Guide Def/agi Tradeoff Analysis

It's widely known that agility and defense don't "stack" - that is, if you have some amount of both, dodging an attack means you don't really get the benefit of the reduced defense.

Conventional wisdom has it that, therefore, if you have extra skill points floating around, you should sink them into one or the other, since you can't get both benefits simultaneously. However, that's not necessarily true. Since skill points give less benefits at higher amounts (e.g. 10 to 11 gains 0.9%, but 70 to 71 gains 0.5%), it actually may be advantageous to spread, say, 30 skill points as 28 Def/2 Agi (or vice-versa, if you have a minimum to maintain in one of them for item usage requirements - the average damage reduction is identical for either).

Using this table, you can determine the optimal spread for a particular number of skill points - simply look at the diagonal corresponding to the number of available skill points (listed on the axes - it doesn't matter which is defense and which is agility, of course). The numbers in the table correspond to the actual damage taken from a nominal 10k attack with a particular Def/Agi distribution, so you simply scan the diagonal looking for the smallest number. Generally, the optimal distribution tends to be near the edges - it's usually just maxing out one of the stats, but in some cases is offset by a few points.


That's only a sample, using the largest screenshot I can take. I've attached the original data as a PDF (because .xlsx files aren't allowed), which uses a 1M damage baseline and has data for values up to 150 (the max allowed in-game with skill point gear).

For those interested, the graph of damage taken for a particular number of available skill points looks something like this:


Note 1 - In cases where they are different, the actual gains from the optimal distributions vs. maxing out one of the stats are minimal - typically in the range of 0.05%-0.25% reduction in average damage taken. This is mostly an academic exercise.
Note 2 - In the case of Str/Dex, since they are additive the optimal scenario (excluding elemental damage benefits) is to assign the same amount to both Str and Dex.

List
A list of every number of available skill points through 70 for which the optimal distribution is nontrivial. For any values not listed here, max/zero is the optimal choice.

Spoiler: Show List

3 | 2/1
4 | 2/2
6 | 5/1
7 | 5/2
9 | 8/1
10 | 5/5
11 | 9/2
12 | 10/2
13 | 8/5
15 | 14/1
16 | 14/2
18 | 17/1
19 | 17/2
21 | 20/1
22 | 20/2
23 | 22/1
24 | 22/2
25 | 20/5
29 | 28/1
30 | 28/2
31 | 30/1
33 | 32/1
34 | 32/2
36 | 35/1
37 | 35/2
42 | 41/1
43 | 41/2
45 | 44/1
47 | 46/1
49 | 48/1
51 | 50/1
52 | 50/2
60 | 59/1
63 | 62/1
65 | 64/1
67 | 66/1

 

whoooaaa
thats a hgue graph

 

I considered trying to figure out an equation to determine the optimal distribution for any value, but that would require regression analysis and multivariable calculus, and I've had my fill of those...

 

Druser be like

 

Defense doesn't reduce elemental damage though, and the base defense of every class may have an impact on the result as well.

 

Just attach an excel sheet on google. That’s what I did with my housing thread.

So what are the best values for def and agility respectively?

 

Spreadsheet (look at the "Per Point" sheet, the red and gray one was my attempt at a marginal formula, which turns out to be very error-prone over larger steps)

The best distribution depends on the number of available skill points (tangentially, this may be an artifact of the representation of the percents for skill points being rounded to one decimal in the display if the calculations actually use more than that - but we would never know unless a developer or someone revealed this to us).

For example, the optimal way to distribute 26 skill points between Def and Agi is just 26/0 (or 0/26 of course). Likewise for 27 and 28. However, the next few optimal distributions are 28/1, 28/2, and 30/1. It's essentially impossible to find the underlying pattern without knowledge of the point-percent conversion formula, hence why I eventually want to just list out all the deviations from max/zero.

 

You can probably get a solid estimate of the point-percent conversion formula by going into excel and writing out each point and percent value. Then find the trendline for exponential regression and it should work out reasonably as an estimate.

 

Someone did this some time ago (link), but the accuracy of that regression is sufficiently off that it wouldn't be able to correctly find minima as small as those in this distribution.

 

To be fair the link you mentioned does not go past 100 skillpoints. Going to 150 might result in an equation accurate enough to suit your needs.

Dukioo’s Wynndata also has all these values up to 150. I don’t know if he has the equation via API, or if he just has all of the percentages for corresponding skill points.

 

I got the 101-150 values via Wynndata. The link doesn't have the list past 100, but based on the comments the equation comes from fitting the full 1-150 set.

I've added a list of the deviations from max/zero in the OP up to 70 sp - I'm thinking that should cover the majority of uses, since I figure at higher numbers, builds are probably going to involve fire/air weapons anyway, in which case the extra damage from a particular choice almost certainly outweighs the slight optimization of defense.

 

Wall of t̶e̶x̶t̶ numbers

 

I'm still fairly certain that base defesene reduction and defense no long stack.

 

So your base defense protects against all damage, defense only protects against neutral, and agility protects against all?

 

I'm fairly certain that Def is multiplied by the class's base defense, so that shouldn't have any effect on the optimal outcome (only possibly on the relative gains).

 

Base defense still only effects nutreal.
But I'm pretty sure they don't stack?
It wouldn't make make much sense to Muilti it.
That would somehow make defense worse then it already is.

 

Lemme test this then.

 

What do you mean by not stacking?

 

I'm pretty sure, it takes the calculates the base defesene then the actual defense stat after.

 

:D