# Fun with math! Thorn's crit multiplier and other goodies

Was doing some testing, and found that thorn’s crit multiplier is really weird.
A completely uncharged arrow are level 3 does 150 damage. That same arrow crits for 224 damage. The crit multiplier is 1.493 rounded.
A fully charged arrow on an uncursed target does 217 damage. In the same circumstances that arrow will crit for 326 damage. So the crit multiplier is actually higher with a charged arrow on an uncursed target at 1.502 rounded.
This is where it gets different, and confused me for a bit. A cursed arrow on a cursed target will do 272 damage. A cursed crit arrow on a cursed target will do 380 damage. This gives us a crit multiplier of 1.397 rounded. The crit multiplier is also multiplied by the curse multiplier. So to find the crit damage of a cursed arrow on a cursed target you would take

1.251.397D=C
D= damage of fully charged arrow on a non-cursed target.
C=total crit damage dealt.

for instance at level seven a fully charged arrow on a non-cursed target does 273 damage.
1.251.397273=476.726 crit damage on a cursed target with a cursed arrow at level seven.
After I did the formula I tested it in game on a nice stationary boulder, and got 478 damage. Considering my crit multipliers are rounded to the nearest thousandth, this is pretty close.

Also the volley crit multiplier is 1.483.
At level seven each volley arrow does 77 damage. If you wanted to hypothetically find the crit damage from landing all 5 arrows into someone’s dome while they are cursed, this is the formula

VH(1.251.483)=C
V=individual volley damage
H=volley arrows hit in dome
C=total crit damage

With this formula we get 713.693 total damage at level seven with all five arrow hit. In game I got 714 damage pop up.
If one were to actually hit all seven arrows into someone’s head from the seven arrow volley, one could do 999.171 damage. Haven’t tested that one in game yet, but the formula has worked for all five arrow volley tests I have done.
All testing was done without gear of any sort.

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Makes Burst Dash’s risky cooldown spending crazy math look weaker haha

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Haven’t actually seen the math on that one. Might have to look it up one of these days

I’d reccomend any of @Nemosis327 threads. He’s spent the most time on Deande here, math and otherwise. Calculated risk makes for fun

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Someone once asked me, “how much damage can volley even do?” They had recently died to a volley headshot in a match, and couldn’t believe the 600 some odd damage they received. I told them it was possible, but at the time I hadn’t done any testing to see just how far volley damage could actually go. Now I am curious.

My new goal is to make a hypothetical absolute most damage possible by a single use of volley under any and all circumstances, no matter how unlikely, to a single battleborn enemy in game formula. Then after I get my hypothetical results, I want to try recreating it in game.

I have already found what I believe to be the most damage possible with only Thorn’s helixes, and gear taken into account. I will post the math at a later date when I have tested a few variables I am not 100% sure about. There are a few tests I need to make before I start posting any results however. Hopefully I should be done with them within a few days. Then before I go any further, I need to farm a legendary piece of gear that is detrimental for this experiment.

I see some good times coming in the future. Can’t wait to share the results.

Ok, putting the volley speculation on the backburner for now. I still need a legendary before I can even test any of my math for accuracy, so it could be a while before I get that far. Now I have a new project.

@loving-hatred you might find this interesting.

Instead; I have a new interesting tidbit of information for you. What if I told you that skill damage could increase your damage with basic arrow attacks.

Would you call me crazy? If so I wouldn’t blaim you, but you would be incorrect about my craziness.

First, thanks @Nemosis327 for shedding some light on how skill gear can increase passive ability damage, or in our case, damage multipliers. He has a great Deande thread that goes into detail about this phenomenon.

Thanks @SirWalrusCrow for being a nice solitary Kelvin I could collect numbers on. Without him this could have taken a lot longer to figure out. This was also the person who was a stationary target so I could find Thorn’s crit multipliers earlier, just didn’t know their forum name at the time.

Let’s get cracking

Ok, so the way it works with Deande’s passive. Skill damage gear is effectively counted twice when her passive, element of surprise, is active and a skill is used. If you want more details on exactly how it works on Deande, go read Nemosis327 thread. It is what gave me the idea to test this in the first place.

Let’s begin. All testing was done at level ten.

