For the Math Heads, Crit % vs +Att

Rule - Heavens Tear

In the auction house often times an item with 2% crit and no other bonuses sells for some rediculous amounts. 2,000,000 is not uncommong for a mag\phys ring with 2% crit.

I've always thought that the +att was better overall but have never been 100%

So lets take a basic mag att ring. Lets say it has 50 base attack and an attack bonus of +21. How does that compare to a 50 base att and a 1% crit?

At what point do the numbers favor one item over another?

Looking forward to some help with the numbers b:surrender

Yondaimez - Sanctuary

%1 crit is to add 1% to the probability of a critical attack.

Nothing to do with th + damage

If it was that way, it would mean %1 crit would became 50,5.

Rule - Heavens Tear

Erm not quite what I meant. When a crit strikes it does a double damage attack vs an increased attack damage on every hit.

A normal strike would be 1000
So on a crit lets say it does 2000
and with increased attack +21 it would do something like 1021 dmg.

(The increased attack math is not correct, but is an example of the theory)

Over lets say 1000 hits, which bonus is better? More +att or more %crit

Fleuri - Sanctuary

I think your benefit from a +1% critical increase depends on lots and lots of factors.

If you want to be comparing two rings, where one gives you +damage and another gives you +% critical, you should probably take some combo of yours, and work out your average damage with each ring.

However, if you fight PvP against people with health charms you might not be interested in average damage -- lower average damage might be better if your chance of landing a kill earlier increases -- and should instead figure your chance of killing some specific opponent with each ring. (But we do not know lots of game mechanics so this can be difficult and you would need to be fighting different opponents so this gets really complex really fast.)

Leonnator - Sanctuary

Well 1% crit=1% more damage in a 100 hits since [99*100%(normal dmg)+200%(1 crit hit)]/100
=(9900+200)/100
=10100/100
=101%

This is asuming crits is 2x normal dmg
So higher dmg=more dmg from critsb:victory

Tryagain - Harshlands

That's pretty simple to figure out, the math is obvious. Assuming a crit is double damage. (this is probably the question you really want to ask)

lets say you do 1020 damage and you attack 100 times, with 1 crit.

(999 x 1020) + (1 x 2040) = 1021020

now lets say you do 1000 damage and attack 100 times, with 2 crits.

(998 x 1000) + (2 x 2000) = 1002000

Some things to take into consideration:
-The higher your damage, the more difference in damage a crit will make.
-It seems that crits sometimes do more than just double damage.
-In PvP a crit is often a 1-shot, whereas a normal attack will just be a heiro tick.

In general, for PvP crits are way more important than damage, but in PvE its the opposite.

Zhoelle - Sanctuary

Yes to above. Generally, higher base damage is better than an increased chance to critical, since the % is so low with criticals.
But, criticals might be the only chance to overcome charms (spike damage higher/faster than what charm can heal). And it's cool to see that big number come up.

Yourmom - Lost City

You guys aren't answering what he asked at all. Someone put the formula up for magic attack damage and I'll do the math.

He's asking which will actually do more damage in the long run, a ring with matk bonus or % crit bonus. I don't know how the matk on a ring translates to actual spell damage without looking at the formula and I don't remember what it is.

Xhinzo - Harshlands

Not maths based but lets say that with the ring your crit chance is 2% and without it 1%. Their is not a significant (like I said not maths based) increase in my opinion to warrant an item selling for those kind of prices. Of course that is up to you. My basis for this is my blademaster. A 1% increase in crit does not really show up as a significant increase in the number of crits per 100 hits.
Another point to note is that a 1% crit increase still exist without the ring so that the person with say +21 damage will do more damage when they do manage a critical (well assuming every hit did the same damage or at least the average damage was within a ver small range).

Now forget the original assumption and look at it this way! Lets say the base crit% of the individual is about 5%. Now all of a sudden having an item with 1% crit becomes very sellable because lets say that individual is able to get a hold of 3 items that raise the base crit % from 5% to 8-10%. In essence its not enough to say that one ring with a 1% crit increase is selling at an exhorbitant amount. It must be considered that persons looking to items to boost their crit% will be looking for multiple gears with such stats. In that regard the "value" of that 1% (in tandem with other modifiers) is more than if it would be operating by itself.

