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I have been led to believe that a pokemon's stats change after evolution because the two forms have different Individual values, which is confusing to me because the pokemon is the same and it should retain its IVs as those are its "genes." I think Defense and the Special stats have a chance of being inherited from the opposite gender parent IN GENERATION TWO while speed and attack are randomized. For example, I just bred my growlithe to know flame wheel and crunch at birth, but I only used two growlithe as parents. Would the baby have a chance at being stronger if the opposite gender parent were an arcanine instead? I'm also about to breed eevees. Should I evolve them into, say, vaporeon so that the baby can possibly inherit its higher defense and specials (compared to other eevee evolutions in general) and become a stronger than normal flareon?

What I'm asking in short is, as far as inheriting Individual values goes, does the level of evolution of a pokemon parent of any given evolutionary line matter? Only answer if you know what you are talking about. Please don't just guess.

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No, the IV's are set and stay the same for the pokemon at a certain point in it's breeding process depending on what generation you are in, gen3 was kinda weird because breeding worked differently for ruby/sapphire than it did for emerald.

The stats change after evolution because the two forms have different base stats. Gen2 gender was determined by the attack iv.

here's a nice page on IV's


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Thank you! Ah, base stats. Eh, I should have guessed. That makes a lot of sense--although it's a little disappointing, this makes things simpler. I wish there were some way to know immediately which IVs were inherited. I try to find stronger parents and I've learned to stay away from weakling ditto!
well, if you have a decent amount of rare candies you can save your game, level the baby and check the "IVs" that you have or check out the parents before you breed them.  if you're playing the actual gen2 use the link below, if you're playing the remade versions of gen2 there is a link on that page to the IV calculator.
Those are good ideas. Thanks again. I had had it suggested to me to breed a male of a species with high specials with a female of another species to get a female with higher than normal specials. Eg. male mareep with female rattata to get a stronger female rattata baby. But now I'm thinking this doesn't make sense because this seems to be trying to pass on base stats which doesn't some species have higher possible IVs?
IVs are added on top of the base stats along with EVs and all pokemon have the same ranges on IVs(or DVs in gen 1-2).  gen 1-2 i beleive the range was 1-15 while gen3 and later it's 0-31.  here's a link that explains how stats are passed on during breeding.  if you're playing soulsilver/heartgold go down to gen4 original silver/gold it's the gen2 description.