Blight at level ten, without any of the blight damage increasing helixes, does 65 damage per .5 second tick. On a cursed target without hextension, it does 81 damage. On a cursed target with hextension, it does 87 damage.
Now let’s add skill damage. If one were to assume that skill damage effects Thorn’s passive damage multiplier the same way it effects Deande’s, then we have an easy formula. Let’s add one 9.1% skill damage gear on hextension blight damage.
1.351.091=1.47285. This is our new curse multiplier.
65
1.472851.091=104.447.
After testing this in-game, I have found that it does not work like this at all. Instead, blight dealt 95 damage. See what happens when we assume?
65
1.35*1.091=95.73525.

Dang. This proves that skill damage does not actually effect thorns passive damage multiplier, right? Still wrong. Thorn’s passive increases all damage dealt to a cursed target by skills and fully charged arrows. Fully charged arrows!

Alright, so a level ten fully charged arrow on a non-cursed target will do 315 damage. On a cursed target (non hextension so only 25%) we get 394 damage. Let’s add the 9.1% skill damage to that.
1.251.091=1.36375. This is our new curse multiplier.
1.36375
315=429.58
I got to level ten in game to confirm my math, and I did 401 damage after curse with 9.1%skill gear. This is nowhere near the number we expected, but it is still more damage then the regular cursed target shot (394.)

Why can’t anything work the way I wanted it to.

After running some numbers through a calculator, I got this.
20.233736%
What is this number you ask? This is the percentage of skill damage percent used to increase Thorn’s passive, but only when the passive is effecting fully charged arrows. You lost yet? Let’s do some more math!
First we must find out our skill damage multiplier.
0.0910.20233736= 0.0184127. This is the skill damage multiplier that now effects our passive. Also known as 1.84127%
1.0184127
1.25=1.27301587*315= 401.000001 damage. Exactly what we got in game earlier!! Woo progress!

Let’s test this with two pieces of skill damage. 9.1% and 5.46% on a level ten cursed target.

.091*.20233736=.0184127
.0546*.20233736=.01104762
1.011047621.0184127=1.02966374
1.02966374
1.25=1.28707968*315= 405.43 damage total.
In game with the same circumstances, I got 406 damage.

Conclusion: with a primary and secondary skill damage gear active, one can increase damage with cursed arrows on a cursed target at level ten by…

12 damage!!!

Kind of a letdown isn’t it.
Oh well, I still had a good time doing this, and it was still interesting exactly how weird some of thorn’s multipliers are.
Too much math. Need beer.

Edit: multiple grammar mistakes, and misspelled words.
@FlamesForAll

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It’s interesting to me but not because of the reason I think you intended, it stands to reason then that even without bleed damage that fully charged arrows will proc shield web/bola’s which would be vicious! Even a thorn who’s a true sniper can tip an even fight with a single well placed arrow

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Shield Web isn’t even useful past level 5 if you take Hexsanguination, because it does pretty much the same thing anyway. Bola’s, though… I like it.

Here is an easier way to look at the damage numbers.

• Charged arrow - 315
• Charged arrow on cursed target - 394
• Nature’s Curse - +25% damage (already accounted for in the 394)
• Skill damage gear - +9.1%

`(394 - 315) = 79 79 x (1 + 0.091) = 86.189 315 + 86.189 = 401.189`

This is because skill damage will only boost the bonus damage granted by Nature’s Curse, not the entire arrow.

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In incursion it means you can make an 18 second window before a sentry shield begins recharging using the bleed damage though

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Great shortcut!

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Oh damn. That is about ten times easier lol.

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I still need to get a bolas and shield web to properly test both of these. As soon as I do it’ll be the first thing I test.

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I have shield web so if we do a private match i can assist there and if it activates shield web interdictor then we can proceed with the assumption that bola’s will activate as well

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Sounds like a plan to me. Maybe not today, but possibly some day soon when we are both on. I need beer and some fun matches after spending several hours doing all that math the difficult way.

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Wait really? So does the legendary effect apply on the first tick of damage or the last?

I would infer that each tick renews the timer

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Hmmm. Maybe I’ll have to test that at some point.

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I can confirm it’s vicious with Kleese

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