Critical healing chance, an approximation (MOD17 UPDATE)

thavi2013 · June 2019

MOD17 UPDATE! New formula tested by Janne and Sharpedge:
critical healing chance = 0.4 x (critical strike / power) = critical strike / (0.25 x power)

I also recommend to check out Janne's page about healing mechanics! https://jannenw.info/pages/mechanics16/heals

My old post from Mod16:
Since the AMA we know that crit healing is based on a ratio between critical strike and power. So I did some tests to find a formula. I was using different ratios while standing in the lava in Mount Hotenow and healing myself with Bastion of Health.

tl;dr: I think the formula is approx: crit chance = 0.333 x (critical strike / power) = critical strike / (3 x power)
cap is 50%

Tests to check the cap:
9k Power and 22k Critical Strike. Result: 222/417 crit heals (53%).
50k Power and 120k Crit. Result: 100/200 (50%).
Conclusion: seems to be capped at 50%. Would make sense because DPS crit chance is also capped at 50%.

Tests to check the relation between Power and Critical Strike:

Power	Critical Strike	Ratio (Crit:Power)	Crit Chance	Chance / Ratio
24k	6k	0.25	7% (8/108)	0.28
26k	13k	0.5	13% (19/144)	0.26
165k	97k	0.59	15% (30/200)	0.25
155k	120k	0.77	28% (111/400)	0.36
100k	97k	0.97	28% (56/200)	0.29
120k	120k	1.0	34% (134/400)	0.34
5.2k	5.2k	1.0	30% (59/200)	0.3
95k	120k	1.26	41% (164/400)	0.33
100k	137k	1.37	42% (84/200)	0.31

As you can see, the "Chance / Ratio" is always around 0.3. So my approximation seems to be good. But all tests were done under the same conditions. For example, not considered in my tests are: scaling, character level, zone level (counter stats) and so on. Moreover, I didn't test for a minimum crit chance. ~~It could also be 0.25 * (crit / power) + 0.05?~~

I hope this is useful for someone.

Amazia
Civil Anarchy

vorphied · June 2019

Thank you for testing!

I'm still going to pretend that this system doesn't exist and continue to build like a sane person, but I appreciate you taking the time to test and sharing the information.

dread4moor · June 2019

thavi2013 said:
Hi all!
Since the AMA we know that crit healing is based on a ratio between critical strike and power. So I did some tests to find a formula. I was using different ratios while standing in the lava in Mount Hotenow and healing myself with Bastion of Health.

tl;dr: I think the formula is approx: 0.3 x (critical strike / power), cap is 50%.

Tests to check the cap:
9k Power and 22k Critical Strike. Result: 222/417 crit heals (53%).
50k Power and 120k Crit. Result: 100/200 (50%).
Conclusion: seems to be capped at 50%. Would make sense because DPS crit chance is also capped at 50%.

Tests to check the relation between Power and Critical Strike:
Power Critical Strike Ratio (Crit:Power) Crit Chance Chance / Ratio
24k 6k 0.25 7% (8/108) 0.28
26k 13k 0.5 13% (19/144) 0.26
165k 97k 0.59 15% (30/200) 0.25
155k 120k 0.77 28% (111/400) 0.36
100k 97k 0.97 28% (56/200) 0.29
120k 120k 1.0 34% (134/400) 0.34
5200 5200 1.0 30% (59/200) 0.3
95k 120k 1.26 41% (164/400) 0.33
100k 137k 1.37 42% (84/200) 0.31
As you can see, the "Chance / Ratio" is always around 0.3. So my approximation seems to be good. But all test were done under the same conditions. For example, not considered in my tests are: scaling, character level, zone level (counter stats) and so on. Moreover, I didn't test for a minimum crit chance. It could also be 0.25 * (crit / power) + 0.05.

I hope this is useful for someone.

Amazia
Civil Anarchy

Very interesting.
I don't quite understand the second dataset at Crit/power 1.0.
Is that 5.2k power and crit? 52K? Is that a typo?

Imma try on a naked preview test toon, this time with fixation of variables.
Null H: With fixed crit stat, no change in crit chance with variance of power.

Appreciate you taking the initiative. This needs to be resolved.

raziel2004 · June 2019

Thanks..

thavi2013 · June 2019

dread4moor said:

Very interesting.
I don't quite understand the second dataset at Crit/power 1.0.
Is that 5.2k power and crit? 52K? Is that a typo?

