Wired: Critical Conditions

[wire]

Effects that alter critical rate and critical damage modifiers for direct damage spells have changed a lot over the years. Keeping up with them has always been a challenge.

Assumptions

It is well documented that Spell Casting Fury contributes a 2/4/7 % crit chance modifier; so much so that this is actually in the AA's description! It was also documented that the first 3 ranks of Fury of Magic each contributed a 2% crit chance modifier after a few changes on live, but before the AA consolidation in 2007. [See here]

I was able to track down only a few references regarding the effects of Fury of Magic Mastery (now Fury of Magic 4-6) and Volatile Mana (now Fury of Magic 7-9) before they were consolidated into the Fury of Magic line. Those references indicate that both of these abilities increased the chance to crit by 1% or 2% per rank. [See here and here]

I don't really remember the source I had for the crit chance modifier of ranks 10-12 of Fury of Magic... it might have been from some beta info for the expansion they came in with. From what I remember, these 3 ranks each increase the chance to crit by 1% or 2%.

Elidroth informed me that Fury of Magic 13-15 should be 23/25/27%. That should place the increase per new rank at 5/2/2% in Underfoot.

There are different opinions on what to use as the crit chance modifier for the fourth Dragons of Norrath progression AA, Power of the Keepers/Dark Reign. I've always gone with 1%, although I've seen variations up to 3%.

Critical Chance AA Tests

To test this, I copied both Wire and my Bard alt over to the Test server and headed into the arena where I could abuse a Test Dummy. Underfoot parses were conducted on the Beta server. I wanted a reasonably accurate result, so I let each sample climb to over 10,000 successful hits with level 81+ critable spells. Each run took around 9 hours. Note: you have to zone after using /resetaa.

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  Crits  Hits   Observed  Expected  Effects

   101   10624  0.0095    0.0100    Power of the Keepers

  2418   17358  0.1393    0.1400    Fury of Magic 3/15
                                    + Power of the Keepers

  2498   14034  0.1780    0.1700    Fury of Magic 6/15
                                    + Power of the Keepers

  4307   18268  0.2358    0.2300    Fury of Magic 9/15
                                    + Power of the Keepers

  2822   10907  0.2587    0.2600    Fury of Magic 12/15
                                    + Power of the Keepers

  4048   13640  0.2968    0.3000    Fury of Magic 13/15

  4075   12604  0.3233    0.3200    Fury of Magic 14/15

  4208   12561  0.3350    0.3400    Fury of Magic 15/15

Observations indicate that Power of the Keepers does indeed increase the chance to crit by only 1%, while the addition of Spell Casting Fury 3/3 and Fury of Magic 3/12 result in a 14% chance to crit, as expected. Fury of Magic ranks 4-6 each increase the chance to crit by approximately 1%, as do ranks 10-12. Ranks 7-9, which used to be Volatile Mana, increase this chance by around 2% each.

Without Power of the Keepers, Fury of Magic 13 increases crit rate by 30%. Subtracting 7% for Spell Casting Fury and 18% for Fury of Magic 12, the increase from Fury of Magic 12 to 13 is 5%, while the increase from 13 to 14 is 2% and the increase from 14 to 15 also appears to be 2%.

Note: Wizards may have a completely different distribution, as their Spell Casting Fury Mastery line consolidates crit AA lines that other classes never received.

Using the observed values, the breakdown of spell crit chance AA looks like this:

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Rank  Rank  Rank  Total  Source
1     2     3

0.01              0.01   Power of the Keepers
0.02  0.02  0.03  0.07   Spell Casting Fury
0.02  0.02  0.02  0.06   Fury of Magic 1-3
0.01  0.01  0.01  0.03   Fury of Magic 4-6 (Fury of Magic Mastery)
0.02  0.02  0.02  0.06   Fury of Magic 7-9 (Volatile Mana)
0.01  0.01  0.01  0.03   Fury of Magic 10-12
0.05  0.02  0.02  0.09   Fury of Magic 13-15

                  0.35   Total

The total chance to crit from AA is 35% in Underfoot.

