Heal/Crit calculations.

[Scottx125]

it does increase, because you try more then once to get the actual results, if you test 100 times to get a head the chance to get it AT LEAST ONCE is like 99,98%

Yes. But percentage wise. Every time you flip that proverbial coin, the chance is still 50/50 to if you are gonna get a heads or tails. Probability creeps in when you no longer consider them individual events. But in the grand scheme it's still 37%. Or fairly close to it. Don't get me wrong, probability does factor in. But let's keep this simple .

Yes but grup heals arent individual event they work as reroll (for sake of semplicity x 6) so if you try group heal with 37% crits the actual avarage numbers of crits over 100 attempts wont be 37 out of 100 times but more like 60 out of 100. Try to belive xD

They are if it only results in 1 ability producing 1 heal that then heals everyone for the same amount (which is what you said earlier). Regardless I've never actually paid attention to that so I'm gonna corral a group of my guildies together tomorrow to test it.

Ok, so with some help from ChatGPT I understand what binominal probability is xD.

So the probability of healing at least 1 person out of 6 with a crit heal at 37% (individually) is:
>= 1 person = 94%.
>= 2 people = 72%.
>= 3 people = 39%.
>= 4 people = 14%.
>= 5 people = 2%.
>= 6 people = 0.02%.

But if it's as said before determined only by 1 cast that applies to everyone. It's 37% flat.

[Tesq]

Yes. But percentage wise. Every time you flip that proverbial coin, the chance is still 50/50 to if you are gonna get a heads or tails. Probability creeps in when you no longer consider them individual events. But in the grand scheme it's still 37%. Or fairly close to it. Don't get me wrong, probability does factor in. But let's keep this simple .

Yes but grup heals arent individual event they work as reroll (for sake of semplicity x 6) so if you try group heal with 37% crits the actual avarage numbers of crits over 100 attempts wont be 37 out of 100 times but more like 60 out of 100. Try to belive xD

They are if it only results in 1 ability producing 1 heal that then heals everyone for the same amount (which is what you said earlier). Regardless I've never actually paid attention to that so I'm gonna corral a group of my guildies together tomorrow to test it.

Thinking it about i always check personal khaine embrance and absorb tactic proc , they may very well be independent to one another, and i did just use the wrong things as reference; it would apply then to dok/wp bubble tactic and not to the group heal then; so i tested it and you are right they are individuals and don't work as re rolls. They work as rerolls just in case for stuff that proc on crits. So ye it's more imp look at diff between wilp and crit

[Absinth]

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Yes. But percentage wise. Every time you flip that proverbial coin, the chance is still 50/50 to if you are gonna get a heads or tails. Probability creeps in when you no longer consider them individual events. But in the grand scheme it's still 37%. Or fairly close to it. Don't get me wrong, probability does factor in. But let's keep this simple .

The difference is that group heal, heals all 6 members of party at once thus it rolls 6 times if it crits, if atleast one of them rolls as crit you heal one person with ti, to put it in perspective having 35% healcrit will result your SINGLE TARGET heals to be going as close to 35% as possible over time, but if you have group heals (assuming full party 6man) your probability is increased six fold as you need a single hit to have a crit, to know what is the chance to get a 35 or below on 6 man cast we have to calculate what is your chance to not hit it

0.65 x 0.65 x 0.65 x 0.65 x 0.65 x 0.65 = 0.088 * 100% = 8.8%

After you know that the chance to not hit 35 or below when rolling 100 is 8.8% we can calculate the chance for it to happen and that is 100% - 8.8% = 91.2%

Soo you have 91.2% to crit atleast one person and ~35% to crit two people, then it goes lower and lower

[Uchoo]

Tesq your understanding of math is..questionable.

Please consult your nearest Binomial calculator or qualified person before putting too much credence into those values. xx

[Tesq]

Guys if you keep reroll the chance increase it do not go lower im not a matematician but the thing scott wrote is the same error another man made into another forum the right formula i wrote it into a prec post or what @absinth wrote above. Still scott was right it wont always crit the whole group so the whole point work only for stuff that crit on heal which is easier to proc on group/area heals. So first post of scott is probable right willp is better than heal crit for average heal output.