That is not a typo, it's indeed 5200 or 5.2k. I wanted to test with smaller absolute values to see if that has any effect. But I'll edit this so that it's better readable!

dread4moor · June 2019

Crit rate is 30% at 5.2K Crit (same 5.2K Pwr)...
Crit rate is 15% at 97K Crit (127K Pwr)?

>90K stat points functionally erased?
Wow. I sure hope that is wrong.
Because if that is NOT wrong in the literal/statistical sense, that IS "wrong" in the logical and equivocal sense.

thavi2013 · June 2019

I'd say, don't focus too much on the absolute values. If you think about it, a certain ratio or counter-stat mechanic makes sense. It gives low IL characters a chance to crit as well as high IL chars. Though I'm not saying this solution is perfect or without any drawbacks.

Looking at my tests with larger samples (400), it seems the factor could be 0.333 (1/3). So maybe more like Crit chance = Critical Strike / (Power * 3) ?

dread4moor · June 2019

thavi2013 said:
I'd say, don't focus too much on the absolute values. If you think about it, a certain ratio or counter-stat mechanic makes sense. It gives low IL characters a chance to crit as well as high IL chars. Though I'm not saying this solution is perfect or without any drawbacks.

Looking at my tests with larger samples (400), it seems the factor could be 0.333 (1/3). So maybe more like Crit chance = Critical Strike / (Power * 3) ?

I'm glad your not saying it makes sense cause it doesn't.
When did low level healers (and ONLY healers, not DPS in this formula) ever complain "gee, I wish I could crit as much as those elite healers".
It's a solution in need of a problem. Tail wagging the dog, etc.

Well, let's get to testing it then.

But we need some more strict controls/methodology:
Preview isolation (empty instance)
"naked" toon (respec, test weapon, minimum gear to add offense slotted radiants and empowered only)

Crit fixed/constant just above cap
Titrate power (crit constant) from min to max with fixed-quantum source (eg. radiants, empowered)
High N value... ugh. This is gonna take a while.

I'm on it...

Edit:
This is my prediction.
35931pw 80215cr
If Crit chance = Critical Strike / (Power * 3) ...
... then the "ratio reduction" will be visible when crit chance drops below cap (which is why you test just ABOVE crit cap with fixed crit):

80215/(P*3)= .49 or .49(P*3)=80215
P= 54568
If this equation is correct, my crit % will begin dropping beneath cap at 54.5K Power.
Working on it...

thavi2013 · June 2019

Did some more quick tests to check if the formula is plausible. As you suggested with Crit fixed. Here are my results (sample size was only 100 per test):

Power	Crit	Expected Value	Test Result
10k	15k	0.5	0.56 (56/100)
12.6k	15k	0.4	0.38 (38/100)
15k	15k	0.333	0.29 (29/100)
25k	15k	0.2	0.23 (23/100)

I think that looks pretty plausible, no big deviations.

dread4moor · June 2019

> @thavi2013 said:
> Did some more quick tests to check if the formula is plausible. As you suggested with Crit fixed. Here are my results (sample size was only 100 per test): Power Crit Expected Value Test Result 10k 15k 0.5 0.56 (56/100) 12.6k 15k 0.4 0.38 (38/100) 15k 15k 0.333 0.29 (29/100) 25k 15k 0.2 0.23 (23/100)
>
> I think that looks pretty plausible, no big deviations.

You are sooo much more patient than me.
I am ready the chew off my arm around Bastion of health #75 lol.
I'm only up to 5 of 10 runs (100 each).
But spoiler: pretty similar results so far.
You've shamed me into finishing, just for SCIENCE.
That is some awesome effort and dedication. Thanks.

thavi2013 · June 2019

dread4moor said:

You are sooo much more patient than me.
I am ready the chew off my arm around Bastion of health #75 lol.
I'm only up to 5 of 10 runs (100 each).
But spoiler: pretty similar results so far.
You've shamed me into finishing, just for SCIENCE.
That is some awesome effort and dedication. Thanks.

Hehe! Yes, testing this stuff is not very exciting.
Thank you also for taking the time to test this. The more independent tests we have, the better.

By the way. I noticed that my crit heals were lower than expected. There seems to be something wrong with crit severity. Time for even more testing!

thavi2013 · June 2019

Here are some ACT results from my latest LoMM runs (for Bastion of Health):

Power	Critical Strike	Expected	ACT Result
180k	95k	17.6%	15.8% (32/203)
180k	95k	17.6%	17.6% (54/307)
155k	120k	25.8%	23.4% (50/214)
155k	122k	26.2%	28.6% (110/384)
138k	138k	33.3%	35.3% (103/292)
138k	138k	33.3%	28.4% (42/148)

The last one is probably not valid, because my game crashed in the middle of the run. Maybe I will repeat this one.
Also, keep in mind that my Power was fluctuating because of buffs (Alabaster, Gurtunk's etc).

