Execute effects and the use of cooldowns

Wraithlin · Class/Spec Late BL Early BL Difference

[top]Introduction

Since the introduction execute-like mechanics such as hammer of wrath and molten fuy there has been a long-standing assumption that the optimal time to use bloodlust and other dps cooldowns is during the period at which dps is at its greatest; namely below 35% health. This article will show that this is incorrect and that, infact, there is no noticeable difference in the total fight length regardless of when bloodlust or trinkets are used. When there is a difference it may favour early or late cooldowns, depending on the circumstances.

The major consideration of this discussion is: When is the best time to use bloodlust? As bloodlust is the only raid-wide fixed duration dps cooldown, it enforces a raid-wide synchronization of dps cooldowns.

Note on links
Many of the posts linked herein are from the benefactors bar forums, non-members will not be able to see the original posts. These links are prefaced with Benefactors Bar

[top]Summary

The correct time to use dps cooldowns, when there are no other extraneous factors, is at that point when the raid can leverage the most fixed-duration cooldowns simultaneously. Execute is not such a cooldown as its duration is not fixed. This will normally mean using cooldowns early in a fight when it is easier to synchronise across the entire raid.

The exception to the above is when a boss fight is such that a specific phase needs to be completed in the shortest possible time (a la C'thun, M'uru/Entropius, RoS... etc.).

Early use of DPS cooldowns can cause problems for classes with aggro-reduction abilities on a long cooldown. One solution is to ensure at least one of your rogues/hunters keeps their aggro-redirection abilities for during the burn period when their damage, and hence transferred aggro, will be maximized. Alternately, save the cooldowns for 85-80%.

[top]TL;DR

(1) Use cooldowns simultaneously.
(2) Obeying (1), use cooldowns early to maximize the number of people and cooldowns available,
(3) If one particular phase needs to be burnt through in the shortest possible time, use cooldowns during that phase, still obeying (1).

[top]Results from Simcraft

The following results were found from SimCraft (simulationcraft - Google Code), the files are attached the end of this article.

Class/Spec	Late BL	Early BL	Difference
Druid_T7_00_55_16	5675	5660	15
Druid_T7_00_55_16_M	5616	5587	29
Druid_T7_58_00_13_SF	5768	5774	-6
Druid_T7_58_00_13_W	5463	5462	1
Hunter_T7_06_14_51	6111	6288	-177
Hunter_T7_15_51_05	5513	5611	-98
Hunter_T7_52_12_07	5323	5425	-102
Mage_T7_00_53_18	5980	5987	-7
Mage_T7_18_00_53	5657	5641	16
Mage_T7_20_51_00	6261	6239	22
Mage_T7_53_18_00	6010	5988	22
Mage_T7_57_03_11	6139	6101	38
Priest_T7_14_00_57	5613	5624	-11
Priest_T7_38_28	2821	2834	-13
Rogue_T7_07_51_13	5373	5354	19
Rogue_T7_08_20_43	6354	6391	-37
Rogue_T7_15_51_05	5446	5416	30
Rogue_T7_23_05_43	6453	6491	-38
Rogue_T7_51_13_07	5657	5641	16
Shaman_T7_16_55_00	5742	5772	-30
Shaman_T7_57_14_00	5452	5466	-14
Warlock_T7_00_31_40	5452	5468	-16
Warlock_T7_00_41_30	5865	5893	-28
Warlock_T7_00_55_16	5608	5607	1
Warlock_T7_02_13_56	5720	5709	11
Warlock_T7_55_00_16	6725	6623	102
Warlock_T7_55_00_16_CoE	6422	6355	67
Warlock_T7_55_00_16_DG	7496	7398	98

Av. Raid DPS	5775.5	5778.8	-3.3

The Biggest winners/Losers are Warlocks and Hunters, even mages see a net change of less than 50dps between early and late BL. Note, warriors, paladins and deathknights are not included. This Simcraft calculation shows that there is only a 0.056% difference in average raid dps (and therefore fight duration) between using bloodlust early and using it late; this supports the hypothesis that there is negligible difference in the fight length when BL is used below 35%.

