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Crit vs Power (Maths inside)
starman1111
Member Posts: 21 Arc User
EDIT: I have not had a lot of time this week to continue this discussion but I would like to promote freehugs9's discussion entitled 'Calculating stats and their effects' at http://nw-forum.perfectworld.com/showthread.php?301761-Calculating-stats-and-their-effects. I have to say that he has surpassed what i have done here already and any future analyses I make will be using his formulas and not the polynomials I have published here.
I encourage all of you to visit his page at http://nw-forum.perfectworld.com/showthread.php?301761-Calculating-stats-and-their-effects and either contribute to the discussion or offer any raw data you may have.
I have been wondering how best to express the usefulness of crit versus power since crit has a diminishing return. I found someone who had already tabulated some data (https://docs.google.com/a/g.uky.edu/spreadsheet/ccc?key=0AgK7NUdr8JPldFlsc1lJZng0MmYtMWFyT2F5TW5lblE#gid=0) and I plugged that in to MS Excel and let that do most of the work in approximating a polynomial function that mimics the Crit Rating to Crit% function.
Let's label crit rating as 'CR'.
Then Crit% = 0.0000000001429 CR3 - 0.0000018879 CR2 + 0.010203 CR - 0.3839
More than nine times out of ten the above formula will give the correct Crit% from the Crit Rating. Interesting but how is it useful?
Well, we can use it to quickly and easily work out how much your next point of Crit Rating is going to increase your Crit%. In this case the derivative is our friend as it gives the rate of change of Crit% in relation to a change in Crit Rating.
So Crit% per point of Crit Rating = 0.0000000004287 CR2 - 0.0000037758 CR + 0.010203
An example of how to use this function: If you have 2000 Crit Rating then your next point of Crit Rating should increase your Crit% by 0.0000000004287 (2000)2 - 0.0000037758 (2000) + 0.010203 = 0.0043662 Crit%. Taking the inverse (1 / 0.0043662) tells us that we need about 229 CR to get another point of Crit%.
Now the above is quite good for working out what Crit Rating will give you but without a way to compare it to Power I think the examination is incomplete. So let's look at how damage is calculated. (Or at least how I think it is probably calculated, happy to be corrected if wrong).
Average Damage = [(WeaponMin + Weapon Max) / 2] * Crit Coefficient * Power Coefficient
Where Crit Coefficient = (1 + Crit%) * Crit Severity
and Power Coefficient = actually to be honest I have done no research here and don't know.
Getting late so I think it is time for me to have a break. Hopefully someone else can take this information and fill in some of the damage calculation blanks for me in the meantime.
Also, if anyone has some more raw tabulated data for Crit Rating converted to Crit% I would love to add it to the data, it would make a better polynomial approximation formula.
One more thing, I have heard and seen that each 25 Power Rating adds +1 damage, but how does that actually get added on, as a percentage increase or a flat increase to base (or average damage)?
I encourage all of you to visit his page at http://nw-forum.perfectworld.com/showthread.php?301761-Calculating-stats-and-their-effects and either contribute to the discussion or offer any raw data you may have.
I have been wondering how best to express the usefulness of crit versus power since crit has a diminishing return. I found someone who had already tabulated some data (https://docs.google.com/a/g.uky.edu/spreadsheet/ccc?key=0AgK7NUdr8JPldFlsc1lJZng0MmYtMWFyT2F5TW5lblE#gid=0) and I plugged that in to MS Excel and let that do most of the work in approximating a polynomial function that mimics the Crit Rating to Crit% function.
Let's label crit rating as 'CR'.
Then Crit% = 0.0000000001429 CR3 - 0.0000018879 CR2 + 0.010203 CR - 0.3839
More than nine times out of ten the above formula will give the correct Crit% from the Crit Rating. Interesting but how is it useful?
Well, we can use it to quickly and easily work out how much your next point of Crit Rating is going to increase your Crit%. In this case the derivative is our friend as it gives the rate of change of Crit% in relation to a change in Crit Rating.
So Crit% per point of Crit Rating = 0.0000000004287 CR2 - 0.0000037758 CR + 0.010203
An example of how to use this function: If you have 2000 Crit Rating then your next point of Crit Rating should increase your Crit% by 0.0000000004287 (2000)2 - 0.0000037758 (2000) + 0.010203 = 0.0043662 Crit%. Taking the inverse (1 / 0.0043662) tells us that we need about 229 CR to get another point of Crit%.