Critical Chance Stacking Tests

Along with AA, there are several spell effects that increase the chance to crit spells. I've listed all the effects I can recall that increase the chance to crit spells:

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Effect  Slot  Source

0.21     1    Auspice of the Hunter

0.21     2    First Spire of Elements

0.03     4    Circle of Power

0.50     5    Intensity of the Resolute
0.15     5    Glyph of Courage
0.10     5    Fierce Eye

0.12     9    Spirit of Vesagran

0.07    11    Third Spire of Enchantment

Note that all of these buffs have a slot associated with their crit chance modifier. We know that spells with crit chance modifiers in the same slot do not stack. For example: Intensity of the Resolute, Glyph of Courage and Fierce Eye will all overwrite one another. However, it has long been argued that buffs with crit chance modifiers in different slots may or may not stack.

If they do not stack, we would expect only the buff with the highest chance to crit to take effect. If they stack, we would expect either an additive, multiplicative or inverse result with two or more buffs.

For the first test, I dropped all buffs except for spell haste. For the second test, I activated only First Spire of Elements and Intensity of the Resolute. For the third test, I activated only First Spire of Elements, Fierce Eye and Spirit of Vesagran. For the fourth test, I managed to get Third Spire of Enchantment Rank 3 and Auspice of the Hunter Rank 4 (until I went LD).

With First Spire and Intensity, we'd expect a 97% crit rate assuming effects in different slots are additive. Similarly, we'd expect a 69% crit rate with First Spire, Fierce Eye and a Bard 2.0 click. First Spire with Third Spire and Auspice should yield a 67% chance to crit.

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  Crits  Hits   Observed  Expected  Effects

   2822  10907  0.2587    0.2600    Fury of Magic 12/15
                                    + Power of the Keepers

  10854  11194  0.9696    0.9700    Fury of Magic 12/15
                                    + Power of the Keepers
                                    + First Spire of Elements (3/3)
                                    + Intensity of the Resolute

   7047  10225  0.6892    0.6900    Fury of Magic 12/15
                                    + Power of the Keepers
                                    + First Spire of Elements (3/3)
                                    + Fierce Eye
                                    + Spirit of Vesagran

   2948   4431  0.6653    0.6700    Fury of Magic 12/15
                                    + Power of the Keepers
                                    + First Spire of Elements (3/3)
                                    + Third Spire of Enchantment (3/3)
                                    + Auspice of the Hunter (4/12)

Looking at the results, the observed crit rates are almost identical to the expected crit rates. Crit rate modifying buffs in different slots are clearly additive. The result can be extended to interactions with other buffs that I didn't explicitly test, like Glyph of Courage, whose effects should also be additive as long as the buffs stack.

Critical Damage Modifiers

The first 3 ranks of Destructive Fury increase critical damage by 25% total. Each other rank further increases critical damage by 5%.

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Rank  Rank  Rank  Total  Source
1     2     3

0.07  0.08  0.10  0.25   Destructive Fury 1-3
0.05  0.05  0.05  0.15   Destructive Fury 4-6
0.05  0.05  0.05  0.15   Destructive Fury 7-9
0.05  0.05  0.05  0.15   Destructive Fury 10-12

                  0.70   Total

Along with AA, there are several spell effects that increase critical spell damage:

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Effect  Slot  Source

0.10     5    Fierce Eye

0.50     7    Glyph of Destruction
0.75     7    Glyph of the Cataclysm

0.30    11    Third Spire of the Pathfinders

Unlike critical chance modifiers, damage modifiers do not stack for direct damage spells. Regardless of the slot each effect is in, only the largest will have any effect. Therefore, one should aim to stagger effects featuring critical damage modifiers.

Glyphs

Glyph of Destruction increases the critical damage modifier by 50%, while Glyph of Courage increases the critical chance modifier by 15%. Which is the best to use? It depends on the situation.

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Modifier  Chance  Duration  Result  Effect

0.50      0.26    120       15.6    Glyph of Destruction
1.70      0.15    90        23.0    Glyph of Courage

0.50      0.38    120       23.0    Equality

On its own, Glyph of Courage yields more of an effect than Glyph of Destruction, even though it is active for a shorter time. This is due to the large baseline critical damage mod versus the relatively small baseline chance to crit.

