New Stun Threshold Reduction Formula--Plots!

These were handy for me, so I thought I'd share.

From the mechanics thread, here is the new stun threshold formula, with diminishing returns:

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Qarl wrote:

Stun Threshold Reduction - diminishing return


When calculating Stun with Stun Threshold Reduction of over 75%, the Stun Threshold Reduction is treated as being:

75 + ( Stun Threshold Reduction - 75) * 25 / ( Stun Threshold Reduction -50 )

instead.

A simplified explanation from sould4hdwn:

"

soul4hdwn wrote:

stun threshold
for values 0 to 75 percent, it is listed number.
for values above 75 percent, it is 75 +[ (full value -75) *25 /(full value -50) ]

% of hp in damage needed for 100% stun chance, (100 - value above) /2
% of hp in damage needed for 25% stun chance, (25 *(100- value above)) /200 or divide previous line by 4

Here's what it looks like (in all plots, dashed lines are the old formula):

link (high quality): http://i.imgur.com/BeMZa52.png

Zooming in above 70% threshold reduction:

link (high quality): http://i.imgur.com/P8HgJcq.png

It rolls over pretty quickly. 85% effective reduction requires >90% listed reduction, 90% effective reduction requires >110% listed reduction, and 95% effective reduction isn't possible below 140% listed reduction.

Stun threshold reduction can be higher than 140% (soul4hdwn calculates 170%, corresponding to 94.8% reduction), but 140% is not too difficult to achieve even without specialized uniques or other equipment.



Here's what it means in terms of the fraction of life required to stun:

link (high quality): http://i.imgur.com/jY5FrQ2.png

Zooming in above 70% threshold reduction:

link (high quality): http://i.imgur.com/ObkYnfZ.png

Even above 110% stun threshold reduction, one still needs to do a sizable amount of damage (>5% of enemy life) to have a 100% chance of stunning. Also, remember that 25% probability to stun is the threshold: lower probabilities do not ever result in stuns.

let me elaborate max effective stun threshold from uniques,passives,support gems is 95%. Assuming cruel Piety has 1.4e7 HP(without ES) to have even chance to stun her you need deal 700 damage,3500 for 100%. It is a little bit far from the reach of non crit Physical damage based build.

Piety health was calculated with 175 min damage 99% stun threshold reduction ground slam. (verdict 0% chance to stun, damage below 25% chance)

can simplify to for textual discription:

stun threshold
for values 0 to 75 percent, it is listed number.
for values above 75 percent, it is 75 +[ (full value -75) *25 /(full value -50) ]

% of hp in damage needed for 100% stun chance, (100 - value above) /2
% of hp in damage needed for 25% stun chance, (25 *(100- value above)) /200 or divide previous line by 4
vs es, double it.

"

bormoth wrote:

let me elaborate max effective stun threshold from uniques,passives,support gems is 95%. Assuming cruel Piety has 1.4e7 HP(without ES) to have even chance to stun her you need deal 700 damage,3500 for 100%. It is a little bit far from the reach of non crit Physical damage based build.

Piety health was calculated with 175 min damage 99% stun threshold reduction ground slam. (verdict 0% chance to stun, damage below 25% chance)

bormoth, where is the 95% number coming from? I couldn't find it referenced by devs.

"

soul4hdwn wrote:

can simplify to for textual discription:

stun threshold
for values 0 to 75 percent, it is listed number.
for values above 75 percent, it is 75 +[ (full value -75) *25 /(full value -50) ]

% of hp in damage needed for 100% stun chance, (100 - value above) /2
% of hp in damage needed for 25% stun chance, (25 *(100- value above)) /200 or divide previous line by 4
vs es, double it.

Thanks! I've put this in the initial post.

One clarifying question: I had thought that ES meant that after the calculation, there was a 50% chance that there would be no stun: i.e. the max stun probability vs es is 50%. Is that incorrect?