Look at it this way. If you had 1 piece of a 5 piece puzzle that would grant the owner of the completed puzzle a very powerful item (most likely that would also be used against you later on), how much would you charge for it?

Surfer_Rosa - Sanctuary

An interesting question, please allow me to take a crack at it using some sketchy bar napkin math. All other things being equal, if your attack was, say 1000, +20 to your attack would not add up as much as what a crit adds to a single attack (the asumption being it doubles it) but in 50 hits. This would mean that in the above +21 vs 2% crit example the numbers should be pretty close BUT it should be pointed out that most players upwards of mid levels do actually deal way more damage than just 1000 so while attack add ons do increase they don't do so in the same proportion crits add up which would make +crit a better choice for all but low level players considering the main criterion to be mean damage over time. Once again, this is SKETCHY BAR NAPKIN MATH, it serves no other purpose but to illustrate a point for us lazy, mathematically challenged individuals.
An extra consideration is that +attack should give you a more consistent performance so it really does come down to personal preference, although +crit should be technically superior and give you a better chance of seeing big numbers (which we all like). An ACTUAL MATH consideration would require real numbers as well as acounting for a number of factors impacting performance.
Edit; Such as what the above poster mentions of +attack being added to existing crit rate, now my head is dizzy...

Yourmom - Lost City

Ok found the formula, someone else feel free to take a crack at it while I'm doing it, see if our math turns out the same.

Magical Attack Formula:
( 1 + ( MAG / 100 ) ) * ( LVL + EQP )

from here http://pwi-forum.perfectworld.com/showthread.php?t=214921


Remember this is the formula for what it shows under your char, the damage is a little bit different.
I'm going to do this based off my char because that's what I'm interested in, so

MAG=270
LVL = 90
EQP = variable still
and I'll use hell venom scarab to figure out damage.

Also, going to use the hh90+6 crit mage sword as my weapon, and level 88 rings with no bonus but crit or magic attack (+28 is the standard bonus compared to 1% crit I believe)

Solandri - Heavens Tear

Yourmom - Lost City wrote: »

Ok found the formula, someone else feel free to take a crack at it while I'm doing it, see if our math turns out the same.

Magical Attack Formula:
( 1 + ( MAG / 100 ) ) * ( LVL + EQP )

Well, if you're considering before vs. after cases, then the first term remains the same so you can just drop it. The ratio of damage before and after adding a +atk ring is just:

(lvl + eqp + ring_atk) / (lvl + eqp)

So the increase is just:

ring_atk / (lvl + eqp)

So for +21 atk to equal 2% critical, your lvl + eqp_atk without the new ring would have to be 1050. If it's less, the +atk does more damage on average. If it's more, the +2% critical does more damage on average. The level 90 magic weapons have a base average magic attack of just 831, so I think it's safe to say that for the vast majority of players, the +21 atk yields more damage than +2% critical. Edit: This assumes the 2% critical takes you from 0% crit to 2% crit. If your starting case has more than 0% crit, then increase in damage from +2% crit is less than 2%. This favors the +21 atk even more.

But of course as has been pointed out previously, the spike damage from a critical is handy for punching through charms. I'm pretty sure the prices +crit bonuses commands mostly comes from this application, not from average damage increase.

Isala - Sanctuary

The math is such a weird thing to figure out, and I really don't know why such a huge price for something Magical, but I know why a Physical ring would sell like that.

Because a lot of people figure that for archers, with their already high Crit ratio, will buy those things up like candy. The more crit they have, the happier the archer. I'm still trying to figure out why on earth a Mag ring would be that high, though.

Yourmom - Lost City

Ok, so I cheated on my math a little, and I used an auto-stat calculator instead of doing it myself.

pwcalc.ru if anyone wants to play with that.

Here's what I'm getting:

My test char, standard LA fox stats, +6 weapon with level 7 matk shards.
xmas blessing, and 2 level 88 matk rings with no bonuses.

