Vitality and healing % (math)

Enialas · 03-30-2007, 07:18 AM

For those who may be interested, I've detemined the equation to derive the healing % that shows under the Vitality tootltip.

B= baseline(amount of vitality neeeded to have 100% healing at a given level)
V= vitality
L= character level
H= healing % shown on chaacter sheet

if L < 11 then B = 35+2*L

if L >= 11 then B = 55+5.5*(L-10)

if V < B then H = 100-(B-V)*8.2/L

if V > B then H = 100+(V-B)*4.8/L

if V = B then H = 100

This has proved accuate in all except one of over 100 different level and vitality combinations that I have used to test it. The only mistake can easily be explained by a rounding error (.649 rounded to .7 in game).

My next step is to work on data collection for healing spells. Hopefully I'll be able to post some solid infomation on the rest of the healing mechanics in a few days. Untill then, I hope this proves usefull to someone.

Calilove · 03-30-2007, 10:39 AM

so what does this mean in terms of vitality+ items vs. healing focus items? Is there an increasing bias towards one or the other? What's the "magic number" (i.e. 4 vit = +1 HF @ lv 30)...

Or, is the take home that one should maintain a certain, increasing VIT# as they level up, and once they cross the B threshold start collecting +healing?

Sickpuppy · 03-30-2007, 11:14 AM

Quote:

Originally Posted by Calilove

so what does this mean in terms of vitality+ items vs. healing focus items? Is there an increasing bias towards one or the other? What's the "magic number" (i.e. 4 vit = +1 HF @ lv 30)...

Or, is the take home that one should maintain a certain, increasing VIT# as they level up, and once they cross the B threshold start collecting +healing?

The +% healing each point of vit will give depends on level. It also depends on whether or not you are above or below the "baseline" (ie. the amount of vit required to have 100% heal at a given level). The OP shows that vit below the baseline gives more heal % per point than once you've passed the baseline. It also shows that (strangely) there is no diminishing returns on +heal from vit. At level 50 each point of Vitality OVER the baseline of 275 Vit will add 0.096% heal.

From what I remember, heal focus is linear like this aswell. I seem to remember someone saying the cap on heal focus is 10*level and, at the cap, the % heal increase is 20%. This means that, at level 50, each point of heal focus adds 0.04% +heal. Per point, vit adds more heal, but obviously you have to take into account that heal focus has a lower value when it comes to item stat calculations. Whether the value makes heal focus a better stat or not is hard to tell unless someone comes up with item stat values.

All these equations are derived, though, and could be wrong.

edit: Also due to the fact that heal focus is a dedicated heal stat I'd assume that per item stat value heal focus would add more +heal. It wouldn't really be logical for it not to when vitality has other nice bonuses.

treyalsup · 03-30-2007, 11:27 AM

Level 29 BMG
309 vitality
124.7% healing from vitality

formula works perfectly!

Some simple obvious observations from formula.

Game expects 5.5 vitality from abilities and gear per level to be "average."

However the game punishes you for being below average almost twice as much as it rewards you for being below average. (8.2 vs. 4.8) so achieving this baseline per level is critical- even if you are trying to do other things with your character. Some races can only put 5(1 base + 4 allocated) points into vitality per level so it will be necessary to equip some vitality gear- for most characters this is moot, I realize, the baseline is not hard to achieve, but who knows you may have some healing focus junkies out there or melee based shamans, caster only bloodmages, etc.

At level 50, 275 vitality to achieve baseline and 483 vitality to achieve 120% healing.

treyalsup · 03-30-2007, 12:02 PM

I've been thinking about the implications of this formula.

How often does this dynamic occur in the game? Is there a baseline for str,dex,con for healers as well? This formula demonstates higher returns below the baseline than above- a move by the designers to discourage min/maxing and reward more balanced characters?

I just checked the formula and it works for my 12 monk. 38 vit=80.9 healing, though a 232 tooltip heal resulted in a 246 heal in game, so who knows how much tooltips reflect actual gameplay. (see multiple shaman mitigation % threads).

