It's quite messy, though of course I'm sure you could get close enough in practice. As I understand it, the API gives you no more information than is in the pet battle log, and that does not always determine unambiguously which pet was responsible for what. Consider the case:
From the lines as they are presented, which Imp did which damage?
It's an awkwardness in the code. You have to keep track of which pet did, or might have done, which damage. The program has to have quite a bit of specific knowledge coded in about reading the abilities, and that would need to be kept up to date.
On a separate angle, I once started in on writing a Pet Battle Solver, that would simulate a pet battle. Running it in brute force mode would run through all possible ways a battle might go. Of course there is RNG, but reasonable decisions could be tuned about that. I stopped when I hit the rat's nest that is the inconsistent abilities and the end-of-round mess. While it could be coded, it would need a lot of experiments to document every possible case, and that was more work than I was up for. However, as I was coding the basic framework, I felt bad about it. This is what happened to Chess. When a computer can play better than almost any human, cheating becomes rife, and it takes so much of the fun out of it.
In that vein, I'm not sure I want to see the Recount culture come to pet battling. It's a pretty shallow game, with only RNG saving it from trivial determinism, but it has its fun, and I don't want it to go down the rabbit hole of mathing everything out.
On the subject of pet battle dummies, yes, I have sometimes wanted that too. You would need one for each family, with an option for the dummy to attack back using a 300-damage ability of every family, and an avoid... ok, going too far here. I don't consider it a big deal, though; there's always some tamer I can test on.
Discuss pet battles, strategy and theorycrafting.
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