So hopefully this isn't a stupid question, but it's something I've always wondered: I have an Eelektrik on level 39 that I could evolve with my Thunderstone, or allow it to level up and learn some awesome moves later on. Obviously, if I evolve it now, as an Eelektross it will have better stat increases as it levels up. But if I do wait and evolve it later, will its stats increase at evolution to what they would be if I had evolved it earlier? In other words, does waiting to evolve it reduce its potential final stats?
I don't think it affects the stats of the pokemon if you evolve it early. But I think every pokemon that is evolved with a stone will stop learning any of the moves it can learn naturally. In your specific case, Eelektrik WILL stop learning moves. He learns his last move, Thrash, at Level 71. IMO, I wouldn't evolve him until at least level 54 when he learns Coil.
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Your pokemon's stats will not be any different if you evolved it at level 39 or waited until 100 to evolve it. Its stats are determined, per level, based on a mathematical formula that inputs the pokemon's base stats(determined by the pokemon's species), the pokemon's IVs(automatically generated when you first encounter it) and the pokemon's EVs(earned every time you KO a pokemon and the pokemon you're speaking of gains experience from it in some way) and the pokemon's nature.
This means, there isn't even a slight bit of luck in how your pokemon's stats are determined. Leveling from level 20 to 21 will give a specific pokemon the same stat change every single time unless you change the EVs somehow before the next time you try to level it, and even then it may not.
The only downside to not evolving your pokemon now, in this situation, is that your pokemon doesn't have the higher base stats it gets from evolving yet. So if you really need it to be stronger right now, that may be your best bet.