Fanclorn · 03-30-2007, 12:45 PM

Quote:

Originally Posted by treyalsup

I've been thinking about the implications of this formula.

How often does this dynamic occur in the game? Is there a baseline for str,dex,con for healers as well? This formula demonstates higher returns below the baseline than above- a move by the designers to discourage min/maxing and reward more balanced characters?

I just checked the formula and it works for my 12 monk. 38 vit=80.9 healing, though a 232 tooltip heal resulted in a 246 heal in game, so who knows how much tooltips reflect actual gameplay. (see multiple shaman mitigation % threads).

Well, tooltips are off. But I will say when buffed with a +vitality buff, I have noticed more on my heals.

Either way, for healing characters I would say Vitality is the first stat to put points in. Sure, your rate of return cheapens as you go up in value, but the important thing is it helps build stronger heals.

As far as Healing Focus goes, here is the formula for it:

( healing focus / max. healing focus ) * 20 = % of additional healing

So, using both formulas you can get an idea of what gear can provide.

redcloud · 03-30-2007, 01:31 PM

Quote:

Originally Posted by Fanclorn

Either way, for healing characters I would say Vitality is the first stat to put points in. Sure, your rate of return cheapens as you go up in value, but the important thing is it helps build stronger heals.

Depends on class though. As a BMG that is not the first stat I put my points into. It's Intel/Wis then yeah Vit. With Vit buff and gear I can compensate. Also... race helps too a little. But really, due to using life taps as main healing I go for dmg, intel/spell foci but thats how BMG set up.

Doesn't mean never use heals always do. But Also have a mode that makes them 25% more effective. So I don't need to spend as much into vit/hf as other healer might. (Some BMGs will still go vit first, and get HF... thats fine but imo not making use of what BMGs can do)

So not all healers need to go vit first, but all should spend points there. And some have it easier than others.

Enialas · 03-30-2007, 07:30 PM

Quote:

so what does this mean in terms of vitality+ items vs. healing focus items? Is there an increasing bias towards one or the other? What's the "magic number" (i.e. 4 vit = +1 HF @ lv 30)...

Or, is the take home that one should maintain a certain, increasing VIT# as they level up, and once they cross the B threshold start collecting +healing?

Right now the only real use for this is accurately detemining what the tooltip will show at different Vitality points and levels. I dont have enough information to say anything else conclusively.

Quote:

The +% healing each point of vit will give depends on level. It also depends on whether or not you are above or below the "baseline" (ie. the amount of vit required to have 100% heal at a given level). The OP shows that vit below the baseline gives more heal % per point than once you've passed the baseline. It also shows that (strangely) there is no diminishing returns on +heal from vit. At level 50 each point of Vitality OVER the baseline of 275 Vit will add 0.096% heal.

Disclaimer - the following may prove to be incorrect, but is the best guess based on the data I currently have

It appears that the Level variable is set by the spell being cast and not your character level. This would mean each spell would gain a different bonus to it's effectiveness based on your vitality.

As to diminishing returns, I have a couple data sets with trends that make me think it does exist. Right now I'm woking with a theory that diminishing returns kicks in after a specified Vitality amount thats determined by the spell cast.

Quote:

How often does this dynamic occur in the game? Is there a baseline for str,dex,con for healers as well?

I haven't collected ay data to verify this, but it looks like the equation I posted is also used to detemine the spell damage % from Int.

Fanclorn · 03-31-2007, 02:36 AM

Quote:

Originally Posted by Enialas

Right now the only real use for this is accurately detemining what the tooltip will show at different Vitality points and levels. I dont have enough information to say anything else conclusively.

Disclaimer - the following may prove to be incorrect, but is the best guess based on the data I currently have

It appears that the Level variable is set by the spell being cast and not your character level. This would mean each spell would gain a different bonus to it's effectiveness based on your vitality.

