PokéBase - Pokémon Q&A
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By Leveling up, breeding, TMs, Tutor and Special moves (from Event, Dream Yard and Island Scan)
Please don't comment why I asked this.

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Okay, for those of you who don't know, the average of a finite set of numbers a, b, c, d...is (a+b+c+d...)/(size of set). It does not involve separating the numbers into "different areas" nor does it involve separating Pokemon that learn most moves from those that learn a little. If you're going to answer the question, then please actually calculate the average of the entire set and not just estimate it or find a range that contains it.
Ok, so if you want the main average...I'll give you the main average.  For the average of 580 Pokemon is about 19.9 moves.  Do the math yourself... 11543 total moves / (divided by) 580 Pokemon. Happy now?
I'm not spending my whole day doing pointless math.

If someone out there is willing to count all the moves and all of the Pokemon and divide that number, say the exact answer.  I don't care!  But, there are apparently some people that care a whole awful lot about the "exact" or "precise" number sequence.  Spend 6 hrs doing that!!  I already did most of that work for you.

Why doesn't someone (mostly sumwun) calculate exactly how many moves each learns.  I may be wrong, I may be right.  But, if you want it short, it is almost completely irrelevant to calculate exactly how many moves is in the average.  If nobody wants to do that, than this question won't be answered..
If the asker asked for pointless math, then we must show him/her/it all the pointless math he/she/it asked for and no less. How relevant these calculations are is to be judged by the asker, not by you. If you don't like this philosophy, then maybe you shouldn't be spending so much time on a QA site.
If no one else will do this, I will.  Don't expect a quick response though it will take me a LONG time

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OK I'm a stats nerd, so I ran some queries on our database for PokemonDb to find the answer. I'm sticking to Ultra Sun/Moon only. Note: our database is missing a few special moves, but they should not affect the average - we'd need to be missing 800 moves for the average to go up 1, and I don't think we're missing that many!

Excluding duplicate moves (e.g. a Pokemon learning the same move via level up and TM), we have 61,249 distinct Pokemon-move combinations across 843 Pokemon. Yes 843 Pokemon - those extra ones are due to alternate forms (we actually have around 100 alternate forms listed, but many of them such as Megas are not counted here).

So the average Pokemon can learn 73 moves! (or 72.656 to be more precise)


My original answer before I updated it was not counting transfer-only moves. I think it's also valid approach. You can call it the "purist method" - counting only the moves a Pokemon can directly learn in USUM. This would also only count breeding moves on the baby Pokemon (e.g. Bulbasaur learns Giga Drain by breeding, but Venusaur technically does not because Venusaur can't hatch from an egg).

Using this method, we have 48,692 distinct Pokemon-move combinations across 843 Pokemon. That gives us an average of 58 moves per Pokemon (or 57.760 to be more precise).

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Wow. Just wow
(yes I did just give Pokemaster a down-vote)
Pokemon DB is completely missing transfer-only moves. There are easily 600 Pokemon that were able to learn secret power in ORAS but not anymore, and several hundred more that were able to learn endure, captivate, sleep talk, and natural gift in Generation 4. Of course, those aren't the only transfer-only moves; they're just the ones most likely to make a difference in the average.
Hmm, fair point sumwun. I'll make sure to add those when I can and update this answer.
OK I've updated my answer now we have the transfer-only moves, and it's much closer to sumwun's answer of 73.7 from Pokemon Showdown. The discrepancy could be partly due to some special moves we are missing, but also they could be counting forms differently - for example counting all the moves that Mega Evolutions have would increase the average.