The size of the pirate fleet you can buy depends on the severity of the pirate threat.  The higher the threat, the larger the fleet you can purchase.

And you can increase it by clicking on the offered amount.

Arthain has it correct, but there is a bug that prevents you from purchasing a lower raid amount. This will be addressed in 1.04.

They said end of this month. They modifying engine a bit,

Suposedly 

• extending time for strip to the core
• changing something regarding VR phase jumping SB 
• corvettes will get their own damage type (probably armour as well)
• general balance 

There are some other things but I cannot remember at the moment

Severity of pirate raid is strength (amount) of ships pirates will attack with.

When you look at the Pirate window under the character icon, the image/face used to show the pirates, there is a Severity Rating bar.  It may be called Threat Level or something else.  Anyways it has approximately 5-6 sections to the bar.  It goes something like Guarded -> Low -> Medium -> High -> Severe -> Extreme.

Don't quote me on the exact wording of the levels but that's how it works out. 

Edit: And yes, the pirate threat rating increases with each pirate raid.  So basically it's something that increases as the game goes on.  It's to prevent people from stock piling gold early on and then hitting a player/computer with an extreme pirate raid before anyone is even able to defend against it.  Even a fully upgraded starbase would have problems against the biggest pirate attack.

Thanks for the info.

Funny enough I find the best "defense" against pirates are a couple of Trade Ports. With all the pirate ships busy chasing the trade ships they never really pose a threat. Without this distraction though they kind of focus more, making them much more dangerous.

Does anyone else ever send missions of pirates to a friendly world just for leveldriving?

I'd like be able to designate myself as the target of a pirate mission (but not necessarily bounty).