As to diminishing returns, I have a couple data sets with trends that make me think it does exist. Right now I'm woking with a theory that diminishing returns kicks in after a specified Vitality amount thats determined by the spell cast.

I haven't collected ay data to verify this, but it looks like the equation I posted is also used to detemine the spell damage % from Int.

Hrm, very interesting stuffs. Them releasing their formulas for a few things could be very cool for the theorycrafters out there (including myself.

)

Kovacs · 04-02-2007, 06:41 PM

Quote:

Originally Posted by Enialas

I haven't collected ay data to verify this, but it looks like the equation I posted is also used to detemine the spell damage % from Int.

Quelian (sorc. lead) posted that the formula int. based spell damage modifiers would work like that exactly but since beta ended I haven't picked up a sorc. so I didn't bother finding the "magic number."

Outstanding work by the way, my thanks.

Twoofus · 04-03-2007, 02:05 AM

Quote:

Originally Posted by Kovacs

Quelian (sorc. lead) posted that the formula int. based spell damage modifiers would work like that exactly but since beta ended I haven't picked up a sorc. so I didn't bother finding the "magic number."

Outstanding work by the way, my thanks.

We where doing the Bounty Hunter quests in seawatch last night, and my wife was very dissapointed that there was no healer gear (again sigh) as rewards.

But after dinging 38 and buying her new spells, she started testing her new heal.
Lo and behold, the medium gear she took as reward was giving her a higher heal nr. So she now just switches gear in and out when she gets drops, to test which one has the better heal for her.

I think she's banking the healing focus gear, in case it changes again.
New gear indeed had vitality, old gear had healing focus. Her vit bonus is now 104% I think, but healing dropped from 300+ to 260 or so.

Earlchaos · 04-03-2007, 06:36 AM

As a dark elf i've no chance to bring my vitality as up as i want. There's a bloody limitation on it (attributes now selfbuffed: 380+ Str, 130 Const, 230 dex, 110 int, 200 vit, 130 wis). I always take str/vit items but anyhow, it's hard to keep vit near 100% heal bonus.

But well, my crits are nice

Enialas · 04-03-2007, 11:02 AM

WhI didn't have as much time to collect data as I wanted this past weekend, but I did manage to get enough to do a solid analysis of Healing Touch 1, Healing Touch 2 and Alleviate 1. Here's an equation update, I am fairly confident that this is close to whats used in game. Errors can probably be attributed to differences to differences in rounding values.

B= baseline
V= vitality
L= value set by spell cast
N= value set by spell cast
P= % bonus to spell fom vitality
H= amount the spell heals for

if L < 11 then B = 35+2*L
if L >= 11 then B = 55+5.5*(L-10)

if V < B then P = 100-(B-V)*8.2/
if V > B then P = 100+(V-B)*4.8/L
if V = B then P = 100

if P < 160 then H = N*P/100
if P >= 160 then H = 1.6*N

Alleviate 1 ( L = 13, N = 155.5 consistent from level 8-35)

vit - cast value / equation value
Lvl 8 Cleric
35 - 120 / 119.7
38 - 123 / 122.64
41 - 126 / 125.58
44 - 129 / 128.53
47 - 131 / 131.47
50 - 134 / 134.41
Lvl 24 Cleric
125 - 186 / 186.22
130 - 189 / 189.09
136 - 193 / 192.53
141 - 196 / 195.4
146 - 198 / 198.27
152 - 202 / 201.72
Lvl 35 Cleric
169 - 212 / 211.48
180 - 218 / 217.8
187 - 222 / 221.81
201 - 230 / 229.85
217 - 239 / 239.04
225 - 244 / 243.63
239 - 249 / 248.8

