Hi all,
lately I've read through some of my holy paladin calculations I have done on another realm and I want to share them with you. The basic questino for me was if it is more valuable to obtain crit items or just go for mp5+addheal. In the following calculations I'm talking about AVERAGE values, not about min/max values. Also the healing coefficients I use are 0,43 for Flas Of Light (FOL) and 0,71 for Holy Light (HL). Another thing to mention for the calculations is that web sources say 54 int is 1% spell crit for paladins, the theorycraft addon says it's 29.5 int for 1% spell crit (maybe a Kronos admin could reveal how it's working on this realm). I will do the calculations for the 29.5. What I won't do is considering the 12% more healing from talents, because it won't make a difference for the calculations (it doesn't matter if the *1.12 scaling applies to the healing value of 1% crit or the healing value of add heal).
First of all we need to aks ourselves the question what makes 1% spell crit on healing spells seem so special? Yes, obviously that talent, that gives you 100% of the spell's mana cost back, after you get a crit with a spell. Also something that sounds very pleasing is the fact that critical heals do 1,5x healing instead of 1x healing, so these lovely crits give you 0,5x bonus healing.
To do proper calulations we need a formula to work with. The addheal you have on your gear is multiplied with the healing coefficient of the spell used. So let's start with the average healing of our FOL and HL:
For future calculations we'll call the base average healing of a spell b and the total average healing done by a spell t. With zero addheal the average healing of FOL1 would be t=b.
Now we assume to have 100 addheal. So according to the FOL coefficient of 0.43, we get 43 addheal, which will make our FOL heal for 67.5+43=110.5.
The calculation is easy here, it's t=b+k*a=67.5+0.43*100=110.5.
Involving crit is also not that complicated. A crit gives 1,5 times healing (in other words (1+0.5)*healing). The crit rate c consists of the % crit on gear and intellect/54 or intellect/29.5.
Be aware that both the intellect talent and Blessing of Kings increase your intellect by 10%. They get multiplied, so 1.1*1.1=1.21 out of 2x10% we get 21% more int (since patch whatever most modifiers stack multiplicative).
c=0.01*(critrate on gear + (1.21*intellect without blessing of kings and talent)/29.5)
Adding our new knowledge to the formula it will look like that:
Here we go! Let's continue with our calculation by adding 1% crit! t=(67.5+0.43*100)*(1+0.5*0.01)=111.1.
Wow! Only 0.6 more healing from that 1% more crit, compared to the 110.5 before! Not as much as expected.
How much addheal would we have to stack instead of that 1% crit to reach 0.6 more healing (or: how much addheal that 1% crit is worth)? Easy calculation!
67.5+0.43*(100+x)=111.1
43+0.43*x=111.1-67.5
x=(111.1-67.5-43)/0.43
x=1.4
As you can see from the FoL1 formula without crit and addheal t=b=67.5 compared to the same formula for FoL6 t=b=363.5 the difference in healing is roughly 300. Now if we want to get to 363.5 healing (average base healing of FoL), we can calculate the amount of addheal needed for FoL1:
363.5=67.5+0.43*x
x=(363.5-67.5)/0.43
x=688
So we need nearly 700 addheal, just to compensate the rank difference and the 105 mana FoL1 costs less than FoL6. But what has this to do with spell crit?
If we are using FoL1, we get (critbonus*critchance*average base healing) 0.5*0.01*67.5=0.3375 healing just from base heal per 1% crit, if we are using FoL6 we would get 0.5*0.01*363.5=1.8175 healing per 1% crit. This means the higher the healing rank cast, the higher the benefit from crit. BUT for EVERY rank of FoL, 1 healing = 2.3 add heal on equipment (calculation: 1=0.43*x <=> x=1/0.43=2.3). So since we are healing with the 35 mana FoL1 most of the time, it's much more beneficial to get 2.3 add heal instead of 1% crit.
