Do multipliers stack additively or multiplicatively? [duplicate]

Question

For example: haste doubles your speed, boots of speed double your speed, and the Dash action doubles your speed.

Intuitively, it should be 2*2*2 = 8 times movement speed. However, the Dash action says "after modifiers" which implies something more like (1 [base] + 1 [haste] +1 [boots of speed]) * 2 [Dash] = 6 times movement speed. Unless it means modifiers to your base movement speed, which would be (1 [base] + 1 [haste] + 1 [boots of speed] + 1 [Dash]) = 4 times movement speed.

I know somewhere in the rules it says that for multiple applications of the same spell, only the strongest one applies, and that different spells with the same effect add together.

One of the sources here is an action, and another is a magic item. (Do magic items get treated like spells?)

The above is an example. The base question is

Do I add or multiply identical effects that multiply values?

I don't care what that value is (ex. speed, damage, money), or what it is from (spell, item, class feature, action, race ability); I'm looking for general rules for how to resolve stacking similar effects that don't give flat bonuses.

Answer 1

There are no general rules that explain how adding/multiplying bonuses work in general

There are a variety of specific cases of how to add or multiply certain things together in the game (eg damage resistance and vulnerability, choice of base AC formulae, identical spell/item effects), but there is no general rule covering when and how to add multiply that applies to every feature in the game¹. As such each case is up to the DM to adjudicate (in the absence of specific cases being specified in the rules of course). The best we can do is apply common sense judgements at our table and try to remain consistent between individual cases.

Your example specifically

However, no general rule is needed to resolve your example since the meaning is clear from reading the descriptions.

Haste says:

the target's speed is doubled

Boots of Speed says:

If you [use a bonus action], the boots double your walking speed

So if you started with a speed of 30:

30 * 2[haste] *2[boots of speed] = 120²

Then, after taking the Dash action, you gain movement equal to your speed according to the description which says:

When you take the Dash action you gain extra movement for the current turn. The increase equals your speed, after applying any modifiers.

So after applying the modifiers of haste and the boots of speed, you end up with a speed of 120. Taking the Dash action then results in a maximum movement of 240 for that turn.³

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^{1 - Obviously a negative is impossible to prove, but I have searched every published book, Unearthed Arcana, and Sage Advice (Tweets and compendium), and there is no general rule to be found in any of them.}

^{2 - Note that it doesn't matter which order you apply haste or boots of speed in here. Both modify your speed by doubling it resulting in a new, higher speed which the next effect doubles again. There is no wording to suggest that speed means anything other than the current speed of the creature.}

^{3 - Note that Dashing does not multiply your speed as you say in the question. It simply gives you additional movement. It is a subtle but important distinction even if the effective math is the same.}

Answer 2

"Do I add or multiply identical effects that multiply values?"

Sage Advice has this:

Mike Mearls says "Identical effects do not stack."

Jeremy Crawford says identical non-spell effects could stack.

As far as I know this has not been resolved any further.