[top]The Mathematics of Execute

[top]Assumptions

Cooldowns provides the same dps boost to the raid as a percentage whenever it is used

Most of the models consider a raid with one bloodlust, and some number of other trinkets/cooldowns.

[top]Proof for multiplicative trinkets

Benefactors Bar

Originally Posted by Wraithlin

$X=DPS$

$B = \text{BL}$

$T = \text{Trinkets}$

$E = \text{Execute Bonus}$

$A = \text{Time Above } 35\%$

$U = \text{Time Under } 35\%$

Now in both scenarios, the damage dealt above 35% must be equal to 65% of the boss health, and the damage dealt below 35% must be equal 35% of the boss health.

$40XBT + (A_{1}-40)X = XA_{2} = 0.65H, \qquad XE= XE(U_{2}-40) + 40BTXE =0.35H$

Rearranging:
$A_{1} = \frac{(XA_{2} - 40XBT)+ 40X}{X}, \qquad U_{1} = \frac{XE(U_{2}-40) + 40BTXE}{XE}$

So:
$U_{1}+A_{1} &= \frac{(XA_{2} - 40XBT)+ 40X}{X} + \frac{XE(U_{2}-40) + 40BTXE}{XE}$

$=\frac{1}{XE}\left( E(XA_{2} - 40XBT)+ 40XE + XE(U_{2}-40) + 40BTXE\right)$

$=\frac{1}{XE}\left( XEA_{2} + XEU_{2}- 40BXTE+ 40BTXE + 40XE -40XE\right)$

$=\frac{1}{XE}\left( XE(A_{2} + U_{2})\right)$

$=U_{2}+A_{2}$

This would mean that, for multiplicative effects:
It does not matter when you pop blood lust and pop trinkets (Above or below 35%), if they are used together.

[top]Proof for additive trinket effects

Benefactors Bar

Originally Posted by Ichal

x: dps above 35%
y: dps below 35% (so y > x)
H: Boss health
A: Multiplicative modifier from popping cooldowns (example: Bloodlust/Heroism)
B: Additive modifier from popping cooldowns (example: Clickable trinket with +damage or AP)
T: Time to kill without cooldowns
T_1: Time to kill with early cooldowns
T_2: Time to kill with late cooldowns

I'm assuming that cooldowns will always work for the full duration, which I've set to 40 sec.

Using no cooldowns you get:

$T = \frac{0.65H}{x} + \frac{0.35H}{y}$

Assuming purely multiplicative cooldowns:

$T_1 = 40 + \frac{0.65H - 40Ax}{x} + \frac{0.35H}{y}$

$T_2 = 40 + \frac{0.65H}{x} + \frac{0.35H - 40Ay}{y}$

With a bit of elimination, it's clear that in this case $T_1 = T_2$ .

Assuming both types of coolodowns:

$T_1 = 40 + \frac{0.65H - 40A(x+B)}{x} + \frac{0.35H}{y}$

$T_2 = 40 + \frac{0.65H}{x} + \frac{0.35H - 40A(y+B)}{y}$

Unless I messed up (not unlikely) this eliminates to: $T_1 < T_2$ (i.e. it's better to pop cooldowns early).

[top]Proof that trinkets should be stacked with BL

Benefactors Bar

Originally Posted by Ichal

$T_1 = \frac{H}{xAB}$

Unlinked:

$T_2 = \frac{H_1}{xA} + \frac{H_2}{xB}$

$T_2 - T_1 = \frac{BH_1 + AH_2 - H}{xAB} > 0$

As x > 0, A,B > 1 and H = H_1 + H_2. Which means T_2>T_1. (Why is the forum ending that with a '='?).

Additive buffs:

$T_1 = \frac{H}{A(x+B)}$

$T_2 = \frac{H_1}{Ax} + \frac{H_2}{x+B}$

$T_2 - T_1 = \frac{x(H_1 + AH_2 -H) + BH_1}{Ax(x+B)} > 0$

So again T_2 > T_1 for the same reasons.

