Hey ho,

first things first: the calculated break points in this post are not meant to be reached for. This post ist purely about showcasing how to reach mathy conclusions for World of Warcraft.

Big thanks are directed at Sadozai and Mis for correcting my shitty mathimproving this post in various ways. Additionaly, those who frequent earthshrine (discord) might’ve seen the formulas there already.

To tackle these questions, I’ll at first always collect all related necessary spell data. After listing that data, I’ll calculate the DPET of each part and combine them to formulas that shall answer the question. What’s DPET? Damage per execution time. This allows to compare spells to each other regardless of their different casttimes. You can use it to compare the worth of different speels. Check out this additional information.

## Lava Burst vs Lightning Bolt with a lot of Crit

Question:

Is there a point, when we would stop casting Lava Burst in favour of Lightning Bolt when stacking crit?

### Spelldata

Lava Burst

• SP: 53.125%
• 100% crit chance
• casttime: 2 sec
• 10 Maelstrom
• Overloads generate 4 Maelstrom

Lightning Bolt

• SP: 70.4%
• casttime: 2 sec
• 8 Maelstrom
• Overloads generate 3 Maelstrom

Earth Shock

• SP: 210%
• casttime: 1.5 sec
• cost: 60 Maelstrom

As you can see Lightning Bolt base spellpower coefficient is higher than Lava Burst. But because Lava Burst always crits Lava Burst generally deals more damage. This still spawns the question for this topic.

### DPET Lava Burst

``````# Lava Burst base damage
lava_burst = lvb_spellpower_coefficient * crit_dmg_multiplier / lvb_casttime
lava_burst = 53.125% * 2.5 / 2
lava_burst = 66.40625%
``````

This part was easy. We calculated the DPET of Lava Burst. But we’re still missing Mastery: Elemental Overload and Maelstrom generation.

``````# Adding Maelstrom
lava_burst += lvb_ms / ( es_cost + lvb_ms * es_casttime / lvb_casttime ) * ( es_dmg - lvb_base / lvb_casttime * es_casttime ) / lvb_casttime
``````

Wait a second! What’re `( es_cost + lvb_ms * es_casttime / lvb_casttime )` and `( es_dmg - lvb_base / lvb_casttime * es_casttime )` there? The first parenthesis adds the fractional Maelstrom generation loss of casting an Earth Shock instead of Lava Burst. The second one calculates the Earth Shock gain compared to casting Lava Burst.

``````lava_burst += 10 / ( 60 + 10 * 1.5 / 2 ) * ( 210% - 53.125% * 2.5 / 2 * 1.5 ) / 2
lava_burst += 8.1771%

# Combined damage
lava_burst = 66.40625% + 8.1771%
lava_burst = 74.5833%
``````

Lava Burst has a combined DPET of ~ 74.6%.

You can get the same result much easier by adding up enough to cast one Earth Shock and then deviding the resulting spellpower by the time it took to reach that.

``````( 6 * lvb_base + es_dmg ) / ( 6 * lvb_casttime + es_casttime )
( 6 * 53.125% * 2.5 + 210% ) / ( 6 * 2 + 1.5 )
1006.875% / 13.5
74.583%
``````

So choose your fightscalculation approach carefully.

### DPET Lightning Bolt

``````# ignoring crit at first
lightning_bolt = lb_spellpower_coefficient / lb_casttime
lightning_bolt = 70.4% / 2
lightning_bolt = 35.2%
``````

Once again we got the DPET first. And are now adding the Maelstrom portion.

``````# Adding Maelstrom
lightning_bolt += lb_ms / ( es_cost + lb_ms * es_casttime / lb_casttime ) * ( es_dmg - lb_dmg / lb_casttime * es_casttime ) / lb_casttime
lightning_bolt += 8 / ( 60 + 8 * 1.5 / 2 ) * ( 210% - 70.4% / 2 * 1.5 ) / 2
lightning_bolt = 9.527%

# Combined damage
lightning_bolt = 35.2% + 9.527%
lightning_bolt = 44.727%
``````

Lightning Bolt has a combined DPET of 44.727%.

Like the Lava Burst section showed, this calculation can be done differently, too.

``````( 7.5 * lb_dmg + es_dmg ) / ( 7.5 * lb_casttime + es_casttime )
( 7.5 * 70.4% + 210% ) / ( 7.5 * 2 + 1.5 )
738% / 16.5
44.727%
``````

