Math Crit Chance Vs Dmg
Aura Kingdom Crit vs Dmg Stat Analysis by imakebirdiescry
When a weapon achieves a crit chance higher than 100%, every attack will crit but it also gains a chance to deal an even stronger crit. As the critical hit chance increases, the tier of critical damage does so as well. Although the coloration remains red after a certain point, crit tiers continue to increase.
- Aug 07, 2015 Spell Crit vs Spell Damage. By xemni » Tue Jul 21, 2015 7:05 pm I played a lot of rogue back in the day, and one of the things i'd read about on Elitist Jerks from time to time is that if you're lacking hit rating, it is in some cases better to take crit pieces over some raw damage, when possible.
- Nov 09, 2011 As long as youre crit chance is below 100%, crit chance runes improve youre dmg by 20,25%. Dmg runes improve youre damage by: 45,51%. Crit Chance. 45,51. x = 20,25 x = 45% If you plan to get more than 45% Crit chance you should not go for Crit. Chance runes. But of course Crit Chance runes improve youre early game. Marks & Quints Crit.
Hi, welcome to my guide to CRIT vs DMG. Hopefully this will be part of a series that will include HP/DEF/EVA, ACC/CRITDMG, and possibly more (if anyone can think of a comparison they would like, please let me know).
Since I want this guide to be accessible and useful for everyone, I will start off with the conclusions of my math.
IF YOU DON’T WANT TO READ A WALL OF MATH, JUST READ THE FIRST PART. HOWEVER, PLEASE DON’T TRY TO ARGUE MY MATH WITHOUT READING IT, THANKS.
How should I build?
If you’re focusing on dealing the most damage possible, build for crit and crit damage. If you’re focusing more on defense (like guardian and bard), build for damage and ignore crit, because crit damage takes up alot of stat option slots that you would rather use for damage reduction, and crit without crit damage does not give you as much damage as DMG does.
In general, if you have over 200% crit damage, building more crit chance will give you more damage. If you have less than that, building more DMG will give you more damage. BUILDING CRIT AND CRIT DAMAGE WILL GIVE YOU MORE DAMAGE THAN BUILDING PURE DAMAGE WILL EVER GET YOU.
In particular, if you are going crit, you should try to get crit damage anywhere you can. This includes Envoy path, Ultimate skill (Callousness), Secret stones (go for the +6% crit dmg ones, even if they don’t affect any of your skills), trophies (aka Fia’s Fairy dust – this item was made for crit builds), and any other crit damage bonuses you can find. If you have to choose between crit chance and crit damage, and are around 200% crit damage already, 1% crit damage is worth about 0.25% crit chance. Obviously the more crit chance you already have, the more useful crit damage is, and the more crit damage you already have, the more useful crit chance is.
Calculations Intro
Since crit runs on RNG, we will use the law of large number averages to calculate an average damage. The simple formula for average damage is therefore as follows:
total damage = DMG * [1 + critrate * (critdmg – 1) ]
ex: You have 15000 DMG, 50% crit chance, and 170% crit damage. Your average damage is therefore 15000 * (1 + 0.5 * (1.7 – 1) ] = 20250.
Now, most of your damage comes from skills. Skills have a base damage and a damage ratio (these can be found here). Say you’re a level 45 wizard and your Meteor skill is level 48. You have a DMG stat of 15000. Then its damage is 1.4 * (9103 +15000).
Now one thing to note here is that increasing your DMG will increase the bonus damage, but not the base damage. A crit, however, will increase the damage of both the base and the bonus components. We can thus give the damage formula for a skill as:
skill damage = skillbonus * (base + DMG) * [1 + critrate * (critdmg – 1) ]
Now that we have a formula for skill damage, let’s take a look at how adding points to crit or damage will affect your overall damage.
Stats
Title bonuses and Eidolon bonuses are always applied at the end. They are not affected by any % increases.
DMG
Each stat point in damage increases your damage by 0.35%. This applies to both your base damage, weapon damage, and any bonus damage from gear. Other percentage increases in damage (from Envoys and from %DMG stats on gear) stack additively, not multiplicatively, with this. For example, say you have 10 points in damage (3.5% increase) and a full set of damage gear (8% increase). This is an 11.5% increase (3.5+8=11.5).
So the overall formula for damage stat is:
DMG = [(base + weapon + gear) * (stat% + gear% + envoy%)] + title + eidolon
This is the damage stat listed in your character window. The only difference between your primary and secondary weapons is the main damage stat listed on the respective weapons. All other % bonuses are applied the same way.
CRIT
When dealing with crit, I will refer to crit stat and crit chance. These are different. Gear/stats dealing with crit are generally added to your crit stat (some exceptions exist). Crit chance is your percentage chance to land a crit derived from your crit stat relative to the target’s level. Crit stat is linearly related to crit chance – that is, increasing your crit stat by 10 gives you the same increase in crit chance whether your crit stat is going from 100->110 or 3500->3510.
