PokéBase - Pokémon Q&A
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I'm looking for a list of all the moves which become better apropos the user's max HP stat. This excludes moves like Final Gambit and Eruption because they depend upon the user's current HP. It also excludes moves like Recover because when working with percentages it always recovers a fixed percentage of HP. Hence, although it depends upon the user's max HP stat yet it doesn't become any better when the user's max HP stat increases.

The only moves that I can think of that fit this criteria are Substitute and Wish. Both these moves have something in common - they can be Baton Passed to other pokémon. When a Substitute is created 25% of the user's max HP is put into the Substitute. This is particularly useful when a pokémon with high max HP passes its Substitute. The same goes for Wish because it recovers 50% of the user's max HP. The user might not be the same as the pokémon which receives the Wish.

Are there any other moves which become better apropos the user's max HP stat? It doesn't need to be Baton Passable.

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If we're talking moves similar to Substitute, there is Belly Drum. It's even baton passable, or at least it would be if there was a Pokémon that could learn both those moves.

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Good thinking, but Belly Drum itself isn't any more effective with a high HP stat, as the question was asking. It still removes the same percentage of health. Substitute and Wish both benefit though, as the Substitute has a higher HP value and the Wish will pass more HP, noticeable if the user switches out in the time before the Wish comes into play.