Reroll always > than 1 dice roll
Its the same thing from D&D to war40k

What you could test @scott is if there is any diff under heat debuff idk.

[BluIzLucky]

Yes, group heal vs single doesn't matter, becuase they are still counted as individual heals, just one has more ticks per cast.
E.g. if you increase healing by 10% from willpower,
1 * 6 * 1.1 = 6.6

You'd still need to get 20% heal crit to increase by the same amount;
1 * 6 + (6 * 0.20 * 0.5) = 6.6

Of course if you are trying to have 100% uptime on crit procs, for RP heal bonus, then you can justify less crit being worth the same as equivalent raw heal bonus from willpower.

Oh, 700 willpower is not low. It's probably average for most defensive WP's I know. Primarily because we rely on stacking heal inc % procs from Knights/RP.

600-700 is "low" because it's your base value as endgame healer, you have invested 0 tactics, talis, renown or potions to get it.
anything you add in to wp from here is a trade-off from other stats.

You'd need to look at the outgoing heal stats in Enemy for Warrrior priest, then adjust the willpower scaling for each skill according to how big a share of total healing it does on average:

This is the scale per wp:
((Base heal + heal per wp * wp) / base heal - 1)

E.g. AM with 10 willpower:
EoV = 50% total , 0 scaling
15s HoT = 35% total, ((2200 + 0.9 * 10) / 2200 - 1) = 0.4% scaling
Other heals = 15% total, 0.3% scaling

Then you get an avg 10 wp scaling of:
0.5 * 0 + 0.35 * 0.4 + 0.15 * 0.3 = 0.185%

Vs 1% heal crit = 0.5%.

It's a bit simplified, you'd need to add your existing willpower, crit % and other modifiers, and then do a "cost per % gain" for both wp and crit (e.g. 160 wp vs 10% crit tactic, renown, etc).

And balance for other benefits of each, but you get the idea.

[Scottx125]

Yeah, I thank you for introducing me to binominal distributions. I believe I understand it. And it's generally just the measure of a % chance in a sequence of events based of the expected number of successes. And therefore is kind of a real-ish way to simulate the effective result. However. But it's all theoretical and ofc knowing %, for one case one person could experience exactly 37% crit chance. Another even at 37% might only have 20%. Highly unlikely but it's possible. I'll come back with some more testing results.

[Scottx125]

Touch of the Divine as well as other AoE heals are individually calculated.

[Omegus]

I'm making the comments below as I read the thread, so apologies if I answer something that gets answered later on.

I am just going to refer to "willpower" as the stat that improves healing output, even though technically it is "willpower and healing power" just to save space when typing. For the purposes of healing they both work the same.

Any calculations that try to compare willpower to crit in the general sense are mostly worthless. Healing abilities are made up of a base heal (typically only affected by the ability rank, which itself is based on career rank and mastery points) and a bonus healing from willpower. The value of the base heal and the amount of bonus healing actually gained from willpower varies from ability to ability. Assuming you are just trying to work out the highest average healing output per second (IMO not a great benchmark...) then any comparisons must be done on a per-ability basis that correctly account for base healing and contribution from willpower.

The base healing is important as the critical heal multiplier increases the total heal value, not just the healing contributed from willpower, so for some abilities that have high base healing and almost no contribution from willpower, crit becomes the only thing that can boost the healing output.

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My calc is that 5 willpower = 1 bonus heal, and that scales in a linear fashion up to the softcap. Crit, is worth ~ 9 willpower. That being calculated from the average heal crit of 1.4 (1.3 + random range of 20% ontop). So if you had gear that has 0 willpower and 1% crit or another piece that has 12 willpower, technically speaking the 12 willpower would outheal the 1% crit.

Firstly, 5 willpower with a 1.4 multiplier becomes 7 willpower, not 9 willpower. Anyway...

5 willpower = 1 "healing per second" (HPS), so 800 willpower is 160 (HPS). The HPS stat is meaningless on its own, but each ability has an HPS multiplier which determines how much bonus healing it gets from the HPS stat, much like how offensive abilities get damage bonus from the melee/ranged/magic DPS bonus (which is based on strength/ballistic skill/intelligence) with a per-ability multiplier. When calculating the non-crit healing value, the formula is:

(Ability base heal) + (HPS * ability HPS multiplier) = final heal.