Healing Touch 2 ( L = 12 , N = 366.1 consistent from level 8-35 )

vit - cast value / equation value
Lvl 8 Cleric
35 - 289 / 288.55
38 - 296 / 296.05
41 - 304 / 303.56
44 - 311 / 311.06
47 - 319 / 318.57
50 - 326 / 326.07
Lvl 24 Cleric
125 - 452 / 452.4996
130 - 460 / 459.82
136 - 468 / 468.61
141 - 476 / 475.93
146 - 483 / 483.25
152 - 492 / 492.04
Lvl 35 Cleric
169 - 517 / 516.93
180 - 533 / 533.04
187 - 543 / 543.29
201 - 564 / 563.79
215 - 584 / 584.3
217 - 586 / 585.76
239 - 586 / 585.76

Healing Touch 1 ( L = 4 , N = 129 consistent from level 1-8, one o both appear to change somewhere between levels 8 and 24 and again between levels 24 and 35)

vit - cast value / equation value
Lvl 8 Cleric
35 - 108 / 107.84
38 - 116 / 115.78
41 - 124 / 123.71
44 - 131 / 130.55
47 - 135 / 135.19
50 - 140 / 139.84
Lvl 24 Cleric
125 - 172 / -
130 - 180 / -
136 - 189 / -
141 - 197 / -
146 - 205 / -
152 - 206 / -
Lvl 35 Cleric
169 - 203 / -
172 - 206 / -
175 - 206 / -
176 - 206 / -
177 - 207 / -
239 - 207 / -

I'm currently working on collecting more data for other spell ranks to determine L and N values, and starting the process for healing focus.

treyalsup · 04-03-2007, 05:18 PM

I'm confused about "L". Isn't "L" level? And then it becomes something else that I'm not sure about- L and N being the variables I am confused about.

How did you determine that the healing bonus from vitality capped at 60%. None of your examples come close to 160% healing from vitality.

In any case your date supports your formulas even if I can't follow them completely.

Enialas · 04-03-2007, 06:12 PM

Quote:

Originally Posted by treyalsup

I'm confused about "L". Isn't "L" level? And then it becomes something else that I'm not sure about- L and N being the variables I am confused about.

How did you determine that the healing bonus from vitality capped at 60%. None of your examples come close to 160% healing from vitality.

In any case your date supports your formulas even if I can't follow them completely.

The values are shown above, but I am sure I could have presented it better.

If you are using the formula to calculate the value that will show on you chaacter sheet tooltip set L = character level

If you ae using the formula to detemine how much a paticular heal spell will cast for set L = number given for that particular spell

Healing Touch 1 L = 4 (accurate for character levels 1-8)
Healiing Touch 2 L = 12 (accurate for character levels 8-35)
Alleviate 1 L = 13 (accurate for character levels 8-35)

N = base healing amount of a particular spell before any modifiers such as Vitality or Healing Focus are applied

Healing Touch 1 N = 129 (accurate for character levels 1-8)
Healiing Touch 2 N = 366.1 (accurate for character levels 8-35)
Alleviate 1 N = 155.5 (accurate for character levels 8-35)

As to the 160% value

base value(N) for Alleviate 1 = 155.5
At 239 vitality, this spell heals for 249. If you use the fomula and input the numbers for this spell at 239 vitality ignoring the line, if P < 160 then H = N*P/100, that caps the bonus at 160 you get an expected heal value of 251.67. This is a significant deviation from other results so somethng else must be going on.

249/155.5 * 100 = 160.13

base value(N) for Healing Touch 1 or N = 129
The amount HT 1 heals stays constant without increasing from 177 to 239 healing, this value is 207

207/129 * 100 = 160.46

base value(N) for Healing Touch 2 = 366.1
The amount HT 1 heals stays constant without increasing from 217 to 239 healing, this value is 586

586/366.1 * 100 = 160.07

base value(N) for Alleviate 1 = 155.5
At 239 vitality, this spell heals for 249. If you use the fomula and input the numbers for this spell at 239 vitality ignoring the line, if P < 160 then H = N*P/100, that caps the bonus at 160 you get an expected heal value of 251.67. This is a significant deviation from other results so somethng else must be going on.

249/155.5 * 100 = 160.13

Hope this clears things up a bit.

