Calculating Rune Arm Damage is IMPOSSIBLE

[Wernerus]

I play an Arti, and I find one of the most effective sources of DPS comes from the rune arm. For some time, I've been tracking posts and trying to figure out how to maximize Rune Arm DPS. Some time ago, a fantastic post was submitted to the boards on this topic:

http://forums.ddo.com/showthread.php?t=351847

More recently, since the U14 update, things have changed, and the information is a bit out of date. First, we now have spell power instead of the old potency et all item boosts.

Additionally, there was a post some time ago where the devs chimed in and indicated they had introduced a new stealth rune arm nerf with U14. Essentially, all rune arms now have a multiplier effect applied to all spell power, and the multiplier is somewhere between 50% to 80%, and varies for each rune arm. The dev justification for this was that rune arms never benefitted from empower or maximize metamagic feats, and with the U14 update, all item enhancements are now additive, not multiplicative with those feats. Since item enhancements had their numbers "buffed", the devs nerfed the rune arms to compensate.

Or something like that. To be honest, it's completely overcomplicated, confusing, and impossible to calculate and plan your rune arm damage now.

So with that in mind, I decided to try and unlock the mysteries of rune arms post U14, and figure out what exactly the damage potential for each rune arm is. Initially, I was quite ambitious, as I have 6 of the 7 tier 5 rune arms (all but Corruption of Nature from U15), and I wanted to figure out what the "stealth nerf" would be on each rune arm, then figure out what the maximum spellpower enhancements might be for each rune arm, and from there, figure out which rune arm could deal the highest potential damage.

Well, after a significant amount of testing, I realized this goal is impossible. However, I will share with you what I have discovered, and perhaps some other people who are interested can chime in with their thoughts or test results.

First, I started with testing Glorious Obscenity. I chose this rune arm because I don't have any enhancements in the acid line, and therefore it should be easy to determine what the actual base damage of the rune arm is, Without any impact from spell power. From the description of the rune arm, firing it at Tier V charge should do damage equal to 8 to 30 + 1 to 10 per artificer level. My toon is a Level 23 character, but since the text talks only about artificer level (not epic level), it should be safe to assume DDO views my toon as a L20 Arti, therefore the average damage should be something like (avg of 8 - 30) + (avg of 20 X 1d10). This works out to 19 + 20 X 5.5 = 129 damage average. A few assumptions worth noting here are:
- I'm assuming that the base damage of 8 to 30 damage will average out at the mid point, or 19 damge. This may not be the case.
- I'm assuming that each d10 per level is an actual d10 rolled, thus 5.5 damage per d10 on average. This may not be the case if DDO is doing some weird thing like rolling 1d5 + 5 for each d10, or some such.
- Finally, I did all my testing on the training dummy. This may not have been the best approach, as I don't really know what the impact to damage is from using the training dummy. I.e., is it helpless, and if so how does that affect damge? Does it get a saving throw? Can a critical hit be scored?

Here are the results I found with Glorious Obscenity, after rolling 100 'hits' with the rune arm off a Tier V charge, and recording the damage numbers:

Mean: 136 damage
Median: 135 damage
Standard Deviation: 13.9 damage
Max: 177 damage
Min: 101 damage

I did observe a handful of damage numbers much lower than this (in the 50 - 70 range) but it quickly became apparant to me that these were significant outliers, and must be caused by some kind of successful "save" on the dummy's part, so I removed those outliers from the results.

So far, these numbers look pretty good. The 136 mean and 135 median is not too much higher than the expected 129 average damage. This could be due to random error from a sample size of only 100 attacks. It could also hint that perhaps the base damage of 8 to 30 does not always average around 19 damage. For instance, the base 8 to 0 damage may actually be averaging out closer to 25 or 26 damage per hit. It seems reasonable to assume that the d10's for each level of artificer are actually d10's being rolled, otherwise a more significant deviation in damage would have been observed at this point.

So the next question then is what is the spell power nerf being applied to Glorious Obscenity? To test for this, I got myself a corrosion scepter and tested another 100 attacks with the scepter equipped. With this scepter, my acid spellpower increased from 0 to 123. The new results are as follows:

Mean: 314 damage
Median: 312 damage
Standard Deviation: 36.3 damage
Max: 403 damage
Min: 219 damage

Again, I removed a few very low damage outliers that appeared to be from successful saves by the dummy.

Now, if we look at the multiplier effect though, 314/136 = 2.31 times multiplier from this spellpower increase. Thus, the spellpower effect appears to be roughly the equivalent of (2.31 - 1) X 100 = 131 spell power!

So the 123 spellpower scepter gave me roughly the expected effect of 131 spell power. At first, this appears to be reasonable, as the difference could have been caused by the limited sample, 131 spell power is pretty close to 123. However, the real problem is that supposedly, the spellpower effect on glorious obscenity should only be somewhere between 50 - 80% of the actual spell power. There doesn't appear to be a nerf at all!


Ok, that's very weird, not what I expected at all. So I decided to move on to the rune arm I use all the time - Lucid Dreams.

This rune arm proved much more difficult to test. First, I have significant spell power in the force line, and Lucid Dreams itself has Potency 48 and arcane lore built in, so there's no way I could test a baseline without seeing some impact from spell power. Base damage from Lucid dreams is 8 - 26 + 1d8 / arti level, so the expected damage of a Tier V shot would be around 107 damage.

I ran two tests with Lucid Dreams. The first was with 148 spell power (48 from potency, 100 from enhancement lines). After 100 hits, I recorded the following:

Mean: 277 damage
Median: 279 damage
Standard Deviation: 22.9 damage
Max: 328 damage
Min: 199 damage

Again, a few low outliers were removed.