Each ability has its own HPS multiplier and it works the same as the primary stat multipliers for damage abilities. Typically for single-target direct healing the multiplier is equal to either the GCD or the cast time (whatever is higher). This is reduced for AoE healing and HoTs, and AoE HoTs typically have the lowest HPS multiplier of all.

The crit version is:

((Ability base heal) + (HPS * ability HPS multiplier)) * (randomised crit multiplier) = final crit heal

The crit multiplier affects the base healing as well as the bonus healing from HPS. Whether it is better to pump stats into crit or willpower very much depends on the ability HPS multipler (which can actually be 0, meaning willpower does nothing) and the ratio between the base heal and the amount of actual bonus healing from HPS * multiplier.

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lots of posts about group heal crit chances

The conversation about this is terrible. Assuming a full group of 6 people and the heal crit chance is 35% from the healer (I am ignoring the hidden base chance to be heal crit which I believe is 5%?):

Each time you use the group heal, each person has a 35% chance of being critically healed. This is one crit check PER PERSON, not one per group, and the result only affects that person. E.g. if I crit heal on Alice, then that does not automatically mean I crit heal Bob. Bob has his own chance to be crit healed. It is entirely possible for a single group heal to crit heal 0/6 people, 1/6 people, 2/6 people, 3/6 people, 4/6 people, 5/6 people or 6/6 people depending on how many of those random crit chance rolls end up succeeding.

Sometimes the healer will have procs which trigger on direct critical heals - including group heals - that affect the person who received the group heal (such as the Zealot/RP's +25% incoming healing tactic). For these procs/effects, the group member that was actually crit healed is the only one who gets the buff. Example: if I crit heal Alice but not Bob, then Alice gets the extra effect from the tactic but Bob does not. Having more people in the group does not increase the chance of other people getting the bonus as the crit heal chance is a per-person check, and the tactic only affects the person who was crit healed.

Sometimes the healer will have procs which trigger on direct critical heals - including group heals - that affects themselves (such as Restorative Burst, which gives the caster a buff that grants them AP per second for a few seconds). The chance of this triggering DOES scale up with the number of people in the group, as it will trigger provided at least 1 person in the group was critically healed. The maths for this is a bit unintuitive, as you actually work out the chance of not getting a single crit and then subtract that from 100% to get the chance of at least 1 crit. Assuming 35% heal crit chance, the chance of not getting a crit is 65%, or 0.65 in decimal notation. The chances of NOT getting a single crit are:

2 people in group (including self): 0.65^2 = 0.4225, or 42.25%. This can also be calculated as 0.65 * 0.65.
3 people in group (including self): 0.65^3 = 0.274625, or 27.46%. This can also be calculated as 0.65 * 0.65 * 0.65.
4 people in group (including self): 0.65^4 = 0.17850625, or 17.85%
5 people in group (including self): 0.65^5 = 0.1160290625, or 11.60%
6 people in group (including self): 0.65^6 = 0.075418890625, or 7.54%

So then, the chances of getting at least 1 crit to trigger something like Restorative Burst on the healer is:

2 people: 100 - 42.25 = 57.75%
3 people: 100 - 27.46 = 72.54%
4 people: 100 - 17.85 = 82.15%
5 people: 100 - 11.60 = 88.40%
6 people: 100 - 7.54 = 92.46%

It will never hit 100% unless your crit chance is 100%, but it can get very close.

[Scottx125]

Firstly, 5 willpower with a 1.4 multiplier becomes 7 willpower, not 9 willpower. Anyway...

5 willpower = 1 "healing per second" (HPS), so 800 willpower is 160 (HPS). The HPS stat is meaningless on its own, but each ability has an HPS multiplier which determines how much bonus healing it gets from the HPS stat, much like how offensive abilities get damage bonus from the melee/ranged/magic DPS bonus (which is based on strength/ballistic skill/intelligence) with a per-ability multiplier. When calculating the non-crit healing value, the formula is:

Oh my god I can't believe I made that mistake, shows the issue of doing maths at 3am in the morning . That makes crit even worse >.<.