How do 25% trait reduction passives and 10% trait reduction from ESO+ work together?

Dagoth_Rac · June 2018

I have ESO+ and all research reduction passives. I see that my 5th trait will take 2 days, 21 hours, 07 minutes, 12 seconds. Which is about 2.88 days. I cannot figure out where this number comes from.

I know 5th trait would normally take 4 days:

First trait = 6 hours (0.25 days)
Second traits = 12 hours (0.50 days)
Third trait = 24 hours (1.00 days)
Fourth trait = 48 hours (2.00 days)
Fifth trait = 96 hours (4.00 days)

I have tried to get to above 2.88 days number via:

Additive: 25% + 10% = 35% reduction. 4 days * (1 - 0.35 ) = 4 days * 0.65 = 2.6 days, not 2.88
Multiplicative: (1 - .25) * (1 - .10) = 0.75 * 0.90 = 0.675 = 4 days * 0.675 = 2.7 days, not 2.88

Does anyone understand the ESO math behind research time reduction and where that 2.88 days is coming from?

Thanks.

ghastley · June 2018

Your multiplier appears to be 0.72, which is consistent with you only getting the 20% rate, rather than 25%. I.e. 0.8 * 0.9 instead of 0.75 * 0.9, so are you sure you have the full passive?

Dagoth_Rac · June 2018

ghastley wrote: »

Your multiplier appears to be 0.72, which is consistent with you only getting the 20% rate, rather than 25%. I.e. 0.8 * 0.9 instead of 0.75 * 0.9, so are you sure you have the full passive?

@ghastley
Great catch! Thank you. I have the extraction passive maxed out, not the research passive.

Hasenpfote · June 2018

keep in mind that the trait reduction passives applies first, after that, ESO+ gets applied, that cause that can reduce the max duration of researchment from 30 days to 27 days and therefore you can further reduce the duration to around 14 days by using a daily masterscrip time reduction item for 3(?) pieces per day.