Next, I equipped an impulse item which brought my total spell power up to 202. Results were slightly higher:

Mean: 318 damage
Median: 316 damage
Standard Deviation: 34.4 damage
Max: 421 damage
Min: 237 damage

Now calculating the rune arm nerf gets tricky. The difference in spellpower between the two tests is 202 - 148 = 54 spell power. Thus, the second test should increase the base damage of the rune arm by 54% over the first test. If the average base damage is around 107 damage, then the first test is 277 / 107 = 2.59 times base damage, and the second test is 318 / 107 = 2.97 times the base damge. Thus the first test is approximately 159 spell power and the second is approximately 197 spell power. Very interesting. This conforms well with the results with Glorious Obscenity, which again would seem to indicate that there is no nerf being applied to Lucid Dreams (159 spell power is better than the 148 spell power of the first test, 197 spell power is just slightly lower than the 202 spellpower of the test).

A final way of looking at it is what was the DIFFERENCE in spell power from test one to two. It was 202 - 148 = 54 spell power. For an extra 54 spell power, damage increased from 2.59 times to 2.97 times the expected base damage, an increase of 0.38 times. In this case, 54 extra spell power did not produce an increase of 54% of base damage, but only a 38% increase, thus there could be a nerf factor of about 74% (0.38/0.54). So maybe there is a nerf. But this number is highly subjective, and also depends on what the actual average base damage is, which may not be exactly 107 damage. For instance, if the base 8 - 26 damage from the rune arm tends to average closer to 8 damage, then total base damage may be as little as 98 damage per hit. If it is closer to the high end of 26 damage, base damage may average as high as 116 damage. Using a different number for the base damage in the previous calculation can result in the nerf factor varying anywhere from 68% to 80%.

Bottom line is that in most instances, I cannot find much evidence of a nerf factor being applied to rune arms, and in the last case, it could be anywhere between 68% to 80% for lucid dreams, and my data is a bit sketchy. You might need sample sizes of as much as 1000 hits to get some more certainty, which seems like an incredible waste of time when the developers could just explain to us exactly how they have nerfed rune arms.

I'd still like to figure out how best to maximize rune arm damage, but at this point, without understanding the rune arm nerf, it appears to be an impossible task.

[Jaid314]

might be easier to test with a higher level character that has only 2 levels of artificer (higher level so you can throw on more impressive gear) and try charging to the lower tiers - that would help you test faster, and would also reduce the variable portion of your damage substantially.

[Ertay]

might be easier to test with a higher level character that has only 2 levels of artificer (higher level so you can throw on more impressive gear) and try charging to the lower tiers - that would help you test faster, and would also reduce the variable portion of your damage substantially.

Good idea. Though it occured to me that the lower average base damage from only 2 artificer levels might granulate the results somewhat, for best results it would maybe best to do it with the 2 artie levels suggested and get some 120 spellpower scepters on lammania and look at the max damage achieved over a reasonably long streak.

Before you do this by hand now, there is a guy with a working combat log parser. I haven't tried it yet so I can't say if this could be measured by it though.

Very much +1ed for the effort on the OPs part. Hidden modifiers are the worst possible way to balance something.

[Loriac]

Were critical hits removed from your numbers?

I'm assuming that the glorious obscenity numbers are crit-free, whilst the lucid dream numbers include (removed?) crits based on whatever ap you've spent.

[Wernerus]

Were critical hits removed from your numbers?

I'm assuming that the glorious obscenity numbers are crit-free, whilst the lucid dream numbers include (removed?) crits based on whatever ap you've spent.

Yes, that's correct. For Glorious obscenity, I had no crits, as I had no gear or enhancement lines giving me any crit procs. For Lucid Dreams, I had the full enhancement lines, which gave me an 18% chance to crit 2.75 times base damage. The combat log clearly identifies when you crit, and it's also easy to tell from the amount of damage dealt, so I removed the crit hits from my numbers.

[nivarch]

Yes, that's correct. For Glorious obscenity, I had no crits, as I had no gear or enhancement lines giving me any crit procs. For Lucid Dreams, I had the full enhancement lines, which gave me an 18% chance to crit 2.75 times base damage. The combat log clearly identifies when you crit, and it's also easy to tell from the amount of damage dealt, so I removed the crit hits from my numbers.

To ease the testing of high level run arms, you can just respec your enhancements. This will remove one parameter making it easier to find the underlying model.

[Noctus]

+1 for rigorously applying The Scientific Method to testing, instead of the too often #play, get a feeling, keep on playing with half an eye on it, rant based on anecdotal "proof"#-style used in the forums by too many people.

[Barhai]

Your numbers on lucid dreams after adding the spellpower items match quite closely the increase in spellpower with a 50% nerf (ie, going from a 1.74 multiplier, to a 2.01 multiplier).

[oweieie]

Maybe they applied the 50-80% to the +potency spell power on lucid dreams, toven's hammer and other rune arms, as the +potency numbers those things have are stupid useless annoyingly low for their level.

[FooWonk]

I tested 13 different rune arms. Generally, elemental rune arms were not nerfed, force rune arms had varying spell power based on current number of charges held. Light based rune arms actually received greater than 100% spell power.

There is a lot of variation in the game mechanics of rune arms now. Divine spells had the same changes/nerfs and devs updated descriptions accordingly.

It'd be nice to have tool tips with up to date game mechanics documented for players.
Per rune arm usage feat...how rune arm charge levels increase DC
Per lucid dreams...50% spell power increase by 5% per charge tier.
Etc...