will be more dangerous ships.
Specific data from the gameplay.constants file:
pirateRaidDef
arrivalDelayTime 6.0
minSupply 1
maxSupply 220
strengthPerOwnedPlanet .10
strengthPerCargoShip .0025
strengthPerBounty .00003
firstWarningTime 900
normalWarningTime 720
minSendRaidTime 30
maxSendRaidTime 90
raidStrengthThreshold:0 0
raidStrengthThreshold:1 .25
raidStrengthThreshold:2 .45
raidStrengthThreshold:3 .7
raidStrengthThreshold:4 .9
pirateRaidComposition:0
requiredShipCount 0
randomShipCount 4
randomShip
type "FrigatePirateScout"
weight 10
randomShip
type "FrigatePirateMedium"
weight 2
randomShip
type "FrigatePirateHeavy"
weight 1
randomShip
type "FrigatePirateAntiFighter"
weight 3
pirateRaidComposition:1
requiredShipCount 0
randomShipCount 5
randomShip
type "FrigatePirateScout"
weight 4
randomShip
type "FrigatePirateMedium"
weight 10
randomShip
type "FrigatePirateHeavy"
weight 2
randomShip
type "FrigatePirateAntiFighter"
weight 3
randomShip
type "FrigatePirateSiege"
weight 2
pirateRaidComposition:2
requiredShipCount 0
randomShipCount 5
randomShip
type "FrigatePirateScout"
weight 2
randomShip
type "FrigatePirateMedium"
weight 8
randomShip
type "FrigatePirateHeavy"
weight 5
randomShip
type "FrigatePirateAntiFighter"
weight 3
randomShip
type "FrigatePirateSiege"
weight 3
pirateRaidComposition:3
requiredShipCount 0
randomShipCount 4
randomShip
type "FrigatePirateMedium"
weight 6
randomShip
type "FrigatePirateHeavy"
weight 7
randomShip
type "FrigatePirateAntiFighter"
weight 3
randomShip
type "FrigatePirateSiege"
weight 3
pirateRaidComposition:4
requiredShipCount 0
randomShipCount 4
randomShip
type "FrigatePirateMedium"
weight 6
randomShip
type "FrigatePirateHeavy"
weight 7
randomShip
type "FrigatePirateAntiFighter"
weight 3
randomShip
type "FrigatePirateSiege"
weight 3