Tree of Savior Forum

[INFO] STR or DEX June 2017

I’ve did a bit of number crunching in order to satisfy my curiosity: which is better, STR or DEX?

What I’ve done is graph the lowest damage and the highest damage of full STR, full DEX, and 1:1 STR DEX.


**June 15, 2017**

[quote]

[details=UPDATE 1: Block Pen and Defense][quote]acc97862 But STR affects the log down formula?[/quote]Working on it now, and also looking at block pen on DEX.

EDIT: ADDING NOW
EDIT2: ADDED >:U[/details][/quote]

**June 16, 2017**

[quote]I’ve revamped everything after taking into consideration the log scale down formula for Defense, and created a graph where you can adjust your additional attack and defense accordingly.

Will potentially include block pen calculations later, but it seems insignificant now.[/quote]

**June 18, 2017**

THE BELOW IS NO LONGER THE CASE HALLELUJAH
My sleepy drunkness didn’t help at all.

Log Down Panic

Update on the formula for Log Down Defense calculations incoming, Crit Attack is fkin included in the calculations.

[MAJOR OVERHAUL INCOMING]
I’ve screwed up, apparently crit attack is counted towards log scale down for defense. Revamping some of the formulas.Until then, I’ll change the conclusions section for the new overview. Sorry for anyone who put in points due to this guide :'D, updating asap.

**June 18, 2017**

Added in a speed variable s for those who want to play around with attack speed.


Conclusions

  • If you’re ability-based and physical, full STR for the most bang for your buck, mixing in CON for survivability and stam if needed. Wugushi is the first that comes to mind since poison doesn’t crit. Highlander(?) maybe as well.

  • Assuming defense, full DEX outdamages at hyper endgame. As in, 5k attack in your F1 window and 96% crit chance. However, this doesn’t factor in attackspeed. For auto-attackers, the breakeven point could be at a lower crit chance. At 2x attackspeed, it only takes 54% crit rate with 1500 F1 Attack Damage vs an enemy with 750 Defense.

  • Assuming no defense, it takes around 67% crit rate for full DEX to beat full STR without factoring in attackspeed. That’s 1100 crit chance AFTER subtracting from the enemy’s crit resist.

  • Most interesting find: 1:1 STR DEX actually underperforms to both pure STR and pure DEX at certain crit rate windows, which varies with weapons and enemy defense. However, it’ll look different with attack speed factored in.

The Tool

Here’s a graph where you can adjust your weapon’s attack value a and the enemy’s defense value d. The graph is at 1/10th scale to make it easier to see, so you’ll need to adjust accordingly (e.g. to try out a weapon with 1555 attack vs an enemy with 1000 defense, you’ll have to use 155.5 and 100 respectively). The values are changeable on the left sidebar.

https://www.desmos.com/calculator/dz6tmmpfdr

a is weapon attack.
d is enemy defense.
s is attack speed.

The red line is FULL STR.
The orange line is FULL DEX.
The black line is 1:1 STR DEX.

x axis is crit %.
y axis is damage/10.

The dots at x = 100 are attack values before the defense calculations.

Limitations
  • Note it is inaccurate at 0 and 10 attack for full DEX due to how log down is calculated. Otherwise, however, it’s enough to show the general trends.

  • Attackspeed was not put into the calculation for 1:1 STR DEX since there’s no accurate measure on its scaling.

Methodology

-Calculations for STR and DEX-

[details===Show==]First, this does not include the attack speed increase from DEX. This tends to be inconsistent due to ping issues, and has yet to be quantified accurately.

Because the calculations are based on average damage for ONE HIT, this is actually more applicable to skills since most of them tend to not be affected by attackspeed.

The formula for a crit is:

While a normal hit is simply:

Combined, we get:

Where “x” is crit chance.

We will use 20 stat points to keep it simple.

Full STR:

20 STR = 50 Attack

x [ (1.5)(50) + 0] + (100 - x) (50)

Simplified:

x(75) + (100 - x) (50)

Full DEX

20 DEX = 100 Crit Attack

x [ (1.5)(0) + 100] + (100 - x) (0)

Simplified:

x(100)

Right from the start, we see a couple things. In terms of RAW DAMAGE, DEX will scale better than STR at a higher crit rate. However, STR isn’t that far from matching up with DEX, and this is against an enemy with no defense.

1:1 STR DEX

10 DEX = 50 Crit Attack
10 STR = 25 Damage

x [ (1.5)(25) + 50] + (100 - x) (25)

Simplified:

x (87.5) + (100 - x)(25)

For the graph, I’ve used the full 330 stat points, and 160 160 for the 1:1 STR DEX.

Graph of raw damage, before calculating defense:

==Show Graph==

[/details]

-Calculations for Log Down Defense Formula-

[details===Show==]Looking at the formula, we see that there’s an AttackA and an AttackB:

damage = (% increase factor) x attackA x min {1, log10 ((attackB / (defense + 1))^0.9 + 1)} + (+ increase)

In the first set of calculations, only attackA was calculated. In terms of raw, undefended damage, it’s pretty accurate. What happens when we factor in the AttackB portion of it?

