Diablo® III

Frustrated by the lack of a definitive comparison between the most popular Cluster Arrow (CA) runes, the common Area Damage (AD) levels and the Grenadier passive, I performed a Monte Carlo simulation of them and analyzed the results.

Overview

The simulation was performed 100,000 times. Over each iteration a damage calculation with the runes Loaded for Bear (LfB), Maelstrom and Shooting Stars (SS) was performed on a set of 1 to 30 targets and with the AD levels 50%, 70%, 90% and 114%. The positions of the targets was randomly generated each time and constrained to a 20-yard radius clump, centered upon the impact point of the CA. The positions of the 4 grenades from LfB were also randomly generated with each set of mobs.

20 yards was chosen as the radius because it's a round, reasonable distance in which 1-30 monsters can be situated.

This picture is useful when visualizing the various radii involved:

http://i.imgur.com/xon2uqe.jpg
And here's a particularly nasty screenshot showing what a distribution of 20 or more monsters in a 20-yard radius would look like:

http://i.imgur.com/nCgNGms.jpg
A smaller simulation of 1 to 5 mobs clustered in a 10-yard radius was also performed to get a general idea of solo performance.

Results

All of the data and some semi-useful charts are available in this document:

https://drive.google.com/file/d/0ByPqxuexlYkDenZtRWJyVUtjek0/view?usp=sharing
The damage amounts you will find are the sum total damage done by one shot of the skill, on average, with differentiation for various levels of AD. This number is raw skill % weapon damage and is suitable to be multiplied by your particular combination of critical hit chance/damage, elemental% damage, weapon damage rolls, elite%, DIBS and so on to determine the truly obscene amount of damage that would be done.

On page 1 is a graph of the raw damage of each rune with various target counts and area damage percentages. Conclusions:

1. LfB outperforms Maelstrom and SS when fired into a clumping of 13 or more monsters randomly distributed within an 20-yard radius. Its performance would obviously be relatively improved if those monsters were more tightly clumped.
2. The relative performance of Maelstrom and SS are similar for all numbers of targets
3. The performance of LfB is obscenely greater than that of Maelstrom and SS at higher target counts, especially when coupled with AD. See below for more details

On page 2 is a comparison of the relative performance of LfB with 70%, 90% and 114% AD vs. 50% AD. A few noteable results:

1. Within a 20 yard clump (keep in mind this is with the mobs distributed randomly, not even clustered at the center), at 10 targets 70% AD outperforms 50% AD by ~12%. 90% AD outperforms 50% AD by ~24% and 114% AD outperforms it by ~38%.
2. At 20 targets, 114% AD outperforms 50% AD by ~60%.
3. In clumps of 22 mobs, each 1% of AD% adds about 1% to total damage done when using LfB. This scaling increases as the mob count goes higher. The importance of AD in trials can not be overstated!

On page 3 is the results of another 100,000 iteration simulation of 10-yard clumps of 1 to 5 targets. This is primarily for comparing solo performance. Conclusions:

1. SS and Maelstrom are tied at 4 targets. Maelstrom is superior at 5 targets, and inferior vs. SS at 3 or less.
2. The 1-target damage in the results for LfB is not accurate against large targets like Rift Guardians. In that case, you should just assume 1650% weapon damage (770% from the strike + 4x220% from the grenades).
3. LfB is generally not competitive to the rocket runes in low target count situations.

On page 4 is a relative comparison of LfB and Maelstrom vs. SS. Some conclusions:

1. At 11 targets, LfB begins outperforming SS by 3-5% depending on AD.
2. At 20 targets, LfB outperforms SS by 27-30%.
3. At 30 targets, LfB outperforms SS by 41-42%.
4. The performance of Maelstrom vs. SS ranges from ~15% better (5 targets, 50% AD) to ~5% (30 targets, any AD)

Pages 5-8 are the raw data. The "Total Damage" columns are the total amount of damage done, including all AD. The "In Zone A" columns are the total of the damage done within the splash radius of the initial arrow (15 yards). Finally, the "From AD" columns are the amount of damage that was done by AD alone. This is an interesting number to compare to the "Total Damage"!

Page 9 is the Grenadier simulation data. Conclusion: at all target counts and levels of AD, Grenadier is a ~7% improvement in DPS with LfB.

Caveats

There are a few things about this simulation that skew it negatively in regards to LfB. In practice the following will enhance the performance gap between LfB and Maelstrom/SS:

1. Many mobs have hit boxes larger than a 2-yard radius. The larger the hit box, the greater the chance of being hit by more grenades.
2. LfB is a fire rune, thus you would normally swap out Pride's Fall/Hexing Pants for a Cindercoat. Given perfect gear, this equates to a 12.5% flat damage buff because of the 20% fire damage on the Cindercoat.
3. The calculations done here (minus the Grenadier simulation), do NOT use the passive Grenadier for LfB, but DO use the Ballistics passive for Maelstrom/SS. Thus, you have an extra passive slot available with LfB.

