[thejeff]

You can get debug output for battles, but I think you have to actually let the battles play to do it.
Of course, you don't have to watch them, you could go do something else.

Start dominions with "-d" (or more d's for more detail). I'm not sure where it puts it on a Windows machine.

I also don't know what it logs when running on the server (SP or hosting a MP game.) You might get battle logs then.

It's also probably faster and easier to watch the battles, slow as they might be, than to try to decipher the debug output.