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If no Attack modifiers are used, those Pokemon are always L7. If there are attack modifiers in play, the level will be different: -6 corresponds to level 1 and +6 corresponds to level 13. So if you use Growl x6, you can catch any Pokemon at level 1; this has a rather surprising side effect when you use it for Mew or a member of a 3-stage evolution line, and follow it up with a low-experience battle.
I know I could get a Tentacool from fighting one of the sailors on the S.S. Anne. If I want it to be level 1, do I use growl 6 times against his last pokemon before I win the battle or is it a total of 6 growl throughout the whole sailor battle?
Has anyone done much testing of the different attack modifiers for levels?
What surprising side effect are you talking about?
The last Pokemon you fight is the one that determines the species with its Special stat, and it'll also determine level with its Attack modifier. You need 6x Growl specifically against that Pokemon to get level 1.
For some Pokemon (Mew and all 3-stage lines except Butterfree, Beedrill, and Dragonite), their experience-to-level formula dictates that at levels 0 and 1, they actually have negative EXP (L1 has -54 to be precise). This oddity was never supposed to come up since the lowest level you're supposed to encounter Pokemon at is 2. However, if you take your negative-experience L1 and put it in a battle where it gains some experience, but not enough to cross the 0 barrier, the fun begins. Experience is stored as an unsigned variable, so the game thinks it has 16777162 EXP. That's enough for level 245, so it tries to level up. But anything above L100 gaining experience is brought "down" to 100, so in this case the still-negative EXP total jumps to 1059860 and your Pokemon gets 99 levels up in one battle. Of course this causes it to skip its entire learned moveset, and if you have, say, Charmander, it evolves to Charmeleon immediately but never gets the chance to go to Charizard if you use this. Be aware of these quirks if you plan to do anything with this.