Because the above is quite general, it applies to all cooldowns, and not just bloodlust/trinket. It is optimal to use all your cooldowns at the same time.

[top]Discussion

Though the results are counter-intuitive there is a (relatively) simple explanation for them. Unlike other dps enhancing effects, execute scales with the mobs HP, and so can be modelled as a flat reduction of the mobs HP; if below 35% every point of damage effectively becomes X points, then the monster's effective hp are scaled by 1/X. If we apply execute as a HP change, not a dps change, it becomes obvious that it does not matter when we BL.

This point was first raised by Shalas:
Benefactors Bar: http://elitistjerks.com/f30/t11107-i...9/#post1089860

[top]Further Examples

Some further examples for those who doubt math:

Benefactors Bar

Originally Posted by Shalas

Vastly simplified example: boss has 800 HP, RDPS is 2, Bloodlust+Trinkets+etc. and low health are both +100% RDPS, low health boost kicks in at 50%.

Bloodlust at beginning:

Seconds	Damage Done
0-39	160
40-159	240
160-260	400

Total fight length of 260 seconds.

Bloodlust at 50%:

Seconds	Damage Done
0-199	400
200-239	320
240-259	80

Total fight length of 260 seconds.

Benefactors Bar

Originally Posted by Mearis

Here are some numerical simulations varying the time when trinkets are used/heroisms are used:

For reference:

boss_HP=300000;
base_boss_HP=boss_HP;
base_DPS=1000;
execute_DPS=1.2;
bloodlust_increase=1.3;
bloodlust_duration=30;
trinket_increase=100;
trinket_duration=15;

Trinket Used From: 0 until: 15
Bloodlust Used From: 239 until: 269
Total Fight Length: 280
Time from 1:80: 239
Time from 80:100: 41

Trinket Used From: 241 until: 256
Bloodlust Used From: 241 until: 271
Total Fight Length: 279
Time from 1:80: 241
Time from 80:100: 38

Trinket Used From: 231 until: 246
Bloodlust Used From: 0 until: 30
Total Fight Length: 280
Time from 1:80: 231
Time from 80:100: 49

Trinket Used From: 0 until: 15
Bloodlust Used From: 0 until: 30
Total Fight Length: 279
Time from 1:80: 229
Time from 80:100: 50

Making the numbers slightly 'patchworky':

boss_HP=20000000;
        base_boss_HP=boss_HP;
        base_DPS=80000;
        execute_DPS=1.2;
        bloodlust_increase=1.3;
        bloodlust_duration=30;
        trinket_increase=200*18;
        trinket_duration=15;

Trinket Used From: 0 until: 15
Bloodlust Used From: 200 until: 230
Total Fight Length: 232
Time from 1:80: 200
Time from 80:100: 32

Trinket Used From: 201 until: 216
Bloodlust Used From: 201 until: 231
Total Fight Length: 232
Time from 1:80: 201
Time from 80:100: 31

Trinket Used From: 191 until: 206
Bloodlust Used From: 0 until: 30
Total Fight Length: 232
Time from 1:80: 191
Time from 80:100: 41

Trinket Used From: 0 until: 15
Bloodlust Used From: 0 until: 30
Total Fight Length: 232
Time from 1:80: 190
Time from 80:100: 42

[top]Exceptions

This model makes a number of assumptions, the largest of which is that multiplicative effects (such and bloodlust) are symmetric above and blow 35%, when this does not hold then the their use will within execute range can change the total fight length. However, it does not mean that it is always the correct to use them during the last 35%:

Originally Posted by MatsT

Joe the Wizard output 100 dps. When the boss drops below 50%, his damage increases to 200 dps due to cool talents. Greg the Lizard Lord can also output 100 dps, but unfortunately he has no talents that increases his damage at low boss health. When Greg pops his bloodlust, Joe's dps is doubled. Greg does not benefit from bloodlust at all. In conclusion.
Above 50%:
Joe: 100 dps without bloodlust, 200 dps with.
Greg: 100 dps without bloodlust, 100 dps with.
Below 50%:
Joe: 200 dps without bloodlust, 400 dps with.
Greg: 100 dps without bloodlust, 100 dps with.