Elanie · 04-04-2007, 10:39 AM

I heard something about healing focus losing its "potency" as you level above a piece of gear. So say a lvl 25 item with 64 heal focus is actually worse than a level 50 item with only 40 heal focus. Do you find this to be true in your calculations?

I have just started taking a piece of gear, put it on, cast a heal (I cast both my HOT and my big heal, since I use the HOT the most, and the big heal will show the biggest difference) then exchange it and cast the heal again and see the difference. I have started saccing a bit of heal focus/vitality for other stats, as long as my HOT stays over 1000 a tick hehe.

treyalsup · 04-04-2007, 01:12 PM

Quote:

Originally Posted by Enialas

If you ae using the formula to detemine how much a paticular heal spell will cast for set L = number given for that particular spell

Healing Touch 1 L = 4 (accurate for character levels 1-8)
Healiing Touch 2 L = 12 (accurate for character levels 8-35)
Alleviate 1 L = 13 (accurate for character levels 8-35)

N = base healing amount of a particular spell before any modifiers such as Vitality or Healing Focus are applied

Healing Touch 1 N = 129 (accurate for character levels 1-8)
Healiing Touch 2 N = 366.1 (accurate for character levels 8-35)
Alleviate 1 N = 155.5 (accurate for character levels 8-35)

As to the 160% value

base value(N) for Alleviate 1 = 155.5
At 239 vitality, this spell heals for 249. If you use the fomula and input the numbers for this spell at 239 vitality ignoring the line, if P < 160 then H = N*P/100, that caps the bonus at 160 you get an expected heal value of 251.67. This is a significant deviation from other results so somethng else must be going on.

249/155.5 * 100 = 160.13

Forgive the stream of conscoiusness thread. I think I get there in the end.

Okay. Just so I understand. L and N are values for a spell that you have dertermined by looking at the data and determining a constant for each given spell?

The problem I am having with this line

if P < 160 then H = N*P/100
if P >= 160 then H = 1.6*N

239 Vit at cleric level 35 isn't 160% healing bonus from vitality. You are hitting a cap which is causing your expected result to deviate from the actual result, but it is not a vitality cap.

I saw this before when, as a bloodmage, I was consistantly using lower level direct heals to avoid overhealing- I found that trying to use spells that were substantially below my level did not scale, in fact they healed for less at higher level than they did when I was lower level. So there is some built in cap for using spells that are too low for you- I think this is what you are encountering with a level 35 cleric casting a spell gained at level 8. This was bugged through the BMG forum and maybe its been fixed. My point is that yes there is a cap there but it cannot be attributed to vitality. Or am I misunderstanding you and what you are saying is that 239 vitality actually hits a 160% cap because 239 vitality is compared to the spell constant level(12) instead of character level (35)?

239 vitality at level 12 would be 169% healing bonus from vitality. CAPPED
225 vitality at level 12 would be 163.6% healing bonus from vitality. CAPPED
215 vitality at level 12 would be 159.6% healing bonus from vitality. not capped.

Bingo.

The vitality bonus from healing is not based on character level but on spell level (L).

If this is true, then casters can actually be hitting the 160% cap even when they are well below 160% on the tooltip when using lower level spells. Still wont happen much. This also explains why if you are leveling and are consistantly at say 110% healing from vitality on the tooltip, that your heals when casting the same spell actually return better results: more vitality does mean better heals- its not all compared to your level.

Interesting that healing touch 2 is gained at level 8 (correct?) but has a L value of 12. That could just be that all the equations kind of change at level 10.

It would be interesting to determine L for a spell gained at higher levels and if L = the level the spell was gained. It would be good to see the results on your level 35 cleric with each heal spell including the ones he would actually use at this point in his career.

Thanks for the work.

treyalsup · 04-04-2007, 01:21 PM

Quote:

Originally Posted by Elanie

I heard something about healing focus losing its "potency" as you level above a piece of gear. So say a lvl 25 item with 64 heal focus is actually worse than a level 50 item with only 40 heal focus. Do you find this to be true in your calculations?