Now the above is quite good for working out what Crit Rating will give you but without a way to compare it to Power I think the examination is incomplete. So let's look at how damage is calculated. (Or at least how I think it is probably calculated, happy to be corrected if wrong).
Average Damage = [(WeaponMin + Weapon Max) / 2] * Crit Coefficient * Power Coefficient
Where Crit Coefficient = (1 + Crit%) * Crit Severity
and Power Coefficient = actually to be honest I have done no research here and don't know.
Getting late so I think it is time for me to have a break. Hopefully someone else can take this information and fill in some of the damage calculation blanks for me in the meantime.
Also, if anyone has some more raw tabulated data for Crit Rating converted to Crit% I would love to add it to the data, it would make a better polynomial approximation formula.
One more thing, I have heard and seen that each 25 Power Rating adds +1 damage, but how does that actually get added on, as a percentage increase or a flat increase to base (or average damage)?
Post edited by starman1111 on
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From what I can tell about power:
Power / 25 = +damage listed on char sheet
Each spell then has a Weapon Damage Modifier and a +Damage Modifier. There are several options:
Damage = WpnCoef * WpnDmg + PwrCoef * PwrDmg
Damage = WpnCoef * (WpnDmg + PwrDmg)
Damage = WpnCoef * (WpnDmg + (PwrCoef * PwrDmg)
Unfortunately I believe this requires a weapon with 0 power to solve, which I have not found yet (but not looked very hard either). I suppose I could rule out the middle option with the data I have, I will look into it.
Happy to surprise you, although to be honest MS Excel 2010 did the calculations via Chart Tools > Layout > Trendline > More Trendline Options > Polynomial (Tick "Set Intercept to 0.0" and "Display Equation on Chart").
Thanks very much for the data, I will include the new combined data set below:
Using this data the new polynomials are (I will include all from 2nd order to 6th order):
y = -1.0925x2 + 9.019x
y = 0.0838x3 - 1.5051x2 + 9.4723x
y = 0.0651x4 - 0.37x3 - 0.5417x2 + 8.8752x
y = -0.0572x5 + 0.576x4 - 1.9568x3 + 1.438x2 + 8.0718x
y = 0.0318x6 - 0.4022x5 + 1.98x4 - 4.5837x3 + 3.6369x2 + 7.4401x
Unfortunately none of these are working out to nice round numbers so they probably aren't the actual equations used in game, however as an approximation and to be used in Crit% calculators they are very useful. I suspect the actual equation may be something to do with sqrt(x).
To comment on the above equations:
The second order one is not very accurate, less than half of the data points fit perfectly.
The third order one is still okay, for Crit Ratings under 600 it is out by 0.1 or 0.2 though.
The fourth order one is better again but for Crit Ratings under 500 it is out by 0.1 or 0.2.
The fifth order one matches all data points over a crit rating of 300.
The sixth order one matches all data points except the highest Rating at 3661 is out by 0.1.
I won't do more work on it right away, I had a Math exam yesterday and an exam on C programming tomorrow. I am happy for this to be a collaborative effort though if anyone wants to add more work to this?
Level 60 Critical Chance Tooltip = 28.8*CriticalStike^1.2/(10190+CriticalStrike^1.2)
http://nw-forum.perfectworld.com/showthread.php?301761-Calculating-stats-and-their-effects
Keep up the good work!
Test stuff -> Determine formula used -> Use formula to predict things -> PROFIT!
There's no "player skill" involved in the formula determining whether you wanna stack power or crit for more raw damage, certain class on-crit effects notwithstanding.
That has no place in the calculations. What it will give when completed is the best option for each of those players. Yes past that point their skill will be the difference to what they achieve.
That is irrelevant as ****, you're an idiot.
You first optimize mathematically, then skill makes the difference.
Damage (total) = Weapon damage + Power effect + Critical effect (lets forget armor penetration at this point)
Where Power Effect = Power value from gear / 25 (this is in damage added to weapon damage)
and Weapon damage = (Min value+max value)/2
Critical effect is more tricky, but if we use Crit% = 0.0000000001429 CR3 - 0.0000018879 CR2 + 0.010203 CR - 0.3839
Then Crit Effect is: Crit%*Weapon Damage as damage added, on average, to weapon damage.
If somebody confirms these are, with the current knowledge we have, correct, I'll make an optimization formula.
edit: parentheses added
edit: crit% needs to take into account base value, which is what?