I noticed people are very sceptical about this formula, because the crit chance is so low: "This cannot be! My crit chance is much higher!!!". Well, I would probably say the same if I had not tested this myself. And I think there is a simple explanation: the crit chance is calculated for each player individually. That means when healing multiple players you will often see at least one crit. Moreover, don't look at Healing Word! Crit for HW is calculated for the very first tick. All subsequent ticks will crit if the first one did.

It would be great if more people would make their own tests and shared the results

chinchyanimal4 · June 2019

Thank you for sharing 😊😊

truhart · June 2019

so in layman's terms power and crit strike is 'better' if value is near each other? or .....

vorphied · July 2019

truhart said:
so in layman's terms power and crit strike is 'better' if value is near each other? or .....

From what the posters here have tested, it appears that you can increase your healing critical chance further if your Crit exceeds your Power. Unless you deliberately try to avoid adding Power bonuses while adding Crit well beyond the DPS cap, you'll see your healing critical chance drop as you gear up. Hopefully this gets revisited along with stuff like those feats that give you bonuses for having two stats with dramatically different caps close in value.

clericalist · August 2019

Does anyone know if the critical heal mechanics has changed with mod 17? I say this because I have come across some videos saying something changed, but what exactly is not known, or is this just rumours?

thavi2013 · August 2019

Janne and Sharpedge tested the changes on preview. The new formula is Critical healing chance = 0.4 * crit / power = crit / (power * 2.5)

Also make sure to check out Janne's mechanics page, it's awesome: https://jannenw.info/pages/mechanics16/heals

truhart · August 2019

This is awesome. BUT can you you put in game terms, for the dummies like me.
I can have 160k power,I can go as high as 60% outgoing healing bonus, Critical strike can be as high as 120k, Crit severity 90%
I cant have all at once whats the happy best stats pls.
Thank you.

vorphied · August 2019

Disappointing that crit healing chance is still dependent on crit/power ratio. I was hopeful that they'd drop this counterintuitive approach, but obviously not.

mrimsogood · August 2019

> @truhart said:
> This is awesome. BUT can you you put in game terms, for the dummies like me.
> I can have 160k power,I can go as high as 60% outgoing healing bonus, Critical strike can be as high as 120k, Crit severity 90%
> I cant have all at once whats the happy best stats pls.
> Thank you.

Outgoing healing is top priority. Power next. Then crit. Last is CS.

Never sacrifice power for crit and never sacrifice outgoing healing for anything

kangkeok · August 2019

mrimsogood said:

Never sacrifice power for crit and never sacrifice outgoing healing for anything

Not entire true though. As a paladin, I actually perform better in boreworm phase after sacrificing power for crit.

brb89 · August 2019

Me too, as a sw: we have very low hmagnitude. With some crit heal i can heal better, obviously i dont aim for crit cap, but with Power near crit i can have a good %. Ill try just to rise them together as much as i can

truhart · August 2019

I'm really healing so much better if I sacrifice power for Crit tbh, just saying. ima DC

arazith07 · August 2019

You don't have to sac power for crit, just get companion gear with crit on it. As long as you aren't lowering other stats to much. But as a healer you don't need as much Acc or CA. That gear can't have power on it anyways, aside from enchants.

waldenmist · August 2019

Any mod17 update on this? Apparently they've changed the formula.

vorphied · September 2019

truhart said:
I'm really healing so much better if I sacrifice power for Crit tbh, just saying. ima DC

Basically all of what arazith07 said. I still think this system is ridiculous, but with the state of endgame content you really don't need to care at all about offensive balance on a healer since the design is clearly to keep healers busy healing and focusing on resource management, which frees up a lot of options while still maintaining Power.

However, critical healing for Cleric and Warlock should be taken with a grain of salt. Paladins gain a special benefit in that their overhealing generates more shielding and is rarely wasted; Clerics and Warlocks gain no benefit at all from overhealing and can never plan on a crit heal.

Yes, your overall healing output will be affected by crits, but depending on the situation and on which powers you're using at the time, it may also be of limited or no practical benefit.

Critical healing chance, an approximation (MOD17 UPDATE)

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