Another example, a BWL/AQ geared paladin with 1000 add heal and FoL1. Benefit from 1% crit is 0.5*0.01*(67.5+0.43*1000)=2.5 healing, which is 2.5/0.43=5.8 add heal. Even with 1k add heal, 1% crit makes only a very minor difference.
Please be aware of the fact that higher ranks of HL and FoL give you more add heal bonus, but they also cost much more mana and - as far as I know - higher ranks of your spells are only used in emergency situations.
Everyone who understood the calculations until now, should be able to do the transfer to do these calculations with holy light. For all those who are too lazy to do them, you can take a look at the spreadsheet:
SPREADSHEET
The mp/5 from 1% crit calculations are the following (also found in the spreadsheet):
(mana cost of the spell)*0.01*(5/casting time)
To make it a little more realistic, add 0.05s to your casting time, so for example out of 1.5s for FoL you get 1.55s. Let's do the calculation for FoL1:
35*0.01*(5/1.55)=1.1/mp5
Please note that this ONLY APPLIES WHEN YOU ARE CASTING PERMANENTLY WITH NO BREAK.
Let's say you have to move for 2.5s every 20s. So your pure casting time is 17.5s, which is 3.5 times the mp5 value. If you were able to cast the full 20s without moving, you would have 4 times the mp5 value.
3.5*1.1mp/5=3.85
4*1.1mp/5=4.4
So in the movement scenario you would have regenerated 3.85 mana, in the non movement you would have regenerated 4.4 mana over 20 seconds (which is nothing compared to regular mp/5 on gear).
Check the Spreadsheet if you want to see how much mana the other healing ranks of your spells bring you per 1% crit.
Please feel free to comment and share your feedback with me.
Best regards!
lately I've read through some of my holy paladin calculations I have done on another realm and I want to share them with you. The basic questino for me was if it is more valuable to obtain crit items or just go for mp5+addheal. In the following calculations I'm talking about AVERAGE values, not about min/max values. Also the healing coefficients I use are 0,43 for Flas Of Light (FOL) and 0,71 for Holy Light (HL). Another thing to mention for the calculations is that web sources say 54 int is 1% spell crit for paladins, the theorycraft addon says it's 29.5 int for 1% spell crit (maybe a Kronos admin could reveal how it's working on this realm). I will do the calculations for the 29.5. What I won't do is considering the 12% more healing from talents, because it won't make a difference for the calculations (it doesn't matter if the *1.12 scaling applies to the healing value of 1% crit or the healing value of add heal).
First of all we need to aks ourselves the question what makes 1% spell crit on healing spells seem so special? Yes, obviously that talent, that gives you 100% of the spell's mana cost back, after you get a crit with a spell. Also something that sounds very pleasing is the fact that critical heals do 1,5x healing instead of 1x healing, so these lovely crits give you 0,5x bonus healing.
To do proper calulations we need a formula to work with. The addheal you have on your gear is multiplied with the healing coefficient of the spell used. So let's start with the average healing of our FOL and HL:
Code:
FoL1: 67.5 (healing 62-73, so average is -> 62+(73-62)/2 = 67.5)
FoL2: 103.5
FoL3: 154.5
FoL4: 209.5
FoL5: 283.5
FoL6: 363.5
HL1: 43.5
...
HL8: 1317.5
HL9: 1680.5 (AQ20 book)For future calculations we'll call the base average healing of a spell b and the total average healing done by a spell t. With zero addheal the average healing of FOL1 would be t=b.
Code:
t=b
t=average total healing
b=average base healingNow we assume to have 100 addheal. So according to the FOL coefficient of 0.43, we get 43 addheal, which will make our FOL heal for 67.5+43=110.5.
The calculation is easy here, it's t=b+k*a=67.5+0.43*100=110.5.
Code:
t=b+k*a
t=average total healing
b=average base healing
k=healing coefficient
a=addheal bonusesInvolving crit is also not that complicated. A crit gives 1,5 times healing (in other words (1+0.5)*healing). The crit rate c consists of the % crit on gear and intellect/54 or intellect/29.5.