Each stat point you invest in crit will give you enough crit stat to raise your crit chance by 0.25%. That means the stat points you invest in crit give you a constant crit chance as you level, but their crit stat value increases as you level.
Most things that give CRIT+X% just add directly to your crit chance without affecting your crit stat. These incluce costumes, envoy path, and secret stones (?unsure, I don’t have any crit chance stones to test). However, a few gear bonuses will actually add a % of your crit stat. These % crit stat bonuses will ignore any crit stat you get from adding stat points, but include all crit stat gained from gear as well as your base crit stat.
The overall formula for CRIT% is:
CRIT% = %CRITBonus + (0.25 * statpoints) + {K * [ %CRITStat * (base + gear) + title + eidolon] }.
statpoints is the number of attack points you have invested into crit. %CRITBonus is the total sum of all your %CRIT bonuses that apply directly to your crit chance (envoy, costume, secret stone, gear). %CRITStat is the total sum of the %CRIT bonuses that apply to your crit stat instead of directly to your crit chance (ultimate skill, some gear). K is a constant of proportionality between your crit stat and your crit chance. This changes based on level. At level 53 my value of K is around 0.007, which means every point of crit stat gives me 0.007% crit chance.
A nice explanation of K by Mythyc:
I was actually compiling statistics on K (or in my case, 1/K [how many points does it take to get a 1% increase in a stat]and with my preliminary results (had to start a character from scratch to get these):
- LVL 1 – 1.55
- LVL 2 – 1.70
- LVL 3 – 1.95
- LVL 4 – 2.30
- LVL 5 – 2.75
- LVL 6 – 3.30
- LVL 7 – 3.95
- LVL 8 – 4.70
- LVL 9 – 5.55
- LVL 10 – 6.50
- LVL 11 – 7.55
- LVL 12 – 8.70
- LVL 13 – 9.95
- LVL 14 – 11.30
- LVL 15 – 12.75
- LVL 16 – 14.30
- LVL 17 – 15.95
- LVL 18 – 17.70
- LVL 19 – 19.55
- LVL 20 – 21.95
- LVL 21 – 23.55
- LVL 22 – 25.70
- LVL 23 – 27.95
- LVL 24 – 30.30
- LVL 25 – 32.75
- LVL 26 – 35.30
- LVL 27 – 37.95
- LVL 28 – 40.70
- LVL 29 – 43.55
- LVL 30 – 46.50
- LVL 31 – 49.55
- LVL 32 – 52.70
etc…
In other words, the difference in points between each successive level is increased by 0.1. 1/K describes the amount of points required to increase a given stat by 1%.
Applies to CRIT, EVA, SPD and DEF.
I found that the formula to find 1/K is:
(N (N+1) / 2) * 0.1 + (1.5 – [N * 0.05])
Where N is your current level.
In your case, 1/K would be:
53(54)/2 * 0.1 + (1.5 – (53 * 0.05)) = 141.95
or
K = 0.00704 (which coincides with your results)
Hope that helps
A more simplified version of the crit formula if you just want to check values quickly:
CRIT% = %CRITBonus + (K * critstat).
Maths on total damage
Jobu dmg hd4 mark 4. The Jobu DMG-HD4 Heavy Duty Gimbal Head MK IV employs smooth friction adjustment to provide optimal control and ease of use with cameras and telephoto lens combinations up to 25 lb. A smaller overall form factor and lower weight over previous generations makes this gimbal easy to pack and carry. A 3' long plate is included for use on telephoto lenses or camera bodies, and a drawstring dust bag. Aug 28, 2015 Andrew R What's in the box: Jobu Design Heavy Duty MK IV Gimbal Head Camouflage Dust-Bag SF-NXK Kit Quick-Release Plate (Arca Type) Allen Keys 1/4'-3/8' Adapter Bushing Jobu Design 5 Year Limited Warranty Note: The included plate is the 3' model. DMG-HD4 - The Jobu Heavy Duty Mark IV Gimbal Head. The Jobu Heavy Duty Mark IV is our standard gimbal head. We highly recommend it for all customers - it hits the mark on all specs: lightweight, easy to pack, exceedingly stiff and fluid in its movements.
Using level 48 Meteor as an example, we have:
skill damage = 1.4 * (9103 + DMG) * [1 + critrate * (critdmg – 1) ]
Sample starting stats are 15000 DMG and 20% crit chance. I plotted a change of 50 stat points’ worth in crit (red line) and indamage (blue line) at different levels of crit damage (130%, 190%, 200%, 210%, 300%). The following plot is what results:
Crit Chance Poe
Here we see that at low crit damage, adding points to DMG will increase your damage more. However, once you go over 200% crit damage, adding points to crit will add more to your damage. Also, we can see that you will get more out of building crit+crit damage than you could ever get out of going pure damage. Also, a 10% increase in crit damage is worth a good 10 stat points’ worth of crit chance.