Now consider the two cases of popping bloodlust early and late in the fight. Let's set boss hp to 100k

Early bloodlust:
40 seconds of 200+100dps, meaning 12k damage.
190 seconds of 100+100dps, meaning 38k damage.
167 seconds of 200+100dps, meaning 50k damage
Total: boss dies after 397 seconds.

Late bloodlust:
250 seconds of 100+100dps, meaning 50k damage.
40 seconds of 400+100dps, meaning 20k damage.
100 seconds of 200+100 dps, meaning 30k damage.
Total: boss dies after 390 seconds.

Originally Posted by Wraithlin

To reverse your example
A = Above X%, Below X%, (with BL)
J = 100, 200 (100, 200)
G= 100, 100 (200, 200)
Joe has an execute talent but does not scale with haste. Greg scales with haste, but has no execute talent.

100k HP, BL early
40*(200+100) = 12k
190*(100+100)= 34k
167*(100+200) = 50K
Total time = 397

100k, BL late
250*(100+100) = 50k
40*(200+200) = 16k
113*(200+100) = 34k
Total = 403s

What matters is the total percentage change in raid dps when cooldowns are used. It is not always clear which part of the fight is optimum for cooldowns: some classes classes will scale better with haste below 35% than above it (eg mages, warriors, warlocks); some will scale worse below 35% than above it (eg hunters, paladins), and some will not change noticeably (eg rogues, druids, deathknights). Overall the differences are very small, and we can consider them insignificant for all real systems.

Originally Posted by Nevets_69

I did up an excel spreadsheet based on his scenarios to really take a closer look. Here's the summary:

	Boss Health	600000																
					Early Bloodlust							Late Bloodlust					
	Early		Late		Early DPS time		Late DPS time				Early DPS time		Late DPS time			
Scenar	No BL	w/ BL	No BL	w/ BL	BL Time	Non BL t	BL Time	Non BL t	Total		BL Time	Non BL t	BL Time	Non BL t	Total
1	2500	3000	2500	3000	40	72		0	120		232		0	120		40	72		232
2	2500	3250	3750	4875	40	68		0	80		188		0	120		40	28		188
3	2500	3010	2550	3075	40	71.84		0	117.6470588	229.4870588	0	120		40	69.41176471	229.4117647
4	2500	3100	3000	3750	40	70.4		0	100		210.4		0	120		40	50		210
5	2500	3240	3700	4800	40	68.16		0	81.08108108	189.2410811	0	120		40	29.18918919	189.1891892

Here are the differences:

	Time Diff		%
1	0			0
2	0			0
3	0.075294118		0.008203782
4	0.4			0.047573739
5	0.051891892		0.006856203

So in the most dramatic case, it's still only a 0.05% difference.

[top]No Bloodlust in the raid

There is a small advantage to splitting trinkets when the raid has no bloodlust at all. In this situation, those without an execute multiplier on damage should trinket early, and those with such a bonus should trinket late; again, the difference is marginal. This only applies to a fight length shorter than trinket CD, otherwise one could double trinket early and late.

Originally Posted by MatsT

Super trinket gives 100dps for 10s, Mage does 200sp, rogue does 100dps, MFury is +10% dps, 20k boss health.

