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Long Run Damage Calculation, Math is Fun!

dps power crit

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#1 Nonlinear

Nonlinear

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Posted 21 November 2012 - 05:47 PM

Hi all,

Don't know if this has been posted before but I was wanting to figure out how to maximize my raw power stats (before weapon damage, traits, skills and boons/conditions are added which can be further tweaked and tested in Heart of the Mists with gear as a control) so I did a little statistics and came up with a metric to determine your relative damage based on your power, crit rate, and crit damage independent of the other stats.  If anything some will find the spreadsheet link handy for tweaking their stats.  

The formula isn't the exact damage you'll dish out since it uses power instead of attack and doesn't incorporate enemy toughness or anything like that, it's more of a way of gauging how much long run damage you will do if you change up your power, crit, and crit damage numbers (e.g. change up your accessories, berserkers vs. knights) compared to another stat setup.  Eventually I would like to add stuff but I can be pretty lazy.

Long Run DPS = Power * (1.0 + Critical Hit Rate * (0.5 + Critical Damage Bonus))

or:

D = P * (1 + C * (1/2 + D))

Where P = Power, C  = Critical Hit Rate (as a %) and D = Critical Damage Bonus (as a %, i.e. 69 Crit Damage -> 69% -> .69)

How I derived it:

When you hit something, you basically have two outcomes, either a regular hit or a crit.  Crits do 150% damage with 0 additional critical damage bonus.  Over the long run, it will boil down to C percent of your hits being critical hits and the rest being regular:

Long Run DPS = Regular Hit Contribution + Critical Hit Contribution

With 150% base Critical Damage Bonus, Critical Damage is calculated as:

Critical Damage = P * (1.50 + D)

and you will do this C percent of the time:

Critical Hit Contribution =  P * (1.50 + D) * C = P * C * (1.50 + D)

So if C is your crit rate then your regular hit rate is 1 - C (e.g. if your crit rate is 40% then your regular hit rate is 100% - 40% = 60%), you will do your regular damage 1 - C (percent) of the time:

Regular Hit Contribution = P * (1 - C)

So you add them together:

Long Run DPS = Regular Hit Contribution + Critical Hit Contribution

D = P * (1 - C) + P * C * (1.50 + D)

Do some factoring....

D = P * (1 + C * (0.5 + D))

And for reference, your crit rate at level 80 is calculated as:

Critical Hit Rate (@80)  = ((Precision - 916) / 21 + 4) / 100

Basically, your base crit rate at 80 with 0 precision is 4% and every 21 precision will give you 1% more crit.

e.g. 1

Assuming you have full glass cannon berserker gear, full power, precision and crit damage from your spec, a crit signet, etc. you can assume a high end of ~2400 power, ~80% crit damage a critical hit rate of ~55%, all unbuffed:

Max LRD = 2400 * (1 + 0.55 * (0.5 + .80) = 4182

I round it up to 4200.  This is just a high end, raw ceiling to compare your numbers to.

e.g. 2

A more practical example (and what led me to this).  My 80 elementalist is using 6pc berserker gear from CoF with soldier runes, staff, and amulet, knight earrings and rings with ruby gems in two of them and a defender backpack with a soldier crest.  Here are its glass cannon stats (I use for PvE dungeons):

ele glass cannon stats
Uploaded 21 Nov 2012 - 16:51

Power = 2,241
Crit Rate = 51%
Crit Damage Bonus = 69%

So LRD = 2,241 * (1 + 0.51 * (0.5 + 0.69) = ~3601

If I changed my four knight accessories to berserker (100% berserker gear) my new stats would be:

Power = 2,331
Crit Rate = 51% (basically the same due to 25 precision on emerald jewels)
Crit Damage Bonus = 88%

So LRD = 2,331 * (1 + 0.51 * (0.5 + 0.88) = ~3,971

The difference is about a 10% increase in long run damage.  The equation comes down to your power P and then an added long term % bonus based on crit and crit damage.  P * (100% + Crit Bonuses)

The reason I came up with this is so I can juggle my stats, add some toughness and vitality and get the most benefit out of it for the least amount of damage loss.  To help, I came up with a rudimentary spreadsheet to calculate stats.  I say rudimentary because it doesn't take sigils/runes into account or traits (although you can add the stat points you get for your spec), but it lets you add crests in your gear and gems in your accessories.  It also doesn't have every single stat combo because I'm not interested in all of them, you can make a copy and add them yourself though in the slot tabs.  It has a few cells at the bottom that compute the LRD and you can put the comparison value in the benchmark to see what the difference will be.

Spreadsheet Link

Some observations:
  • With 0 precision at level 80 your base crit rate is 4% (see formula above) and with 0 crit damage % your base crit damage % is 150%.
  • Power is your best bang for your buck damage stat and scales the best, even with 0 precision and crit damage, every point of power gives you an extra 2% long run damage and scales better as you get more of the other two stats, any amount of crit and crit damage % raise the 2% percent even more (LRD = P * (1 + 0.04 * (0.5 + 0)) = P * (1 + 0.02) = P * 102%).
  • With 0 crit damage %, 1% of crit rate will increase your long run damage by 0.5% (LRD = P * (1 + C * (0.5)) = P * (1 + C/2)
  • With 50% crit damage %, your crits do 200% damage (double damage), this means that once you get above 50% crit damage %, 1% of crit will increase your long run damage by 1%


#2 Linfang

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Posted 21 November 2012 - 05:48 PM

And now I know why I failed in math

#3 Nonlinear

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Posted 21 November 2012 - 06:00 PM

View PostLinfang, on 21 November 2012 - 05:48 PM, said:

And now I know why I failed in math

That's what the black box is for.

Just plug your power (P), crit rate (C, as a percent, 60% = 0.60) and crit damage % (D, again as a %) into the formula:

D = P * (1 + C * (0.5 + D))

Then plug in what you are thinking of doing (can get a lot of the numbers using this spreadsheet, you'll have to add rune/sigil bonuses yourself but can easily add up the stats by hand and add them in the formulas), crit rate is your total precision minus 916 (base stat) divided by 21 then add 4 for base crit rate= (P - 916)/21 + 4

Whichever number is higher will give you more damage in the long run.

Edited by Nonlinear, 21 November 2012 - 06:02 PM.


#4 Adaina Telnadris

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Posted 21 November 2012 - 06:05 PM

View PostNonlinear, on 21 November 2012 - 06:00 PM, said:

That's what the black box is for.

Just plug your power (P), crit rate (C, as a percent, 60% = 0.60) and crit damage % (D, again as a %) into the formula:

D = P * (1 + C * (0.5 + D))

Then plug in what you are thinking of doing (can get a lot of the numbers using this spreadsheet, you'll have to add rune/sigil bonuses yourself but can easily add up the stats by hand and add them in the formulas), crit rate is your total precision minus 916 (base stat) divided by 21 then add 4 for base crit rate= (P - 916)/21 + 4

Whichever number is higher will give you more damage in the long run.

This information made my day. Especially the factoring. Thanks for the break down!!

#5 Matsy

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Posted 21 November 2012 - 06:07 PM

My mind esploded.
Sounds usefull though ;p





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