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For example, does Big Root heal more HP than Miracle Seed when using Giga Drain (which heals the user up to 50% of damage dealt)?

Would abilities affect the answer? For example, would the answer change if Venusaur in Overgrow range were using Giga Drain?

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Should we assume there are no mechanic changes in gen 9? Otherwise this question is definitely not allowed.
Yes, we can assume. More damage vs More HP.
We don't know about Gen 9. If you're happy with an answer assuming current mechanics, then you can just ask a question about the current generation.
I changed the question based on this. The example I added involves the same numbers as the Ceruledge example based on what we currently know.
Fair enough.
Which is better: more damage from Giga Drain with Miracle Seed OR more health from the move with Big Root?
Doing more damage still makes it rely on the SpD of the opponent, but using the Bigroot is more fixed. I feel like it depends on the situation
It is only a fair comparison if the target's SpD is held constant, so that doesn't make sense.

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For clarity, I'm going to take a pedantic mathematical approach to this question.

If d is the damage dealt by an unboosted HP-draining attack and p is the percentage of this damage restored to the user (in decimal form), then:

Healing with 20% boost items = d * 1.2 * p
Healing with Big Root = d * p * 1.3

1.3 > 1.2, therefore Big Root always causes more HP to be healed than items providing a 20% boost*. This result is not changed by extra boosts (such as from abilities) that apply in both scenarios, because a*b > a*c if b > c.

Big Root is always outclassed by damage-boosting items. This is especially true in the case of items like Life Orb and Choice Specs/Band that do more damage and heal the user more than Big Root as a result.

* Except in the case where damage is low enough that the difference gets lost during rounding. It is more correct to say Big Root heals at least the same amount, but more helpful to say it is always higher.

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Very good. I'll use Big Root next time.
The answer recommends against that, in case it was not clear. The opportunity cost of approx 8% more healing is a 20% boost in damage, which is not worth it ever.
Oh, gotcha. Ok, then. Thanks again.
I figured more damage was valued better than more health.
If you have an item that boosts damage more than or equal to 30%, go for it in all cases.

If you have an item which boosts less than 30%, go for Big Root if your sole purpose is healing. If its doing damage, then go for the item.
That's the dilemma:
More Health from Big Root = Less Damage...
More Damage from Charcoal = Less Health...
If you're using a Charcoal (20% extra damage), then refer to the calcs mentioned by Fizz. You'll be doing 20% more damage but healing around 8% less than a Big Root. So Charcoal is the preferable item, unless your sole purpose is healing (then go for the 8% extra healing of a Big Root).
Ok. So, for Damage + Health, go with Charcoal.
Just Health is only Big Root.
Got it.
If your sole purpose is healing, then you should use Leftovers not Big Root.
I have an inkling that, when Ceruledge is available in SV, I'll use his new HP-restoring move paired up with Charcoal to both deal more damage and heal for more HP...