Increasing the chance to crit increases the overall effect of Glyph of Destruction, since its damage modifier is active more often. The influence of any effect that increases the chance to crit spells by 12% or more will make Glyph of Destruction the better overall choice.

Similarly, an effect that increases both the critical chance and damage modifier can raise questions. Take Fierce Eye and Glyph of Destruction for example:

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Modifier  Chance  Duration  Result  Effect

2.20      0.26    120       68.6    Glyph of Destruction
1.70      0.26    120       53.0    Base
                            15.6    Difference

1.80      0.36     60       38.9    Fierce Eye
1.70      0.26     60       26.5    Base
                            12.4    Difference

2.20      0.36     60       47.5    Glyph of Destruction
                                    + Fierce Eye
2.20      0.26     60       34.3    Glyph of Destruction
1.70      0.26    120       53.0    Base
                            28.8    Difference

                             0.8    Overall Difference

Here, the sum of each effect's impact over their duration is less than the overall impact of both effects occurring simultaneously. It's slightly better to use both together instead of one after the other.

Conclusions

Observations indicate that crit chance modifiers are additive, crit damage modifiers are not additive, and it is possible to reach a 100% crit rate by stacking multiple effects. Applying these results should increase your DPS.

Now that you're wired, have fun critting!

[Redius]

Nice writeup Wire; I look forward to your next installment of useful information!

[Sillaen]

Very nice indeed. From my testing and observation, I had the crit chance calculated at 28% and have been using 28% in my spell spreadsheet calculations. The 26% you showed seems more conclusive though.

[Haiden]

I just want to say first off that you are a machine. The main reason for posting though is that I have a question. Is crit rate capped at 100%?

[dorfillya]

I just want to say first off that you are a machine. The main reason for posting though is that I have a question. Is crit rate capped at 100%?

How could you crit more than 100% of the time?

[Haiden]

I just want to say first off that you are a machine. The main reason for posting though is that I have a question. Is crit rate capped at 100%?

How could you crit more than 100% of the time?

It is always more, more, more with people. There are always 2 directions to go if you cannot go over 100% can you go under 100%? I assume a crit is simply a check of your % chance vs. a random number from 1-100. In alot of games you cannot go to 100% in all checks, there is some chance to fail them. I was asking more along the lines of can you only crit 95% of the time not can you crit 105% of the time. I have yet to see a crit just fire off without me casting a spell.

[dorfillya]

I just want to say first off that you are a machine. The main reason for posting though is that I have a question. Is crit rate capped at 100%?

How could you crit more than 100% of the time?

It is always more, more, more with people. There are always 2 directions to go if you cannot go over 100% can you go under 100%? I assume a crit is simply a check of your % chance vs. a random number from 1-100. In alot of games you cannot go to 100% in all checks, there is some chance to fail them. I was asking more along the lines of can you only crit 95% of the time not can you crit 105% of the time. I have yet to see a crit just fire off without me casting a spell.

Ah, sorry, I misunderstood where you were coming from on that.

[Mindrix]

Missed this for a few days.

I can confirm that the Crit Rate ranks 7 to 9 were supposed to be 2% each and the ranks 10 to 12 are 1% each. The total AA buyable critical rate increases is 25% + 1% from DoN AA. This was told to me directly by Nodyin. Good to know he could read this data correctly. And confirmation things are working properly is nice.

On the Critical Damage, that only is true of DDs. DoT critical damage increases do stack, if different slot.


Thanks again Wire for the confirmation on the nuke additive effect. Saves the rest of us a lot of trouble.

[wire]

I picked up a Circle of Power ring for my Bard and realized it too increases the chance to crit direct damage spells. It's in slot 4, so should stack with everything else out there. I've added it to the list of effects. If anyone can think of anything else, lmk. Too bad Kumbaja is offline.

[Hzath]

Hey, Wire I wanted to say thanks and that you are pretty much my hero.

I'm not a magician, I'm a beastlord, but I admire the hard work and dedication you show and just wanted to say thanks.

I also wanted to let you know I linked this post over at http://www.beastlords.org" onclick="window.open(this.href);return false;, I was curious about this information so it's probably safe to assume others were as well. If you have a problem with this let me know and I'll of course take it down.

Thanks again for all your work,
Hzath