It's complicated by the fact that we (I) don't really understand how it works now, either...
But I assume you have tables that generate say "oh no, [Hard] [emergency rescue] [S-Event] in [Andor Sector]" or similar. And any other events in Andor.
Now, you look the Deployment to find out what ships are available? Based on the painstaking deployment plan, to find out which if any ships might be able to help.
In Theatre Commander Decides Deployment, the essential answer to 'can ships roll to respond to an event' is 'yes'! Of course a ship can go rescue those miners. The first time.
That 'yes' that gets less certain over the Quarter. The TCs are good at their jobs, so ships are always available for the first event in a Sector. Second, third events reduce likelihood of having responders available to roll.
Adding fins and chrome to this, some TCs prioritise their Border zones. Some prioritise Diplo-Events rather than S-events. This might be where you derive the cap on the number of ships you make Response Rolls for.
Future VA Theatre Commander Straak has virtually no limit to the number of Rock Discovery Events he has ships respond to, but might be capped at two for irrational, emotional trade summit disputes. (I'm thinking here you have useable categories from your Event tables. Maybe not, in which case perhaps drive it from the resolution Stat involved).
The overall 'available ship curve' could perhaps be based on formula of
our quest success over time, if those numbers are stored and crunchable.
(Edited a fair bit)