Crit Chance Pokemon
acurracy Vs. dmg nodes *Disclaimer - not feedback - just trying to get a discussion on the topic that affects gameplay Lets say accuracy is naturally at 80% (I believe this is a lowball - probably 85% is more accurate, but for the sake of this we will go 5% lower) lets say you have a weapon that attacks 1 time per second and does 50-150 per attack. DPS is 100 but then reduce it by 20% to account for accuracy to make it 80 dps A single accuracy node is unlikely to give more than 1% each node, but let's make it 3% each node of accuracy - just to prove my point coming up The math should be the same regardless of how many nodes you put into either accuracy or damage - so lets do the math for 3 nodes that you are wondering where to place. First example you place nodes in accuracy, this brings your accuracy to 89% (using 3% per node) So your DPS changes from 80 to 89. Now let's say you put the 3 nodes into dmg, each being 10% increase - screw it, let's say 6% which is extremely low, considering most are 10% or will equate to 10% once the you get to the final node in a cluster of nodes. so that is a 18% increase (using 6% dmg nodes as a lowball to prove the point) The damage on the bow is turned from 50-150 to 59 - 177 Changing dps to 118 before accuracy. Now we have to account for the 80% accuracy 118 * 80% = 94.4 So going accuracy nodes = 89 dps Damage nodes = 94.4 Which may not seem like that much until you realize I comepletely butchered the damage nodes by doing the math 4% under average and comepletly over valued accuracy at 3% per node. ---- For those who want realistic math and not over and under exageration to find out exactly how absurd the difference is - most accuracy nodes have some other 'bonus' that is simply too weak of a bonus to make it worth it. Lets use the attack speed accuracy nodes to the right of ranger start. the total for all 3 is 20 dexterity, 9% AS, and 36% accuracy, and let's say acuracy goes up by 1% per 8% increased accuracy, so 36/8 = +4.5% increase to accuracy and let's say base is same as before at 80% same weapon 50-150 dmg, 1.0 attack per second The new weapon AS after 9% increase is 1.09 APS and the accuracy is 85% (Let's round up from the 4.5 increase - make it an even 5%) the dex will give 4% increased evasion and 40 flat accuracy So, (50+150)/2 = 100 * 1.09 = 109 * 85% = 92.65 DPS Now lets just do 3 dmg nodes - each being 10% (Average % increase on tree) so with a 30% increase 50-150 turns into 65 - 195 = 260/2 = 130 * 1.0 = 130 * 80% = 104 DPS 3 accuracy nodes = 92.65 DPS 3 damage nodes = 104 DPS In conclusion, accuracy nodes are underpowered. I am using static electricity jewel, and the accuracy/AS/and dex (dex gives +20 so it's +20 to max lightning dmg) IS STILL NOT ENOUGH to justify getting those nodes unless you are filling in what you are next to because it is late and getting to other damage nodes would take too long (Which, when you do get there after using 'filler' for lack of a better word you should remove the filler nodes and place them into the damage nodes for much higher DPS) Didn't do the math on the crit accuracy - but am pretty sure that it also is worse than dmg nodes in most, if not for all weapons. *My extremely under qualified opinion that holds no weight at all is that they should remove accuracy as a mechanic and should replace the passive effect of 1 DEX = 2 accuracy with 1 DEX = 2 flat evasion and should replace accuracy nodes with a more powerful version of the 'bonuses' to getting the accuracy nodes. Change the AS/Accuracy nodes just attack speed to 6% to 8% per node ( 18-24% total) and the crit/accuracy nodes to 60% crit chance + 10% increased crit multiplier or 75% increased crit chance for the 3 nodes TL:DR Accuracy is not worth putting points into unless it is per chance while getting to a group of damage nodes. Last edited by RichardBachman on Nov 1, 2015, 2:36:48 PM | Posted by on Nov 1, 2015, 2:30:19 PM |
What else is new. There's a reason Accuracy-based builds take five or more Damage clusters and one Accuracy cluster. That said, your calculations are very deceptive because there's a whole lot more Increased Damage in total compared to Accuracy, and it's only the last couple points that really matter. Going from 200% to 220% Increased Damage is nowhere near as good as going from 0% to 20% - and that is the point where Accuracy clusters become relevant. Early on you can just coast on Dex and Accuracy gain from levels, Chance to Hit doesn't start dropping to 80% until way later, when you already have a bunch of Increased Damage. Last edited by Vipermagi on Nov 1, 2015, 2:39:16 PM | Posted by on Nov 1, 2015, 2:38:05 PM |
