ability percentage stacks?

[Blitzgon]

As strange as the title is worded, I have a question on exactly how abilities that offer a percentage buff stack on one another. How does the game calculate bonuses such as having Fey Illumination and Rouse on a fairy or the passive 5% from nocturnal sect and 40% from Synastry.

I curious if anyone knows if the percentages are stacked, calculated on a buff priority order, or if it calculates it in the order of buffs applied.

[Vulcwen]

Everything is multiplicative, order doesn't matter at all.
So.. having both a 5% and 40% increase in healing means a ((1.05 * 1.4) - 1) * 100% = 47% increase in healing overall.

[Blitzgon]

That would make sense, do you have data or a link to something to show this?

[Gemina]

That would make sense, do you have data or a link to something to show this?

No data or link is needed to validate it. It is simply using the formula provided in the descriptions by both abilities.

[Vulcwen]

No data or link is needed to validate it. It is simply using the formula provided in the descriptions by both abilities.

Eh.. that's not an argument. Tooltips can be wrong, and have been in the past, besides they provide no information about how they combine.
It's a generally accepted theory that it's multiplicative, and I have tested it a bit a few months ago. I can't find a recent source with test data however, so I have no valid proof ready. I might get back to this later, to show some data :P

[Nekotee]

Because in comparaison
In the crafting area percentage are cumulative

Your skill have 80% base chance
Adding steady hand (+20%) make the skill go (80+20) = 100%
And not (80*1.2) = 96%

Need data to validate that

[Vulcwen]

Alright, some data

Rouse = +40%
Fey Illumination = +20%
If additive, we expect 60% as combined value, if multiplicative, we expect 68%.

20 non-crit samples without buffs and with both buffs:

base  rouse + fey illumation
2030	3424
2007	3424
2024	3465
2016	3320
2049	3474
1949	3285
2008	3389
2015	3460
2031	3444
1968	3470
2010	3462
1971	3376
1952	3276
2048	3368
2032	3407
1959	3372
2038	3351
2049	3432
2002	3389
2049	3301

Average:
- Base: 2010.35
- Rouse + Fey Illumation: 3394.45

3394.45/2010.35 = 1.6885
So +68.85%, a strong indication it's multiplicative.

Still not entirely a proof.. and a statistical test requires more data as the data isn't normally distributed, but I think this is enough to assume it's multiplicative.

Also @ nekotee.. yes, it appears probability-related stats do stack additively. Which makes sense from a design perspective.. It makes all those buffs situation-independent, making it easy to reason about them.

[JackFross]

Also @ nekotee.. yes, it appears probability-related stats do stack additively. Which makes sense from a design perspective.. It makes all those buffs situation-independent, making it easy to reason about them.

Looking at the wording is all you need to do to verify this.

Steady Hand:
Improves action success rate by 20% for the next five steps.

Internal Release:
Increases critical hit rate by 30%.

Blood for Blood:
Increases damage dealt by 30% and damage suffered by 15%.

Divine Seal:
Increases spell-based HP restoration by 30%.


If you think about what these mean, it makes sense that the latter two are multiplicative while the former two are additive. Consider stacking two instances of each of those skills.

My "action success rate" and "critical hit rate" are already in the form of a percentage. Increasing by a percentage would logically be an additive change.

My "damage dealt," "damage suffered," and "spell-based HP restoration" are not percentages, but values. Increasing a value by a percentage would logically be a multiplicative change.


Think of it this way.

Say I deal 100 damage with an attack.
I now use Blood for Blood to increase my damage by 30%.
My attack now does 100 + 100x30% = 100 + 30 = 130 damage.
Now, I'll use Heavy Thrust. This increases my damage by 15%.
My attack now does 130 + 130x15% = 130 + 19.5 = 149.5 damage.

You can do this in the opposite order and get the same result.
100 + 100x15% = 100 + 15 = 115 damage.
115 + 115x30% = 115 + 34.5 = 149.5 damage.


And then let's look at critical hit rate.
Say I have a 10% chance to have a critical hit.
I use Internal Release to increase my critical hit rate by 30%.
Now I have a 10% + 30% = 40% chance to hit critically.
On top of this, my Dragoon hits Battle Litany to increase it again by 15%.
Now I have 40% + 15% = 55% chance to hit critically.

It wouldn't make sense to use the same formula I used for attack damage for critical hit rate, and the same can be said vice versa.

[Vulcwen]

Looking at the wording is all you need to do to verify this.

From my previous MMO I learned you can never be certain something works like you think it does based on the tooltip, until you verify it with actual data. While FF14's QA is much better than that MMO, there can still be things that are bugged in some way, and just don't work as expected. In fact, in that MMO, all buffs worked additively, regardless of how it was worded (seen both variants, and some more).

Besides, even for percentages, multiplicative wording could make sense:
for example: Doubles your critical hit rate..
as doubling generally means the same as increasing by 100%, wording like "increases your critical hit rate by 100%" would likely be perceived as doubling the crit chance you had before, rather than that you always crit.

So while there is certainly a case that one option is more intuitive than the other, it's still ambiguous about what it actually means.

[JackFross]

"Increases your critical hit rate by 100%" would mean "you will always get a critical hit" though. That's not confusing wording. "Doubling" is implicitly multiplicative, whereas "increases" is implicitly additive.

The thing is that ALL buffs in this game are additive, they just add in different ways, based on common sense. If you "increase" your "rate" by x%, it's just an additive increase of that %. If you "increase" your "value" by x%, you increase that value by an amount equivalent to that % of the value. It's addition mixed with multiplication, but still addition at the end of the day.


It's not even taking tooltip text to be the word of law, to be honest. It gives strict %'s which are guaranteed to be correct, save for a mis-translation error, and those %'s can be directly inferred to have certain properties.

To assume that a 30% damage increase stacks with a 20% damage increase in such a way that the end result is a 50% (rather than 56%) damage increase is a little bit silly! That would be counter-intuitive to the idea of increasing damage. If you simply think logically for a moment about what it means to "increase your damage by a certain percentage" it stands to reason that one buff would stack multiplicatively on the last.


It's all logical and intuitive the way I outlined it, and there has been countless research done by people much smarter than I am that verifies what common sense dictates.