### Solving for crit chance

Compare Lightning Bolt to Lava Burst and find the necessary crit_chance to make Lightning Bolt at least equal if not greater than Lava Burst. To do so we’re going to use the simplyfied calculations. We need to use the full calculations, though, because we need to apply the crit_chance at all the correct places.

``````(es_ms / lb_ms * lb_dmg + es_dmg) * (base_multi + crit_multi * crit_chance) / (es_ms / lb_ms * lb_casttime + es_casttime) >= (es_ms / lvb_ms * lvb_spellpower_coefficient * (base_multi + crit_multi) + es_dmg * (base_multi + crit_multi * crit_chance)) / (es_ms / lvb_ms * lvb_casttime + es_casttime)
(es_ms / lb_ms * lb_dmg + es_dmg) * (base_multi + crit_multi * crit_chance) / (es_ms / lb_ms * lb_casttime + es_casttime) >= es_ms / lvb_ms * lvb_spellpower_coefficient * (base_multi + crit_multi) / (es_ms / lvb_ms * lvb_casttime + es_casttime) + es_dmg * (base_multi + crit_multi * crit_chance) / (es_ms / lvb_ms * lvb_casttime + es_casttime)
(es_ms / lb_ms * lb_dmg + es_dmg) * (base_multi + crit_multi * crit_chance) / (es_ms / lb_ms * lb_casttime + es_casttime) - es_dmg * (base_multi + crit_multi * crit_chance) / (es_ms / lvb_ms * lvb_casttime + es_casttime) >= es_ms / lvb_ms * lvb_spellpower_coefficient * (base_multi + crit_multi) / (es_ms / lvb_ms * lvb_casttime + es_casttime)
(es_ms / lb_ms * lb_dmg + es_dmg) / (es_ms / lb_ms * lb_casttime + es_casttime) * (base_multi + crit_multi * crit_chance) - es_dmg / (es_ms / lvb_ms * lvb_casttime + es_casttime) * (base_multi + crit_multi * crit_chance) >= es_ms / lvb_ms * lvb_spellpower_coefficient * (base_multi + crit_multi) / (es_ms / lvb_ms * lvb_casttime + es_casttime)
((es_ms / lb_ms * lb_dmg + es_dmg) / (es_ms / lb_ms * lb_casttime + es_casttime) - es_dmg / (es_ms / lvb_ms * lvb_casttime + es_casttime)) * (base_multi + crit_multi * crit_chance) >= es_ms / lvb_ms * lvb_spellpower_coefficient * (base_multi + crit_multi) / (es_ms / lvb_ms * lvb_casttime + es_casttime)
base_multi + crit_multi * crit_chance >= es_ms / lvb_ms * lvb_spellpower_coefficient * (base_multi + crit_multi) / (es_ms / lvb_ms * lvb_casttime + es_casttime) / ((es_ms / lb_ms * lb_dmg + es_dmg) / (es_ms / lb_ms * lb_casttime + es_casttime) - es_dmg / (es_ms / lvb_ms * lvb_casttime + es_casttime))
crit_multi * crit_chance >= es_ms / lvb_ms * lvb_spellpower_coefficient * (base_multi + crit_multi) / (es_ms / lvb_ms * lvb_casttime + es_casttime) / ((es_ms / lb_ms * lb_dmg + es_dmg) / (es_ms / lb_ms * lb_casttime + es_casttime) - es_dmg / (es_ms / lvb_ms * lvb_casttime + es_casttime)) - base_multi
crit_chance >= (es_ms / lvb_ms * lvb_spellpower_coefficient * (base_multi + crit_multi) / (es_ms / lvb_ms * lvb_casttime + es_casttime) / ((es_ms / lb_ms * lb_dmg + es_dmg) / (es_ms / lb_ms * lb_casttime + es_casttime) - es_dmg / (es_ms / lvb_ms * lvb_casttime + es_casttime)) - base_multi) / crit_multi

crit_chance >= (60 / 10 * 53.125% * (1.0 + 1.5) / (60 / 10 * 2s + 1.5s) / ((60 / 8 * 70.4% + 210%) / (60 / 8 * 2s + 1.5s) - 210% / (60 / 10 * 2s + 1.5s)) - 1.0) / 1.5
crit_chance >= 0.6823
``````

The cool thing about doing these kind of calculations in spreadsheets is: it allows us to verify our results with simple try and error. This means we can just enter the calculated 68.23% crit into the crit character field at the top of this spreadsheet (after creating a copy of it) and see…it matches.

The first one who solved this previously wrong calculation was HawkCorrigan#1811. The issue was, that previously the comparison calculation applied crit to the ms dpet of Lava Burst, which already had some Lava Burst spellpower calculation. This double dipping on crit was wrong. You can now see the corrected formula above.

The linked spreadsheet has the old, new, and a calculation with added mastery into it. Enjoy!

## Lightning Bolt during Storm Elemental vs baseline haste

To tackle this question we first need to know how Storm Elemental stacks work differently than haste. Haste reduces the casttime of a spell by division. `new_casttime = base_casttime / ( 1.0 + haste )` Storm Elemental stacks on the other hand reduce the casttime directly.

Type Value
Haste 30%
SE stacks 10 (30% casttime reduction)
Base casttime 2 seconds
Hasted casttime 1.538 seconds
SEed casttime 1.4 seconds

Additionally we need to know, that the GCD during Storm Elemental uptime is locked at 0.5 seconds for Lightning Bolt and Chain Lightning. So once we have a shorter cast time than 0.5 seconds we found this haste break point.

After getting this out of the way, let’s head into this fairly easy calculation. First we calculate the new casttime with Storm Elemental 20 stacks.

``````LB = base_casttime * ( 1.0 - se_stacks * 0.03 )
LB = 2 * ( 1.0 - 20 * 0.03 )
LB = 0.8 seconds
``````

Now the last step is to calculate how much haste we need to get Lightning Bolt casttime to 0.5 seconds.

``````goal_casttime >= casttime / ( 1.0 + haste )        | * ( 1.0 + haste )
goal_casttime * ( 1.0 + haste ) >= casttime
goal_casttime + goal_casttime * haste >= casttime  | - goal_casttime
goal_casttime * haste >= casttime - goal_casttime  | / goal_casttime
haste >= ( casttime - goal_casttime ) / goal_casttime

haste >= ( 0.8 - 0.5 ) / 0.5
haste >= 0.6
``````

This means: once we have more than 60% haste (looking at you Bloodlust!), Lightning Bolt will be cast faster than our GCD with 20 stacks. Breakpoint found.

My spreadsheet with all of the above

Sadozai much better spreadsheet (talent checkboxes, better formatting, better structure. It’s the Epic to my Uncommon spreadsheet)

Reminder: The breakpoints of this post aren’t meant to be reached for. This post is purely a nice-to-know!

Yours sincerely,
Bloodmallet(EU)