I understand that each caught pet can have several pre-set stats. I see a lot of people are discarding certain stats and only looking for a specific one... but how do you decide which are the good ones, and which ones suck? Should I keep pets with the highest HP, attack, or speed?
There's no absolute "right" or "wrong" stat to aim for, and it's really up to what you feel works best for your pet team.
Personally, I've been going with high speed since it usually allows my pet to go first. Sometimes going first can make or break the battle (this doesn't always work out in my favor though). Attack and health are rated about the same in my book.
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I was literally about to post the same question here. Your answer makes a lot of sense though. I've noticed a number of battles that were close, and if I could just have gone first, would have made it. So I think I'll be looking for speed a lot. It's hard to choose, they all seem to have a bonus to them in battle.
My Golden Civet has 325 speed at level 25 so faster than most. I haven't found a good way to use him though. Do like that my Fawn has 305 speed since he is my healer and dodges most attacks.
I go for power. My favorite is my crab with Emperor Crab at 325 power. With shell shield and renewing mists he outlasts any enemy and when he hits them with his claw he packs a punch Crimsom Geode is also deadly with 329 power at level 23
High speed has one drawback - many of the dragonkin have a "Tail Swipe" attack that does significantly more damage when they go last. Fighting flying snacks with my Crimson Whelpling is my favorite way of leveling my pets now -- the level 23-25 wild flying pets almost always have higher speed, so I start off well. But generally yeah, I go for high speed too.
I was lucky enough to pick up a Scourged Whelpling with high health and low speed. This works very nice with Plagued Blood since he get double heal when using it and the high healthpool is keeping him alive, so in certain situations there's advantages to other stats than speed. But for most pets I prefer to go first.