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If I catch a Zubat a level 9, and evolve it into a Golbat, without fainting, using vitamins, massages, or herbal medicene, roughly how long 'til it evolves

How long have you had this Zubat/Golbat? I have a somewhat decent idea of how to give you an answer. x)
too many variables to actually answer this question, that is if you're asking the amount of time it will take.
like the other comments have said, it is impossible to give an answer. This is because there are more ways to affect happiness than the ones you have listed. It gets some for levelling up, sure, but you also increase happiness for every 256 steps you take while it is in your party. So how soon it evolves depends on how much you are walking around between it gaining levels.

1 Answer

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Despite my comment, I decided to attempt an answer.

Ok, so a Pokemon needs a happiness stat of 220 to evolve (255 is max Happiness, if you are interested).

When you catch it, assuming you use a regular pokeball, then Zubat will start with 70 happiness.

Assuming you just rare candy it to level 22, when it evolves it will have 121 happiness. I say Rare Candy it, because then you will not be taking steps, and so the only happiness it will gain will be from level.

Now if you walk 25,344 steps, and then level Golbat up 1 level it will evolve. Alternatively, Rare Candy it to level 59 and it will evolve (again Rare Candy so you aren't raising its happiness by walking). Realistically you will use a combination of these methods, so it should be less than either number.

This assumes you never use it in a battle against Gym Leaders, Elite 4, or the Champion, as that increases happiness, that it never faints, and that once it hits level 22 it doesn't gain another level.

You can decrease the amount of time needed by catching it in a Friend or Luxury Ball, or making it hold a Soothe Bell. As you mentioned in the question, vitamins, massages, and hair cuts (depending on your game) will make it evolve sooner. This is what everyone meant by so many variables, so your Zubat will probably take less than that amount of steps to become a Crobat, simply because you will probably level him up some when you're walking around with him, or will do something else to boost happiness, so this is only accurate if you follow the exact conditions I used when calculating it.

edited by
Note: I didn't see the Emerald tag when I wrote this, so some of these features (e.g. Hair Cuts) aren't in Emerald. The numbers still stand, though.