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Comparsion: Solace of the Fallen VS Tears of the Vanquished.
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Post by
Rouen
This is a comparsion of the mana gained from
Tears of the Vanquished
and the non-heroic version of
Solace of the Fallen
. This is just a reference for other holy paladins out there who stack intellect, it shows that this trinket is very worthwhile to have.
Tears provides 500 mana every 45 (roughly) seconds. 500 / 45 (To determine mana regained per second, not MP5) = 11.11* mana per second.
Solace of the Fallen, once stacked, provides 128mp5. 128 \ 5 = 25.6 mana regained per second.
Tears provides 84 intellect (1260 mana) which your Divine Plea will return more mana because of it. Let's assume that you have 30k mana and you just swapped in Tears so you now have 31,260 mana. Divine Plea activates every minute.
Divine Plea @ 30,000 mana returns = 7500 Mana
Divine Plea @ 31,260 mana returns = 7815 Mana.
Since the trinket procs every 45 seconds, instead of a full minute, I'm going to chop off 25% of the mana regained since 15 seconds x 4 = 1 minute, then 15 x 3 = 45 seconds. The total extra mana gained from using the Tears trinket is 315 mana. Divide this by 75%
315 x 0.75 = 236.25
If you count the mana returned by Divine Plea using this proportion and the mana proc from Tears, you would gain 236.25 + 500 =
736.25 mana every 45 seconds.
Now, lets figure out how much mana Solace of the Fallen would return in 45 seconds, assuming it has completed stacking.
128 times 9 (Since 5 x 9 = 45 seconds) equals 1152 mana returned every 45 seconds.
This is a difference of 1152 - 736.25 = 415.75 mana every 45 seconds. Dividing it down further to MP5, Solace of the Fallen provides (415.75 \ 9)
46.19 more MP5 then Tears of the Vanquished.
This MP5 number does not include the extra mana you start with because of Tears, which is 1260 mana, or the extra mana returned from Divine Plea. Due to this factor, I will use a 5, 8, and 10 minute long encounter to show the differences between these trinkets. This explaination will not factor in Ilumination critical heal returns or Replenishment.
MP1
means Mana Per Second, as opposed to MP5.
Boss Fight 1A Conditions
Mana: 30,000
Trinket: Solace of the Fallen
Duration: 5 Minutes (300 Seconds)
Caveats: Divine Plea must be used every minute. Each one will return 7500 mana in this test.
128 MP5 \ 5 = 25.6 MP1
25.6 x 300 = 7680 mana
Divine Plea (7500) x 5 = 37,500 mana returned.
37,500 + 7680 = 45,180 mana returned over the course of this fight.
Boss Fight 1B Conditions
Mana: 30,000
Trinket: Solace of the Fallen
Duration: 8 Minutes (480 Seconds)
128 MP5 \ 5 = 25.6 MP1
25.6 x 480 = 12,288 mana
Divine Plea (7500) x 8 = 60,000
60,000 + 12,288 = 72,288 mana returned over the course of this fight.
Boss Fight 1C Conditions
Mana: 30,000
Trinket: Solace of the Fallen
Duration: 10 Minutes (600 Seconds)
128 MP5 \ 5 = 25.6 MP1
25.6 x 600 = 15,360 mana
Divine Plea (7500) x 10 = 75,000
75,000 + 15,360 = 90,360 mana returned over the course of the fight.
Conditions and results for Tears of the Vanquished are below. You will notice that I add 1260 at the end of each mana gained result. Since you start with 1260 extra mana, it will get added to the regained to be fair.
Boss Fight 2A Conditions
Mana: 31,260
Trinket: Tears of the Vanquished
Duration: 5 Minutes (300 Seconds)
Caveats: Divine Plea must be used every minute. Each one will return 7815 mana in this test.
500 Mana per 45 \ 45 = 11.11 MP1
11.11 x 300 = 3330
Divine Plea (7815) x 5 = 39075
39075 + 3330 + 1260 = 43,665 mana returned over the course of the fight.
Boss Fight 2B Conditions
Mana: 31,260
Trinket: Tears of the Vanquished
Duration: 8 Minutes (480 Seconds)
500 Mana per 45 \ 45 = 11.11 MP1
11.11 x 480 = 5332.8 mana
Divine Plea (7815) x 8 = 62,520
62,520 + 5332.8 + 1260 = 69112.8 mana returned over the course of the fight.
Boss Fight 2C Conditions
Mana: 31,260
Trinket: Tears of the Vanquished
Duration: 10 Minutes (600 Seconds)
500 Mana per 45 \ 45 = 11.11 MP1
11.11 x 600 = 6666
Divine Plea (7815) x 10 = 78,150
78,150 + 6666 + 1260 = 86076 mana returned over the course of the fight.