I think that people are just refering to the fact that as you level it requires more focus in order to hit the 20% cap from focus items. Level 30 requires 300 focus to achieve 120% modification. So you level and are now 300/310 and showing 119.6% modification. Many look at the tooltip and think that they are now doing less damage with the same spell having gained a level. Actual in combat tests will show this not to be true.

As far as item level affecting the focus value, that sounds like BS and would mean that tooltips. character display have no meaning whatsoever.

Enialas · 04-04-2007, 08:30 PM

Finally got a reasonable set of data for all the heals on my 35 Cleric, except for Power of Renewal. Combined with the healing focus data I've been collecting, and noticing a few patterns, I'm petty confident that this new formula is correct. There is still at least one rounding error in it somewhere so some of the values may be one re two points off from what you see in game. I'm also leaving Healing Touch 1 out for now until i can fully explain it, since it doesnt seem to function exactly as the other spells do. Some of the variables are changed (again) from the previous 2 equations I posted.

V = Vitality
F = Healing Focus
L = Level you can fist train the spell at (see list below)
B = Base healing amount of the spell (see list below)
R = Half the rate at which you get new ranks of the spell line (see below)
A = Amount of vitality that gives 100% healing for the spell
P = % bonus to spell fom vitality
H = Amount the spell heals for

if L+R < 11 then A = 35+2*(L+R)
if L+R >= 11 then A = 55+5.5*(L+R-10)

if V < A then P = 100-(A-V)*8.2/(L+R)
if V > A then P = 100+(V-A)*4.8/(L+R)
if V = A then P = 100

if P > 160 then set P =160
if F > 10*L then set F = 10*L

H = N*P/100+N*(F/10*L)/100

Spell Values

R = 4 for all ranks of Healing Touch, Rejuvinate and Shroud of Health
R = 5 for all ranks of Divine Light and Alleviate

Spell Name - L / B
Healing Touch 2 - 8 / 366
Healing Touch 3 - 16 / 621
Healing Touch 4 - 24 / 895
Healing Touch 5 - 32 / 1187
Rejuvenate 1 - 10 / 733
Rejuvenate 2 - 18 / 1179
Rejuvenate 3 - 26 / 1657
Rejuvenate 4 - 34 / 2165.5
Divine Light 1 - 12 / 299
Divine Light 2 - 22 / 491
Divine Light 3 - 32 / 700
Shroud of Health 1 - 14 / 555
Shroud of Health 2 - 22 / 825
Shroud of Health 3 - 30 / 1112
Alleviate 1 - 8 / 155.5
Alleviate 2 - 18 / 282.5
Alleviate 3 - 28 / 421.5

Enialas · 04-05-2007, 01:15 AM

I attached a spreadsheet fo anyone who wants to test the values. If its off by more then 1 or 2 from ingame values please let me know.

Quote:

Originally Posted by Elanie

I heard something about healing focus losing its "potency" as you level above a piece of gear. So say a lvl 25 item with 64 heal focus is actually worse than a level 50 item with only 40 heal focus. Do you find this to be true in your calculations?

I can easily see a situation where someone might infer something like this.

Let's take a hypothetical level 29 Cleric with 260 healing focus. Since each spell has a different cap for healing focus at 10 times the level the spell is gained, all of his spells except for Alleviate would be getting the maximum 20% bonus from focus. While running through a dungeon he get's a spiffy new item that increase his Healing Focus by 30 without changing vitality. He puts it on and starts casting heals to see how much they have increased, only to notice that Alleviate is the only spell to change and it only gains 2/3 the amount that going fom 230-260 focus gives.

When noone in group or general chat is able to offer any explanation he quickly logs out of the game fustated and angry. Not long after that a new post shows up on Silky Venom titled "HEALING FOCUS IS NERFED".

If any Clerics over level 35, Bloodmages, Shamans or Disciples ae interested in helping me collect data please PM me.