' Umm, this might be just a nitpick, but what would we need evasion for if there's no accuracy? :) Accuracy nodes aren't that bad these days, they usually have other useful bonuses like attack speed or crit. And you do need some amount of them, for right side builds taking only a few nodes makes a difference because of high base. Unfortunately, for left side builds they will do jack shit without some flat accuracy on gear, so if I'm about to suggest anything at all, it's giving some base accuracy along with percentage on every acc node. High accuracy is a must for a crit build because it checks twice so its effect on dps is squared. Есть один путь - наверх! ◄[www.moddb.com/mods/balancedux]► ◄[www.moddb.com/mods/one-vision1]► | Posted by on Nov 1, 2015, 2:43:38 PM |
Accuracy is never worth it over damage nodes. 0 - 20% is not bigger than 200-220% it is actually increased by the same amount. Example: 100 dps weap +20% dmg = 120 100 dps weap +200% dmg = 300 + 20% = 320 DPS The damage remains the same, the accuracy goes down, but even letting it hit absurdly low numbers you will be better off getting damage nodes. I think I understand what you are saying - at low level there isn't as much of a nerf to your damage because your accuracy is pretty high early on. Even so, it is still better to get damage because regardless of what level you are, damage will out scale the negation caused by low accuracy. The math is to scale, it's why i used an even hundred DPS as base to make it easier to understand. Damage is better. Math is math as far as I'm concerned, and if I messed up my math, by all means, let me know and show your work, as I have, so I can understand it better. @Raics I am not sure what you mean, accuracy and evasion are two different things, one is your chance to hit, and once is your chance to avoid being hit. As far the double check you discuss, I have to do the math, I think it will be a close call and you may be 100% correct - but will post the math when I'm done 'mathing' - (Was supposed to be a pun for mapping - I feel lame now) Last edited by RichardBachman on Nov 1, 2015, 2:56:19 PM | Posted by on Nov 1, 2015, 2:48:52 PM |
' Relative increase is what counts, going from 100 to 120 is 20% more and going from 300 to 320 is 6% more. If spending 3 points on the tree on damage would push your damage up by 5% and three accuracy nodes would increase your chance to hit from 80 to 86%, accuracy would be better because that would be 7% more dps. For a crit build that would be 15% more because of double-dip, that's a major boost. Есть один путь - наверх! ◄[www.moddb.com/mods/balancedux]► ◄[www.moddb.com/mods/one-vision1]► | Posted by on Nov 1, 2015, 2:55:55 PM |
'0 - 20% is not bigger than 200-220% it is actually increased by the same amount.' I never said it a larger increase - I said it was a better increase, which as Raics has already explained, is a relative term. '@Raics I am not sure what you mean, accuracy and evasion are two different things, one is your chance to hit, and once is your chance to avoid being hit. ' They are two sides of the same coin. Chance to Hit is determined by comparing Accuracy Rating to Evasion Rating; Chance to Evade is simply 100 - Chance to Hit (also works the other way around, of course). If Accuracy ceases to exist, then Evasion Rating doesn't work because the formula is missing a value. Why do you think your Accuracy decreases as you fight higher level monsters? Because higher level monsters have more Evasion Rating. :) Last edited by Vipermagi on Nov 1, 2015, 3:03:29 PM | Posted by on Nov 1, 2015, 3:02:17 PM |
so let me get this straight, if ones accuracy is low, like 80%, then there is only an 80% chance of engaging the others evasion response. meaning there is a 20% chance to be miss before the evasion is even engaged. (as though a native 20% chance to dodge) git yer accuracy up to 99.9% and that 'native chance to dodge' doesn't exist. accuracy doesn't defeat evasion. I agree that most of the time +damage causes more than +accuracy, and also agree that accuracy helps more late game when one already has a lot of +damage nodes. | Posted by AgnosiousD on Nov 1, 2015, 3:12:01 PM |
' Yes, so if we remove accuracy, evasion is a dead stat. Есть один путь - наверх! ◄[www.moddb.com/mods/balancedux]► ◄[www.moddb.com/mods/one-vision1]► | Posted by on Nov 1, 2015, 3:12:18 PM |
raics, how are they tied again? I didnt quite get what you and viper were saying. | Posted by AgnosiousD on Nov 1, 2015, 3:14:29 PM |
' You get chance to hit by comparing attacker's accuracy score with defender's evasion score, you got the exact formula on wiki. Есть один путь - наверх! ◄[www.moddb.com/mods/balancedux]► ◄[www.moddb.com/mods/one-vision1]► | Posted by on Nov 1, 2015, 3:19:44 PM |