To recap, here is the list of total mana returned per test, side by side.
Solace of the Fallen \\ Tears of the Vanquished \\ Numerical Difference \\ Percentage Difference
5 MIN: 45,180 \\ 43,665 \\ 1515 \\ 3.47 %
8 MIN: 72,288 \\ 69.112 \\ 3176 \\ 4.60 %
10 MIN: 90,360 \\ 86,076 \\ 4284 \\ 4.80 %
TLDR: Tears of the Vanquished is a damn fine trinket when compared to a iLevel 245 trinket. The difference is statistically small.
Note to Readers: Feel free to pick this apart. If you see an error with my numbers, please point them out so they can be corrected.
Post by
Rouen
Here is the same set of 5, 8, and 10 minute tests, but this time with Replenishment factored in. It will assume 100% uptime on replenishment and Divine Plea used every one minute. Numbers are directly borrowed from the first set of tests (first post) and the math used to find them is not shown again here. They are included to show the addition of total mana gained, but with replenishment this time.
Solace of the Fallen Results
Boss Fight 1A Conditions
Mana: 30,000
Trinket: Solace of the Fallen
Duration: 5 Minutes (300 Seconds)
30,000 x 0.002 = 60 MP1
60 x 300 = 18,000
37,500 + 7680 + 18000 = 63,180 mana returned over the course of this fight.
Boss Fight 1B Conditions
Mana: 30,000
Trinket: Solace of the Fallen
Duration: 8 Minutes (480 Seconds)
30,000 x 0.002 = 60 MP1
60 x 480 = 28,800
60,000 + 12,288 + 28,800 = 101,088 mana regained over the course of the fight.
Boss Fight 1C Conditions
Mana: 30,000
Trinket: Solace of the Fallen
Duration: 10 Minutes (600 Seconds)
30,000 x 0.002 = 60 MP1
60 x 600 = 36,000
75,000 + 15,360 + 36,000 = 126,360 mana returned over the course of the fight.
Tears of the Vanquished Results
Boss Fight 2A Conditions
Mana: 31,260
Trinket: Tears of the Vanquished
Duration: 5 Minutes (300 Seconds)
31,260 x 0.002 = 62.52 MP1
62.52 x 300 = 18,756
39075 + 3,330 + 1260 + 18,756 = 62,421 mana returned over the course of the fight.
Boss Fight 2B Conditions
Mana: 31,260
Trinket: Tears of the Vanquished
Duration: 8 Minutes (480 Seconds)
31,260 x 0.002 = 62.52 MP1
62.52 x 480 = 30,009.6
62,520 + 5332.8 + 1260 + 30,009.6 = 99,122.4 mana returned over the course of the fight.
Boss Fight 2C Conditions
Mana: 31,260
Trinket: Tears of the Vanquished
Duration: 10 Minutes (600 Seconds)
31,260 x 0.002 = 62.52 MP1
62.52 x 600 = 37,512
78,150 + 6666 + 1260 + 37,512 = 123,588 mana returned over the course of the fight.
Total Results of Original Test + Replenishment Factor
Solace of the Fallen \\ Tears of the Vanquished \\ Numerical Difference \\ Percentage Difference
5 MIN: 63,180 \\ 62,421 \\ 759 \\ 1.21 %
8 MIN: 101,088 \\ 99,122 \\ 1966 \\ 1.98 %
10 MIN: 126,360 \\ 123,588 \\ 2772 \\ 2.24 %
When Replenishment is factored into the test, the differences between them in regards to mana regen is smaller then without it factored in. The end result of Solace of the Fallen being the better trinket over time has not changed. The primary bonus of using Solace over Tears of the Vanquished is having the 150 spellpower on top of having all the regen provided by Tears of the Vanquished.
Post by
316895
This post was from a user who has deleted their account.
Post by
svirve
Time SotF TotV Difference
5 MIN: 45,180 43,665 1515 3.47 %
8 MIN: 72,288 69.112 3176 4.60 %
10 MIN: 90,360 86,076 4284 4.80 %
Much prettier.
I did a similiar comparison between dual solace vs
talisman of resurgance
and
pandoras plea
combo,
here
.
I'm not trying to brag or anything but, people are too stuck with the INT is king mindset.
As far as trinkets go, dual solace is
the
best combo for a holy paladin to go atm.
Going to go through your math later, can't atm. Looks cool on first glance though.
P.S. Just a quick note, you spelled comparison wrong in the thread title =)
Post by
svirve
Some things that lept to mind.
I noticed you did the DP calculations which i at first had assumed you missed, nice one.
The calculation itself is flawless. Your int to mana conversion is not though.