Be aware that both the intellect talent and Blessing of Kings increase your intellect by 10%. They get multiplied, so 1.1*1.1=1.21 out of 2x10% we get 21% more int (since patch whatever most modifiers stack multiplicative).
c=0.01*(critrate on gear + (1.21*intellect without blessing of kings and talent)/29.5)
Adding our new knowledge to the formula it will look like that:
Code:
t=(b+k*a)*(1+0,5*c)
t=average total healing
b=average base healing
k=healing coefficient
a=addheal bonuses
c=0.01*(critrate on gear + (1.21*intellect without blessing of kings and talent)/29.5)Here we go! Let's continue with our calculation by adding 1% crit! t=(67.5+0.43*100)*(1+0.5*0.01)=111.1.
Wow! Only 0.6 more healing from that 1% more crit, compared to the 110.5 before! Not as much as expected.
How much addheal would we have to stack instead of that 1% crit to reach 0.6 more healing (or: how much addheal that 1% crit is worth)? Easy calculation!
67.5+0.43*(100+x)=111.1
43+0.43*x=111.1-67.5
x=(111.1-67.5-43)/0.43
x=1.4
As you can see from the FoL1 formula without crit and addheal t=b=67.5 compared to the same formula for FoL6 t=b=363.5 the difference in healing is roughly 300. Now if we want to get to 363.5 healing (average base healing of FoL), we can calculate the amount of addheal needed for FoL1:
363.5=67.5+0.43*x
x=(363.5-67.5)/0.43
x=688
So we need nearly 700 addheal, just to compensate the rank difference and the 105 mana FoL1 costs less than FoL6. But what has this to do with spell crit?
If we are using FoL1, we get (critbonus*critchance*average base healing) 0.5*0.01*67.5=0.3375 healing just from base heal per 1% crit, if we are using FoL6 we would get 0.5*0.01*363.5=1.8175 healing per 1% crit. This means the higher the healing rank cast, the higher the benefit from crit. BUT for EVERY rank of FoL, 1 healing = 2.3 add heal on equipment (calculation: 1=0.43*x <=> x=1/0.43=2.3). So since we are healing with the 35 mana FoL1 most of the time, it's much more beneficial to get 2.3 add heal instead of 1% crit.
Another example, a BWL/AQ geared paladin with 1000 add heal and FoL1. Benefit from 1% crit is 0.5*0.01*(67.5+0.43*1000)=2.5 healing, which is 2.5/0.43=5.8 add heal. Even with 1k add heal, 1% crit makes only a very minor difference.
Please be aware of the fact that higher ranks of HL and FoL give you more add heal bonus, but they also cost much more mana and - as far as I know - higher ranks of your spells are only used in emergency situations.
Everyone who understood the calculations until now, should be able to do the transfer to do these calculations with holy light. For all those who are too lazy to do them, you can take a look at the spreadsheet:
SPREADSHEET
The mp/5 from 1% crit calculations are the following (also found in the spreadsheet):
(mana cost of the spell)*0.01*(5/casting time)
To make it a little more realistic, add 0.05s to your casting time, so for example out of 1.5s for FoL you get 1.55s. Let's do the calculation for FoL1:
35*0.01*(5/1.55)=1.1/mp5
Please note that this ONLY APPLIES WHEN YOU ARE CASTING PERMANENTLY WITH NO BREAK.
Let's say you have to move for 2.5s every 20s. So your pure casting time is 17.5s, which is 3.5 times the mp5 value. If you were able to cast the full 20s without moving, you would have 4 times the mp5 value.
3.5*1.1mp/5=3.85
4*1.1mp/5=4.4
So in the movement scenario you would have regenerated 3.85 mana, in the non movement you would have regenerated 4.4 mana over 20 seconds (which is nothing compared to regular mp/5 on gear).
Check the Spreadsheet if you want to see how much mana the other healing ranks of your spells bring you per 1% crit.
Please feel free to comment and share your feedback with me.
Best regards!
(20 April 2016)