Assumptions

* Each mob was modeled as having a 2-yard radius hitbox. This is the same as the player. If a larger hit box was used, this would favor LfB
* The cluster arrow skill splash radius is 15 yards (according to Nyan)
* The four grenades from LfB are assumed to land in random locations within 4 to 10 yards of the point of impact. See this screenshot for justification:

http://i.imgur.com/6jUUYfC.jpg
* The grenades from LfB are assumed to have a 4-yard radius AoE
* A target can be struck only once from rockets

Final Words

Depending on interest, it is very simple for me to run further tests with different mob counts, clump radii and average hitbox size. I could even be arsed by a select few (>^^)> to throw MfD Grim Reaper in there.

Reserved.

Nice post.
Congrats.

very cool.

so would you say it is worth having grenadier on a CA-LFB build instead of say Steady Aim?

i figured as far as passives custom engineering is a must as is awareness, i tend to use CTW in grifts with Steady Aim. curious if its worth dropping SA for gren?

02/11/2015 01:11 PMPosted by sickness

very cool.

so would you say it is worth having grenadier on a CA-LFB build instead of say Steady Aim?

i figured as far as passives custom engineering is a must as is awareness, i tend to use CTW in grifts with Steady Aim. curious if its worth dropping SA for gren?

Yeah CtW and CE are musts.

EDIT:

A more thorough comparison of SA vs. Grenadier:

http://us.battle.net/d3/en/forum/topic/16283529024?page=1#19

I made a post about area damage a while ago, but was too lazy to continue working on it. I may go back to work on it to give a more accurate DPS chart for my clan. Keep in mind that at the time I made this post, density isn't as good as it is now :P
http://us.battle.net/d3/en/forum/topic/13842144651

Whenever I'm not lazy, I could go back to it. Your results seem to match mine. Yours should be slightly lower due to the fact that you assume mob radius = 2.

As for CA:
CA radius is 15 yards.
Grenades idk, hard to say cause they keep spawning randomly. Seems to be randomly within 5 yards of the initial hit. I'd say probably closer to 5 yard radius grenades?

All my testing is using illusory boots, zei's stone of vengeance, min=max gear, THUD, screen recording software and legacy nat's set for discipline regen (cdr+rcr+focused mind is another replacement). I just spam caltrops -> tort ground to have the monster stand still, and use multiple circle overlays from turbohud to help me visually see the circle. I guess you don't have to use THUD, if you know another program which has the algorithm to draw the circles. The min=max gear + zei's is to help confirm distance when I stand where I shot.

As for grenadier, I couldn't confirm if it actually increased the size of the grenades or if it does indeed let you hit more monsters from grenades.

My clan has used 1xSS and 1xLfB instead of 2xLfB for our high trial keys, and it does work. However we still found that we did slightly better w/ LfB even when factoring in physical damage for grim reaper. We haven't gotten a 63 key with this setup (highest 62), while we have gotten 63 keys with 2xLfB. This could be due to the 20% extra elemental from cindercoat. Not sure. Andi's visage maybe worth a try on physical spec since we used pride's fall. Idk anyone who has a CA/phys/CHC andi's visage. Will give up the socket in the helm if we do this, which will result in less CDR.

Anyways, (>^^)>

02/11/2015 03:35 PMPosted by VocaloidNyan

I made a post about area damage a while ago, but was too lazy to continue working on it. I may go back to work on it to give a more accurate DPS chart for my clan. Keep in mind that at the time I made this post, density isn't as good as it is now :P
http://us.battle.net/d3/en/forum/topic/13842144651

Whenever I'm not lazy, I could go back to it. Your results seem to match mine. Yours should be slightly lower due to the fact that you assume mob radius = 2.

As for CA:
CA radius is 15 yards.
Grenades idk, hard to say cause they keep spawning randomly. Seems to be randomly within 5 yards of the initial hit. I'd say probably closer to 5 yard radius grenades?

All my testing is using illusory boots, zei's stone of vengeance, min=max gear, THUD, screen recording software and legacy nat's set for discipline regen (cdr+rcr+focused mind is another replacement). I just spam caltrops -> tort ground to have the monster stand still, and use multiple circle overlays from turbohud to help me visually see the circle. I guess you don't have to use THUD, if you know another program which has the algorithm to draw the circles. The min=max gear + zei's is to help confirm distance when I stand where I shot.

As for grenadier, I couldn't confirm if it actually increased the size of the grenades or if it does indeed let you hit more monsters from grenades.

My clan has used 1xSS and 1xLfB instead of 2xLfB for our high trial keys, and it does work. However we still found that we did slightly better w/ LfB even when factoring in physical damage for grim reaper. We haven't gotten a 63 key with this setup (highest 62), while we have gotten 63 keys with 2xLfB. This could be due to the 20% extra elemental from cindercoat. Not sure. Andi's visage maybe worth a try on physical spec since we used pride's fall. Idk anyone who has a CA/phys/CHC andi's visage. Will give up the socket in the helm if we do this, which will result in less CDR.

