Resistances and ‘Diminishing Returns’

Something that seems to be coming up a lot on the boards at the moment is the way that resistance bonuses are calculated and the belief that this leads to diminishing returns.

This isn’t actually the case.

The misunderstanding stems from the fact that your final resistance is calculated with this formula:

Resistance = 1 – (1 / (1 + Total Resist Bonus)

For example, if you have a total +50% phaser resist bonus, your phaser resistance will be 33.3% (1 – (1 / 1.5)). If you have a total +100% phaser resist bonus, your phaser resistance will be 50% (1 – (1 / 2)).

Certainly seems like diminishing returns, right?

But percentage resistances aren’t linear, they’re exponential:

  • If you have 0% resist and you add 1%, you reduce incoming damage by 1%
  • If you have 90% resist and you add 1%, you reduce incoming damage by 10%
  • If you have 99% resist and you add 1%, you reduce incoming damage by 100%

So, if a ‘+X% resist’ bonus just increased your resistance by X%, you’d be getting exponential returns. The formula doesn’t give diminishing returns, it converts that exponential return into a linear one.

For example, with a 50% bonus, you get 33.3% resist, which means it’ll take 50% more damage to destroy your hull. With a 100% bonus, you get 50% resist, which means it’ll take 100% more damage to destroy your hull.

The thing to remember is that the resist bonuses listed on items like certain engineering consoles isn’t the percentage of resist the item will give you, it’s the percentage of additional damage the item will let you take.

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2 Responses to Resistances and ‘Diminishing Returns’

  1. LagunaD says:

    So how do debuffs that reduce damage resistance work with that formula?

    In particular, if the target has no Resist Bonus, what is the effect of (say) a -30 Resist debuff?

    It would seem that stacking enough debuffs could lead to division by zero, if negative resist effects are treated additively with positive resist bonuses.

    On the other hand, if the resist bonus in the formula can never be negative, it makes debuffs fairly useless.

    • Stalfos says:

      -100% would give an actual value of -50% to their resistance giving double damage. -30 would give about -23%.

      Division by zero not possible as +/-100% actual value can’t be reached except by infinity resist debuff.

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