Every rating has a diminishing return (as you can see from the very good post about ratings), but dps returns are another thing on top of that.
Crit is capped at 100% obviously, regardless of diminishing returns from the rating, so you have to also calculate how much of a dps increase is that value, considering your current rating AND your current percentage.
Simple example (numbers are made up for easyness):
at 0 rating 100 critRating gives you 1% critChance which is +.75% damage
at 1000 rating 100 critRating gives you .9% critChance which is .75*.9 = +.675% damage
These are diminishing returns of the rating.
At 0 crit 1% crit gives you an additional .75% damage (you step from 100% damage to 100% + 1*.75%)
1000 crit rating is worth 10% (made up number for the sake of the example), so you would step from 107.5% (made up to simplify) to 108.175% damage which means you only gain an effective .628% damage which is about 7% less.
So getting the real DPS increase of crit, due to its nature and rating DR, is something that requires a spreadsheet cause you can't exactly add .75% damage for 1% crit at every point and you prolly can't judge just eyballing an item without having a strong knowledge of the dps conversion of power. Add to this critical severity or on-crit effects and you end up with a very hard-to-estimate choice when values are very close.
I plotted the values derived from formulas in the rating post and the value of conversion in the following 2 tables
By itself it won't tell you if that rating is better than another, but it more or less tells you where the DR starts to kick in, and contrary to rating->DPS conversion, these tables are the same for every class.
EDIT: also I don't know if stats are budgeted differently (example, look at the values of hit points, how much are worth vs ratings when budgeting items?)
Damage total = ((Avg Wep Dmg + Power Scaling) * Feat Scaling * ArP)*(1-Crit%)+Crit%*Severity*((Avg Wep Dmg + Power Scaling) * Feat Scaling * ArP)
Yup, I totally forgot about crit severity.
And I did point out that ArP would be left out, forgot to mention that powers or feats would not be included either.
Well, you won't get any real information if you leave out any dps parameter unfortunately. Since power scales linearly there will be some combinations of weapon damage, crit and arp where power trumps all (at low and high rating levels) and some other combinations where arp or crit are better.
In theory you should also include the coefficients for every spell (which is different for every encounter, at will and daily) and the rotation you plan to use. There is no simple formula that will tell you if power is better than crit regardless of your current gear, you need a spreadsheet. You generally derive the relation between crit and power doing the opposite, ie calculating the dps increase of X crit rating vs X power given a starting point then see what's higher.
Right, they are calculating it in a vacuum, an environment we never play in.
Its not the raw damage which is the only question, its the comparison between burst DPS and sustained DPS that helps even more in making those decisions. Right now burst DPS is worth a lot more in this game, but if we ever see raids with extremely high HP bosses there will become a need to determine which of the two is more valuable, per encounter.
Here's my Dps spreadsheet for dps GF, you can prob alter it for other classes. (You will have to modify stat to % equations in some cases because I included the base values GFs get (such as 2% base cooldown reduction from wis)
The (1-Crit%) stuck in there is erroneous. Normal damage is done 100% of the time, not just on a non-crit. Your formula calculates the extra damage from a crit but ignores the underlying normal damage done on a crit. Also you left out damage bonus %.
It should be:
Damage total = ((Avg Wep Dmg + Power Scaling) * (1 + Dmg Bonus %) * Feat Scaling * ArP) + (Crit% * Severity * ((Avg Wep Dmg + Power Scaling) * (1 + Dmg Bonus %) * Feat Scaling * Arp)
Class feats would modify this further. For example for TR you can easily factor in Nimble Blade effects (chance of damage buff for non-crits):
TR Damage total = ((Avg Wep Dmg + Power Scaling) * (1 + Dmg Bonus %) * Feat Scaling * ArP) + ((Avg Wep Dmg + Power Scaling) * (1 + Dmg Bonus %) * Feat Scaling * ArP) * 1.4% * Nimble Blade Ranks * (1 - Crit%) + (Crit% * Severity * ((Avg Wep Dmg + Power Scaling) * (1 + Dmg Bonus %) * Feat Scaling * Arp)
etc..
What the hell?! It's a formula for determining when to stack crit or power. Are you drunk?
I encourage all of you to visit his page at http://nw-forum.perfectworld.com/showthread.php?301761-Calculating-stats-and-their-effects and either contribute to the discussion or offer any raw data you may have.