Anyways, (>^^)>

Cool, I'll re-run it with a 15-yard radius CA splash and 5-yard grenade leash

EDIT:

A final value of 4-10 yards was determined for grenade leash range. The simulation data and OP has been updated.

so which is a better passive to use for lfb build? Grenadier or ballistics?

02/11/2015 05:39 PMPosted by Dolemite

so which is a better passive to use for lfb build? Grenadier or ballistics?

Definitely not Ballistics. LfB releases grenades, not rockets.

Ok, revised results are up. Nyan might test what the grenade leash range for LfB is. I definitely don't think it's 5, in fact my original guess of 8 was probably too low (see screenshot).

We're still not 100% on whether the splash radius of LfB grenades is 4 or 5. Does anybody know? If it's 5 instead of 4, that would improve the LfB results.

this spec is seriously no joke. Im killing the majority of elites in t6 rifts quicker than dh's who are 200 paragon levels higher than me. It's retarded how im melting faces with almost 100% uptime on CA thanks to reapers wraps and blood vengeance. Fire spec with CA LFB is no joke.

@Nyan&Shadow - so with all this fantastic math, has CA finally been defined as "better" then MS for 4-man GR's?

Or was it always better? lol, And MS is just a cheaper spender.

Great thread. (>^^)>

i think the result of this highlights that if your tanks can group mobs tightly, 2x LFB dh will vastly outperform 1x LFB and 1x MS. however, if not, then the coverage and damage efficiency of MS will have a lot more value to your group.

the idea of the gren passive is new to me though, never really considered it. i always ran with the idea that i needed to maximize the damage of the initial burst from CA, not the follow up damage from the grenades. so there is a lot of potential learning that comes out of this discussion.

thx for the nice comparison Shadow.

Would be nice if the curves for one rune had the same colour (LfB always red) and the %AD had one corresponding symbol (50% AD always square :-)

OP, this is friggin fantastic post. I love finding this stuff during lunch hour.

So, did we decide if Grenadier is the better option vs Steady Aim? with the LfB? I am going to try it tonight regardless.

Also, what are we finding with the Leg Gems on a LfB build, BP, BT and Zei's?

Thanks for the great post.

questions related to Group Grifts and LfB.

So i should rather use grenadier or archery instead of steady aim when running high GR lfb group and stack area damage for trials and elite damage for runs (this 2nd is my own knowledge).

Correct?

02/12/2015 09:06 AMPosted by Rudi1337

thx for the nice comparison Shadow.

Would be nice if the curves for one rune had the same colour (LfB always red) and the %AD had one corresponding symbol (50% AD always square :-)

Boom! Thank you for that, the graphs were driving me nuts! I uploaded a new version with an intelligent color/symbol scheme.

(>^^)>

02/12/2015 09:19 AMPosted by Ajflick42

So, did we decide if Grenadier is the better option vs Steady Aim? with the LfB? I am going to try it tonight regardless.

02/12/2015 09:28 AMPosted by Notrius

So i should rather use grenadier or archery instead of steady aim when running high GR lfb

Ok, I think the math says "meh" in regards to Grenadier in group situations. With the 20-yard clump, Grenadier gives about ~7%. I ran another test with a 15-yard clump (which is admittedly very small), and it's a bit higher. (NOTE: for early readers of the OP, this is a large difference between the original Grenadier values that were achieved with an 8-yard CA splash radius).

If we assume perfect group buffs and Wolf+BotP in effect:

Wolf: 30%
2 Toxins: 20%
2 Strongarms: 60%
Shield Glare: 20%
Piranhas: 30%
Haunt: 20%
BotP: 20%
BBV: 30%
MfD: 20%
45% CA: 45%

Total: 295%, w/ Steady Aim: 315%

4.15 / 3.95 = ~5.06%

So that means, even if every star I can think of aligns properly, Steady Aim only slightly underperforms Grenadier. Take away several of those buffs and SA begins to pull ahead.

02/12/2015 09:19 AMPosted by Ajflick42

OP, this is friggin fantastic post. I love finding this stuff during lunch hour.

Thank you guys for the positive feedback! That makes this effort so worth it.

(>^^)>
This zombie appears to have 1 yard hitbox radius
http://puu.sh/fPpAr.jpg

This grenade doesn't hit the monster:
http://puu.sh/fPkVf.jpg
Which is slightly more than 5 yards away from it's hitbox

This grenade does hit the monster:
http://puu.sh/fPmtb.jpg
Which is ~5 yards away from it's hitbox

So pretty sure at this point it's 5 yard grenade radius?

Let's see what happens if I add grenadier.

These 2 grenades doesn't hit the monster:
http://puu.sh/fPnj1.jpg
Which is ~5 yards away from it's hitbox

Another picture:
http://puu.sh/fPnzt.jpg

In other words, grenadier doesn't appear to increase the grenade radius at all on the non-cluster bomb runes.

As for the projectile of the grenades, they seem to vary between 4 to 10 yards. Not sure if it's uniformly distributed, but maybe you could assume so?

<(^^<)