The Attack B Portion

min {1, log10 ((attackB / (defense + 1))^0.9 + 1)}

“min” will ensure that when log10(…) is greater than 1, it will keep the multiplier at 1.

The log10 Portion

log10 ((attackB / (defense + 1))^0.9 + 1)

More specifically, let’s take a look at the AttackB/Defense part. This means that the damage reduction will be proportional to your attack and the enemies’ defense. Here’s some rough plug n’ chug with some values:

[quote]Format: (Proportion of Attack/Defense) - (Damage that gets through)
0.10 - 5%
0.55 - 20%
1.00 - 30%
2.50 - 50%

12.0 - 100%
[/quote]

It takes an attack that’s roughly 12x greater than the enemies’ defense to get all the damage in without a reduction. Getting all the factors together would require case-by-case analysis, so I made a bunch of assumptions instead.

Enemy Defense: 1495 (random lvl 330 boss monster from tosbase)
Starting attack: 0 (before applicatoin of stats)
Stat points: 330

Weapon damage: 1500 (rough guestimate of “just started endgame” weapon)

Graph using these values:

==Show Graph==

Try some of the values in the adjustable graph, and play around with it. (see beginning of post for instructions)
https://www.desmos.com/calculator/dz6tmmpfdr

As we can see, full DEX suffers greatly because it’s unable to “penetrate” defense due to insufficient Attack Damage. Will gems, transcendences, buffs, and every damage mechanism make these even? Potentially yes, assuming we can get around 90% crit rate with 5000 attack damage from your weapon versus a 750 defense enemy. Do note though, this is without including Attack Speed into the calculations.

With Attack Speed, the ridiculously high requirements get lowered even further. However, since ping is involved, I’ve decided to just include a speed factor in the graph for everyone to play around with.[/details]


Resources

[details===Show==]


Any corrections are appreciated.

8 Likes

But STR affects the log down formula?

Forgot to include that. I was strictly looking at the attackA portion of:

damage = (% increase factor) x attackA x min {1, log10 ((attackB / (defense + 1))^0.9 + 1)} + (+ increase)

Taking the attackB portion into account would give even more reason to go full or mostly STR. However, DEX also provides block penetration. I’ll probably do another calculation including these some time later.

Updated with a graph tool to visualize how Defense affects overall damage, and the function to factor in basic weapon damage.

Revamped the whole post with fancy schmancy level 2 forum magic.

1 Like

[EDIT: INFO HERE IS NOT ACCURATE. Read at your own risk.]

Major info and calculations incoming potentially. Crit Attack actually might actually be included in the Log Down Defense calculations, which induces a whole explosion of construed numbers and self-induced panic.

Relax, this info is pretty much false. Crit atk does not change log down calculations

Edit: This is easily tested with a critical and min_atk = max_atk on semi-high def monsters

Relaxed, I shot my foot and found out that it was just a dream. Sleepiness ftfw.

“Crit rate” as in the raw number shown on your F1 window? or is your x axis referring to crit %?

If the latter, how does one find out crit % from the crit rate shown on F1. Whats the scaling/diminishing returns?

x axis is crit %.

In the case where crit resist is 0, we can simply find our crit% via (F1 Crit Chance)^0.6

The returns diminish the higher you go.

For ~66.8% crit%, you’ll need 1100 crit chance.

For virtually 100% crit%, you’ll need 2154 crit chance.

Still, your comment on the crit rate/chance/% clarity is justified, I’ll work on clarifying the crit chance/rate/% thing next edit. ToS could’ve used better terms for clarity on their part >.>

yea IMC’s in game UI doesnt explain or give enough details on virtually everything and anything. its annoying af.

If i am not mistaken, then is this the final version? i saw the June 18 update mentions up here as “I’ve screwed up, apparently crit attack is counted towards log scale down for defense. Revamping some of the formulas.Until then, I’ll change the conclusions section for the new overview. Sorry for anyone who put in points due to this guide :'D, updating asap.”.

Soooo my question is…

At what value of a weapon physical attack, is it more worth it to invest in red or green gems.

So theoretically for now unless someone goes and does it, A Full DEX build is still a stronger if not equal match to a STR build?

A full DEX auto-attack build with absurd amounts of crit and weapon damage WILL out scale full STR. Note how conditional this is; it applies to very specific classes with specific builds.

Full STR is more than viable now, as well as various ratios of STR DEX depending on the build you’re going for. Tailor it to your own needs., it’s much less of an “one stat rules all” now than before

1 Like

Autoattack archer builds have kneeling that gives patk equal to 2x dex if they went archer 3 and maxedit. At this point, full dex is going to be always better than str at any point ever since bringing cheapo monstrance scrolls will boost it by 30%. Also kneeling + swift step already gives like 350 crit rate which is already great to start with for dex…