Divine intellect itself puts each int at 16.5 mana per int, on top of that it's safe to assume kings as well, which gives us 18.15 mana per int.
Tears gives you 1524,6 extra mana (with the proper conversion). Which is 1524,6*0,25/60=6,3525 mana per second, or 31,7625 Mp5 if you'd like, through DP.
Also putting Tears at a 100% uptime on the proc is quite bold. It does not have a 100% proc chance and it's not safe to assume constant casting.
I'm not saying it's wrong to do it, it's the only right way as a matter of fact. Comparing the two during optimal conditions (you might as well get 10 sec of no casting with solace as well) will show which one is always the better one.
Though i feel that you should atleast note in the comparison that the relativity of Tears having a 100% uptime is quite low.
Right now i'm off to work, with a little luck i'll have time to give this all a good read through when i get home =)
Enjoying it so far, great job!
Post by
valundar
One thing you don't want to forget to mention.. is that all these calculations are just for the mana.
Don't forget to mention that you also get a ton of +sp from the solace on top of it.
Post by
Rouen
Divine intellect itself puts each int at 16.5 mana per int.
You are right about Divine Intellect, I didn't factor that in. I'll update the math, but statistically the difference is so small that it won't change much. I will post again when the change is done, I need to update a lot of numbers for this so I won't do it right away.
on top of that it's safe to assume kings as well...
I didn't factor in a number of things to keep this from getting overly complicated. For example, you are correct when saying I made the assumption that Tears will proc as soon as it is off cooldown. Realistically, this is almost never possible. The fact remains that this trinket is bugged and will proc off a paladin's fart, ticks from Replenishment will proc it for example. As for factoring in Kings, again, I opted out of it. For the mana pool figures of 30,000 and 31,260 (The incorrect Tears mana pool), those are treated as if you are unbuffed (unbuffed intellect). I did that to keep the numbers relatively clean and easily understood. If someone cares enough to try and factor in Kings, my math is clearly shown so they can easily reproduce the tests with + 8 intellect on the 2A-2B-2C tests.
Another reason I didn't factor in Kings is the fact that as of patch 3.2, there are two different kings of mass King's buffs, the 8% and 10% versions. To work out every possibility is beyond what I'm willing to do, since the end results will generally be the same: Solace of the Fallen provides a greater amount of regen over time then Tears can.
Post by
svirve
One thing you don't want to forget to mention.. is that all these calculations are just for the mana.
Don't forget to mention that you also get a ton of +sp from the solace on top of it.
When Replenishment is factored into the test, the differences between them in regards to mana regen is smaller then without it factored in. The end result of Solace of the Fallen being the better trinket over time has not changed.
The primary bonus of using Solace over Tears of the Vanquished is having the 150 spellpower on top of having all the regen provided by Tears of the Vanquished
.
The last paragraph.
I didn't factor in a number of things to keep this from getting overly complicated. For example, you are correct when saying I made the assumption that Tears will proc as soon as it is off cooldown. Realistically, this is almost never possible. The fact remains that this trinket is bugged and will proc off a paladin's fart, ticks from Replenishment will proc it for example. As for factoring in Kings, again, I opted out of it. For the mana pool figures of 30,000 and 31,260 (The incorrect Tears mana pool), those are treated as if you are unbuffed (unbuffed intellect). I did that to keep the numbers relatively clean and easily understood. If someone cares enough to try and factor in Kings, my math is clearly shown so they can easily reproduce the tests with + 8 intellect on the 2A-2B-2C tests.
Another reason I didn't factor in Kings is the fact that as of patch 3.2, there are two different kings of mass King's buffs, the 8% and 10% versions. To work out every possibility is beyond what I'm willing to do, since the end results will generally be the same: Solace of the Fallen provides a greater amount of regen over time then Tears can.
What more would you factor in that would not increase both results equally?
Since we're discussing paladins here why would you consider using the ghetto kings?
Factoring in kings doesn't make it complicated, it makes it more realistic.
Reading the first reply to this post, the numbers weren't easily understandable, thus there's no point in attempting to make them that. Factoring in kings doesn't make it any less user-friendly for that matter either.
Mention some assumptions in the beginning, one being 100% uptime on tears the other being BoK. Could be worth mentioning that you're assuming DP is used on cooldown in the assumptions as well.
You don't have to supply an example mana pool to do any calculations, doing so actually only makes it more complicated. Since this means you first have to calculate the Mp5 from DP and replenishment with the base mana pool then you have to calculate the Mp5 from DP and replenishment with the increased mana pool, then subtract the first from the latter. Instead of just doing 84int*18,15ManaPerInt*0,25GainFromDp/60OverAMinute*5ConvertToMp5
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