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ZoS math! Need some help!

Wreuntzylla
Wreuntzylla
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Alright, so I have the following sprint cost reductions:

Prisoner: 50%
Well-Fitted: 24 % (6 purple pieces)
CP: 12%
Fiords: 15%

50+24+12+15 = 101%

Lose about 1% stamina per second while sprinting.

So, I am thinking, well maybe there is a cap.

BUT!

Fiords + Darkstride = 100%

NO STAMINA LOSS WHILE SPRINTING!!!

Any ideas what the issue is?
  • Ahzek
    Ahzek
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    My simple guess would be CP passives applying multiplicatively. But i have never done testing on sprint cost
    Jo'Khaljor
  • WhiteMage
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    Ar you saying you have tested those two sets together and they reduce your sprint cost to zero? If so, I would say that is not WAI. The thing about additive bonuses is they can break things if you can stack them. Multiplicative bonuses behave much nicer. What I would expect from a 100% reduction is halving the normal value if you have a single 100% reduction. As you add more, according to my toying with a calculator, it converges to a .3678 multiplier, or 1/e. Two 50% percent reductions should be a .4444 multiplier.

    Ofc there's many ways the could do it... I would probably add up all the reductions, call it X, and plug that into (1+X/100)^(-1) where X is the sum of the percent reductions.

    For anyone who's curious, the equation that converged to 1/e was (1+1/X)^(-X), though it probably isn't that surprising.
    The generally amicable yet sporadically salty magplar that may or may not have 1vXed you in Sotha Sil. Who knows?
  • Wreuntzylla
    Wreuntzylla
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    WhiteMage wrote: »
    Ar you saying you have tested those two sets together and they reduce your sprint cost to zero? If so, I would say that is not WAI. The thing about additive bonuses is they can break things if you can stack them. Multiplicative bonuses behave much nicer. What I would expect from a 100% reduction is halving the normal value if you have a single 100% reduction. As you add more, according to my toying with a calculator, it converges to a .3678 multiplier, or 1/e. Two 50% percent reductions should be a .4444 multiplier.

    Ofc there's many ways the could do it... I would probably add up all the reductions, call it X, and plug that into (1+X/100)^(-1) where X is the sum of the percent reductions.

    For anyone who's curious, the equation that converged to 1/e was (1+1/X)^(-X), though it probably isn't that surprising.

    This isn't damage or stat regen. You can't do anything while sprinting and the sets make you completely useless for combat. This is a harvesting build. So no, I would not think it would be multiplicative and I am curious why you would.
  • Reorx_Holybeard
    Reorx_Holybeard
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    Fiords + Darkstride = 100%

    NO STAMINA LOSS WHILE SPRINTING!!!

    Can you confirm you meant Fiords + Darkstride (65%) instead of Prisoner + Darkstride (100%)? The latter makes sense to remove sprint cost entirely but not the former. Testing I just did doesn't give me 0% sprint cost with Fiords + Darkstride (confirmed).

    The formula I verified around update 10 for sprint cost was:
    SprintCost = Base * CP * Buff * Set * Item
    

    So sprint cost modifiers stack multiplicatively in the 4 categories and additively within a category (i.e., DarkStride + Prisoner = 50% + 50% = 100%). This seems to match my quick testing I just did on live:
    • Base @ CP160 = 546 Stamina(confirmed)
    • Darkstride = 273 Stamina (confirmed)
    • Darkstride + Fiord + 7% Well-Fitted = 177 Stamina (178 in-game)
    • Darkstride + Prisoner = 0% (confirmed)
    • Your Initial Case = 127 Stamina (theory)

    So everything seems to match the theoretical formula unless someone can find a specific case that does not. I also happened to come across a strange bug with weapon swapping and the Fiord set:
    • x5 Darkstride (Shield, Boots, Belt, Shoulders, Guards)
    • x5 Fiord (Necklace, Ring, Helmet, Chest, Bracers)
    • Sprint Cost = 177 as expected
    • Swap to other weapon bar with no Darkstride (so x4 Darkstride)
    • Sprint Cost = 432 as expected
    • Swap back to original bar
    • Sprint Cost = 219 stamina (177 expected)
    • Unequip and re-equip any Fiord item (re-equiping a Darkstride item does nothing)
    • Sprint Cost = 177 as expected

    I'm unsure why the Fiord set breaks even through it is Darkstride on my weapon bar...strange. Perhaps double-check if that is the case in your setup. It looks like initially Fiord + Darkstride work additively as expected (15 + 50% = 65%) but after the bar switch they switch to working multiplicatively (0.15 x 0.50 = 0.75) until you re-equip a Fiord item. Also this only appears to happen with Darkstride items in your weapon slots. Fiord weapons seems to work fine and don't have this issue when weapon swapping. It also happens with Prisoner + Darkstride weapons.

    Update: I've confirmed that Prisoner + Darkstride gives you 0% sprint cost in-game.
    Update: More detail on the Darkstride weapon swap issue.
    Edited by Reorx_Holybeard on October 30, 2016 5:15PM
    Reorx Holybeard -- NA/PC
    Founder/Admin of www.uesp.net -- UESP ESO Guilds
    Creator of the "Best" ESO Build Editor
    I'm on a quest to build the world's toughest USB drive!
  • WhiteMage
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    So no, I would not think it would be multiplicative and I am curious why you would.

    Just because it doesn't make any sense to break rules or deviate from standard formulas in your own game without a really good reason.
    The generally amicable yet sporadically salty magplar that may or may not have 1vXed you in Sotha Sil. Who knows?
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