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[Update 21] Nord "Rugged" passive — a mathematical analysis

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As of today's dev notes regarding the upcoming racial changes, the new effect of the Nord "Rugged" passive will be changed to provide 3960 Physical and Spell Resistance, in contrast to its current effect of 6% damage reduction. Some posters have claimed this will be universally worse than the current version, because "3960 resistance = 6%", and doesn't work against bleeds.

However, the math is a little more complex than that: while 3960/660 = 6% more armor in an absolute sense, it doesn't take into account the marginal gain, relative to how much armor you already had.

For example:
going from 29040 > 33000 resistance (the cap), your armor value goes from 44% > 50% (6% as expected). But, inversely, the amount of incoming damage you receive has decreased from 56% > 50%, meaning you have gained 1-(50/56) = 10.7% more survivability relative to your baseline, much more than the presumed 6%. In other words, adding extra resistances becomes more effective the more armor you previously had, increasingly exponentially until you hit the resist cap.

The old Rugged passive, on the other hand, is applied multiplicatively during mitigation calculations, and thus always adds 6% regardless.

Here is a graph depicting how much mitigation the new passive will provide, dependent on your build's existing resistances. As how much resistance you effectively have also depends on your opponent's penetration, I've also accounted for different penetration values (0, 5k, 10k, 15k):

3kU2TaV.png

Some observations:
  • Under normal circumstances, you can expect it to equal or outperform the old version, giving anywhere from 6 - 10.7% mitigation.
  • If you are being over-penetrated by your opponent (lel), the new Rugged can be significantly worse than 6%, but this should be rare on most builds.
  • If Rugged overshoots the resist cap, it will be partially wasted (which explains the dip from 10.7 > 8.3 on the "0 pen" curve).

In summary, you can expect the new iteration of Rugged to perform better than it currently does, as long as you aren't currently nearing the resist cap or being overpenetrated. One notable exception would be bleeds, since they completely ignore resistances.

There will be no difference vs. Oblivion damage, since this always ignores resistances AND %-based mitigation.

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