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Is there a way to measure how overrepresented or underrepresented each Pokémon is, correcting for the fact that Pokémon introduced earlier have more regional Pokédexes they had the potential to appear in?
This is only true if you completely ignore the Grand Underground. I slept on it too because I figured "it's just the Underground again with a new name, why should I care" but PonStefon made a case earlier in the thread for it being a game-changer—it gives you access to Pokemon which either are...
Per GBATek, "it is not possible to link between [Game Boy Advance] games and [Game Boy] games, [partly] because of different cable protocol, and [partly] because of different signal voltages".
You don't need to do this; the game is balanced around the new experience mechanics. Just build a team of six and don't grind, you'll be at around the same level as the AI the whole way.
Do you have proof that that's the case for normal Sticky Web? The video that was posted in the mechanics research thread used Court Change, so it could just be that you can't trigger Defiant/Competitive with your own hazards (which is no different than not being able to trigger it with your own...
Dragonfree (author of some extremely comprehensive guides to capture rates in Gen 1-7) has been digging into the catch rate thing; there's definitely a reduced capture rate if your active Pokemon is lower-level than the target (until you beat the game) but it's not clear as yet how much worse it...
Gamefreak could have been replacing the whole movepool every generation since the series began, because the consistency you're talking about only matters if you could battle across generational lines. They make changes to old moves all the time - Tackle went from 35/95 to 50/100 to 40/100; Fire...
As I recall, online trades/battles have a matchmaking system, but you can ensure that you connect to a specific other person by sharing a secret with them outside the game. That's everything the GTS did implemented in a better way than the GTS ever did.