I've done a bit of looking, but haven't been able to find a solid answer on this. What exactly do the capture maps add to? I've read in one place it adds to all the base stats like a sven, and in another that it adds to the base training the horse is captured with.

So I guess my question is do the maps increase inheritable traits, or do they just make it so the horse can show sooner?

In guessing it increases the changes of capturing an EEE

Maps increase the chance of capturing a stronger horse with better rating.