Rogue trinket early, mage trinket late:
10s @ (100+100) + 200 = 400 = 4k total
51.67s @ 100 + 200 = 300 = 15.5k total
10s @ 100 + (200+100)*1.1 = 430 = 4.3k total
19.4 @ 100 + 200*1.1 = 320 = 6.2k total
Total time = 91.07s

Both trinket late
65s @ 100 + 200 = 300 = 19.5k total
10s @ (100+100) + (200+100)*1.1 = 530 = 5.3k total
16.25s @ 100 + 200*1.1 = 320 = 5.2k total
Total time = 91.25s

[top]Acknowledgements

This discussion was first raised by Binkenstein in the benefactors Bar, who placed it in his blog:
- Benefactors Bar: http://elitistjerks.com/f30/t11107-i...8/#post1088118
- Bloodlust & the "Execute" Talents - Elitist Jerks

The mathematics of the starting models were developed by Wraithlin and Ichal.
- Benefactors Bar: http://elitistjerks.com/f30/t11107-i...0/#post1091180

The assumption of symmetric bloodlust effect was noted by Zakalwe.

Examples were calculated by Shalas, Wraithlin, Songster, Mearis, Neveats, MatsT and others.
Benefactors Bar: http://elitistjerks.com/f30/t11107-i...9/#post1089860
Benefactors Bar: http://elitistjerks.com/f30/t12376-r...8/#post1139701
[Math] Bloodlust/Heroism timing

[top]Copyright Information

This article is the original work of Wraithlin (Owner of the Wraithlin user account on elitistjerks.com), except where reference is made to other contributors. The article and all future versions of the article are licensed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. Reproduction of the article in full or in part, or derivative works based on the article, including translations, are permitted as long as:

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Fatoe · 12/09/09, 10:07 AM

Wonderful post, although there are a few things I would like to add.

I think that there are two diffrent kind of cooldowns: haste and damage cooldowns.The diffrence between them is that it is useful to stack haste + damage cooldowns at the same time, or damage + damage cooldowns. Although, stacking haste + haste is not worth it, according to my calculations/

Lets take for example a frost mage who is spamming frostbolt. Now assume that he is totally naked and is only wearing [Scale of Fates]. That means that his only haste abilities are Icy Veins and [Scale of Fates]:

Normal  :  3 sec cast  --> 13.33 casts in 40 seconds
Trinket  :  % spell haste = (432) / (32.79) = 13.2    New Casting Time = (3 sec) / (1 + ((13,2%)/(100))) = 2.65 sec cast  --> (20 sec)/(2.65 sec) = 7.55 casts in 20 seconds
Icy Veins : New Casting Time = (3 sec) / (1 + ((20%)/(100))) = 2.5 sec cast --> (20 sec)/(2.5 sec) = 8 casts in 20 seconds
Trinket + Icy Veins : New Casting Time = (3 sec) / (1 + ((13,2% + 20%)/(100))) = 2.25 sec cast --> 8.88 casts in 20 seconds

In other a 40 sec test:
Normal (40 sec) = 13.33 casts
Trinket (20 sec) + Icy Veins (20 sec) = 7.55 casts + 8 casts = 15.55 casts
Icy Veins + Trinket (20 sec) + Normal (20 sec) 8.88 casts + ((13.33)/(2)) casts = 15.545 casts

Benefit: 0.05 seconds
NOTE: benefit will increase by amount of haste you already have (by gear or bufs) (personally I have a ~4% damage boost by not stacking trinket + Icy Veins)

Also, I think there is another reason why using bloodlust early is better than using bloostlust when a boss has lower than 35% health:
By using it early, it will decrease the amount of time that you can't use any execute effects. In other words: if you use it early, you can start earlier using execute effect against the boss. Which will result into a quicker death (I am sorry but I havent tested this yet, will come soon hopefully.)

Erdluf · 12/09/09, 12:46 PM

Fatoe,

You need to be careful when doing math for stacked Haste effects. Effects that increase HR are additive with each other. Most other affects (and I assume that Icy Veins is in that category) are multiplicative. Changing your

3/(1+.132+.2) = 2.25 sec cast

to

3/(1+.132)/(1+.2) = 2.21 sec cast

would reverse your conclusion.

Spellcasters whose rotation has an instant-cast (or a 1.5s cast) spell, have a soft haste cap at just 50% haste, which is very easy to reach, particularly with Bloodlust. Depending on your gear and complete rotation, you might have a reason to avoid stacking haste cooldowns.