"

FrederickHermanJonesJr wrote:

"

bormoth wrote:

let me elaborate max effective stun threshold from uniques,passives,support gems is 95%. Assuming cruel Piety has 1.4e7 HP(without ES) to have even chance to stun her you need deal 700 damage,3500 for 100%. It is a little bit far from the reach of non crit Physical damage based build.

Piety health was calculated with 175 min damage 99% stun threshold reduction ground slam. (verdict 0% chance to stun, damage below 25% chance)

bormoth, where is the 95% number coming from? I couldn't find it referenced by devs.

"

soul4hdwn wrote:

can simplify to for textual discription:

stun threshold
for values 0 to 75 percent, it is listed number.
for values above 75 percent, it is 75 +[ (full value -75) *25 /(full value -50) ]

% of hp in damage needed for 100% stun chance, (100 - value above) /2
% of hp in damage needed for 25% stun chance, (25 *(100- value above)) /200 or divide previous line by 4
vs es, double it.

Thanks! I've put this in the initial post.

One clarifying question: I had thought that ES meant that after the calculation, there was a 50% chance that there would be no stun: i.e. the max stun probability vs es is 50%. Is that incorrect?

I think the 95% is assuming you have all the stun thresshold reduction gear, passives, skills and gems (i.e. reduced weapon, reduced belt, lvl 20 gem, ground slam, all the passives) you still cant get over 95% stun thresshold reduction. This seems to be in line with my math too. When I was playing around with the formula it seems to converge around effective 95% reduction.

Thank you for your help with the graphs, they're really useful.

get all threshold passives,maxxed stun support best belt(non unique unique there are can be better, and this hammer.
put value into formula above.

Es just gives 40% chance to evade stun w no matter what(if not changed) while you have ES, and seems not part of formula. Don't know how it interracts with chance to evade stun passives.

P.S. Diminishing returns get so bad that you may not even bother to get alot of it.

"

bormoth wrote:

get all threshold passives,maxxed stun support best belt(non unique unique there are can be better, and

this hammer.
put value into formula above.

Es just gives 40% chance to evade stun w no matter what(if not changed) while you have ES, and seems not part of formula. Don't know how it interracts with chance to evade stun passives.

P.S. Diminishing returns get so bad that you may not even bother to get alot of it.

"

FamousTrip wrote:

I think the 95% is assuming you have all the stun thresshold reduction gear, passives, skills and gems (i.e. reduced weapon, reduced belt, lvl 20 gem, ground slam, all the passives) you still cant get over 95% stun thresshold reduction. This seems to be in line with my math too. When I was playing around with the formula it seems to converge around effective 95% reduction.

Thank you for your help with the graphs, they're really useful.

Thanks, got it. Using the maximum stun threshold reduction that soul4hdwn calculated (170), the effective reduction is 94.8%, which is now in the text. As you said, for the time being, 95% is more or less an effective maximum.

"

FrederickHermanJonesJr wrote:

One clarifying question: I had thought that ES meant that after the calculation, there was a 50% chance that there would be no stun: i.e. the max stun probability vs es is 50%. Is that incorrect?

ah, sorry, i might have gotten confused by the long time ago explanation of es with stun interaction. having es means 50% less chance to be stunned. key words "less" and "chance" so may actually be 1.5 times on the final result. although that gets ugly very fast despite nice even number due to the diminishing returns making horrid values.

edit: somewhat relevant http://www.pathofexile.com/forum/view-thread/11707/filter-account-type/staff/page/6#p542785 two avoid stun answer responses.
es is "50% cannot be stunned", so it'll be more like "50% chance is max chance to stun vs es".

in the past with the old linear threshold math, the 50% cannot be stunned was highly annoying but didn't really stop me from stunning outright. definitely felt less stuns happening but not a full 50/50 but i had limited tests vs es then.

Ok, I've deleted reference to ES in the initial post. You're right--it gets more complicated fast, so we can just keep this focused on the new formula.

sorry about edit spam just then.