An Empirical Warrior Dual Wield DPS Calculator

[Launch]

I couldn't find a fully fleshed out, empirical calculator for the mean damage per second of a dual wielding warrior (or any class for that matter) that properly interprets the impacts of all the important statistical variables, so I made one. Here it is.

Searching the forums yields a few older, less dynamic examples of this sort of effort like Yaolin's work from ~5 years ago. This is good work, and it along with the discussion in the corresponding thread served as a starting point for what I have put together. Mainly over a couple hours this morning - so there's a good chance I've done something that needs correcting.

Yaolin's spreadsheet allows for the comparison of any duel wield combination with the use of a relative value metric he calls "DPS Rating." This works quite well and scales properly with the most impactful parameters (attack speed, chance to hit) but doesn't handle proc damage (which scales differently and independently), or the more complicated relationship between a character's Strength and his damage per hit distribution. Finally, the DPS Rating doesn't have a tangible relationship to actual in-game damage per second - it just says, under some general conditions, how one set of weapons compares to another.

Initially my impetus for creating this was to properly value proc damage and answer a hypothetical question like this: is a 10/20 weapon with a 60DD proc better than a 11/20 weapon with no proc? Note that the damage per second of the proc is fairly easy to calculate - its the empirical calculation of the weapon's damage per second that's harder to get to. So I wound up with a full calculator with inputs for Level, Dexterity, Strength, Haste, and Chance to Hit, along with the parameters of a given Primary and Offhand weapon of course. Using great parse data from Sakuragi's Warrior Guide as a benchmark, the model comes pretty damn close for every single combination Sakuragi has documented.

I'll get to the key logic assumptions as I walk through an example output: a Level 60 Warrior with 255 Dexterity, 255 Strength, 100% Haste and a 70.5% chance to hit using a Sebilite Croaking Dirk (10/18) Primary and a Fist of Zek (16/30) Secondary.

Note that it's hard to find good data on Chance to Hit (and it scales with character vs. NPC level difference), but the best data I found was here. This example has a level 60 rogue landing hits ~75% of the time against a level 20 NPC; I've seen some commentary elsewhere saying hit rates range from 65% to 75%, and assuming a ~70% midpoint as the mean Chance to Hit lines up my model output with Sakuragi's parse data.

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In Sakuragi's Warrior Guide he parses the damage per second of this exact weapon combination "at Level 60, 255 dexterity, 100% haste" at 63 DPS. With an assumed 70.5% chance to hit and an assumed 255 strength, my model calculates a total DPS of 62.73. Pretty damn close.

Here's a table of my model's calculation for each of the combinations that Sakuragi documents. The average DPS difference is ~0.25 over the 12 combinations. Note that these parses and modeled calculations of them exclude proc damage - it's pretty clear looking at the data that Sakuragi's DPS column doesn't include the damage from procs.

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Using information from what looks like early P99 testing I structured the damage per hit distribution in a pretty straightforward way: 10% of hits take place at the Minimum Value, 20% at the "Magic Value" and 10% at the Maximum Value. The remaining 50% of hits take place at random values bounded by the Minimum and Maximum that are never equal to the Minimum, Maximum, or Magic Number. I didn't even have to try any other complicated distributions: this simple approach seemed to fit Sakuragi's data given an assumed 255 Strength and ~70% Chance to Hit. Note that in the above 10/18 Primary, 16/30 Secondary assumption that decreasing strength from 255 to 155 cuts the modeled DPS to 57.54 from 62.73. 100 strength is worth ~5 DPS, all else held constant.

Finally, I couldn't find a lot of information on Triple Attack Chance, but there is a mention in Yaolin's old thread that at level 60 half of Primary double attacks become triple attacks. With a 70.5% Chance to Hit, that results in the following for any given swing: 29.5% misses, 34.66% singles, 17.92% doubles, 17.92% triples in my calculations, at level 60.

I use the similarly documented duel wield and double attack chances of (Level + Skill) / 500 for Dual Wield Chance and (Level + Skill) / 600 for Double Attack Chance.

Obviously this all scales with NPC level (and AC) vs. Character level - but I would assume it does so linearly, making a higher DPS combination according to my model always the higher DPS combination. Here's a really high DPS combination, with procs included this time: two Scepters of Destruction.

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Sakuragi's proc-excluded parses of two Scepters of Destruction was 73 DPS. My model calculates it at 72.97 excluding procs (again, pretty damn close), or 87.37 including them - if you were curious.

Disclaimer: my warrior is level 51 on Project 1999 and I haven't opened any EQ parsing software since 2004. I'm sure some raiding warriors can figure out if the output from my calculator is garbage or seems to make some sense.