Starting matk is 4350-4989
Starting crit is 8%

http://pwcalc.ru/pwi/?char=3179d6821f013626



Test char with 2% crit rings
Same stats, but crit is now 12%
(not gonna bother making it)

Test char with +28 matk rings
Crit is still 8%
matk is now 4565-5204

http://pwcalc.ru/pwi/?char=26f6704a974469e3



Now, to damage calculations

Hell venom scarab is = matk + 100% of weapon damage + 2534.

My hh90 sword here gives 899-1065 matk. For simplicity, I'm going to use the average of this value as my weapon damage, and use the average of my matk range.

My control char and my crit build are going to have an average raw damage of 8185.5.

My matk build char is going to have an average raw damage of 8400.5.


Taking crit into account:

Assuming that crit works at the rate that it says it will, over 1000 attacks, my crit build will have 120 crits, and my others will have 80 crits.

Assuming a crit is straight double damage: that's an extra:

Crit build: 982260
matk: 672040
control: 646840

adding everything together, we have a total damage of:

Crit: 9167760
matk: 9072540
control: 8832340

and an average damage of:

crit: 9167.76
matk: 9072.54
control:8832.34


So, in this example, getting 2% crit rings on both your hands will gain you about 95 extra damage per hit on average for venomous scarab.

One thing to keep in mind, this spell only gains the benefit of 100% weapon damage. As your spells rely more on weapon damage, your own matk stat will count for less, so crit will come out even further ahead.

Asterelle - Sanctuary_1381265973

Solandri - Heavens Tear wrote: »

Well......
So for +21 atk to equal 2% critical, your lvl + eqp_atk without the new ring would have to be 1050. If it's less, the +atk does more damage on average. If it's more, the +2% critical does more damage on average. The level 90 magic weapons have a base average magic attack of just 831, so I think it's safe to say that for the vast majority of players, the +21 atk yields more damage than +2% critical.

You are assuming the TT90 weapon is unrefined and unsocketed and you are not including the equipment mag damage from the rings.
TT90 mag sword at a modest +4 refinement is +86 dam bringing the average dam of the sword to 917.
Add in a flawless sapphire and its 942. 2 lousy lvl 88 npc rings of scorching heavens add at least 68 mag damage each bringing the total equipment magic damage to 1078. This is enough to make the 2% crit do more average damage by your calculation.

Fleuri - Sanctuary

Also, you should maybe keep in mind: most skills do a different amount of damage than your magic attack.

Also, does ring damage get counted in "weapon damage" which gets used for calculating some skill damage?

Anyways... when you have a good critical chance, increasing your critical chance has diminishing returns, and when you have a high attack, increasing your attack has diminishing returns. Ideally, you need to be finding a balance.

OMGLAZERZ - Heavens Tear

The theoretical math behind damage! b:pleased


Adding more crit% statically increases your damage output by .99010% per crit% increase from 1% base crit (or whatever it currently is sitting at). This means that regardless of how much damage you do, your damage will increase by that percentage over an extended period of time, and if your damage output increases at some point in the future (higher rank spell, better equipment etc) you will gain the same benefit that you did before, and you will do more damage since the increase is based purely on a percentage increase.


However, that being said, adding more +M. Attack/P. Attack is dependent on what your current damage output is. If your damage is currently sitting at 1000 damage per attack, and you add enough M/P attack to increase your damage output to 1010, then you will increase your damage output by 1%, but if you get a new rank of spell, and your damage output increases to 2000 per attack without that equipment, then, unless the increase afforded by the previously added equipment also increases by that same factor (new damage/old damage), then you will actually start getting less than a 1% damage increase, and the damage increase from the gear in question will stay the same.


This means that equipment that adds x damage gives a static increase to damage that will never change even if your damage without it increases which means that as your damage without it increases, the percent increased by having that +damage increase goes down in effectiveness while gear that increases crit percentage will always increase the amount of damage done over time by X*.0099010*(# of Attacks).


Another way to look at it!

If the equipment you're considering adds X% of your current damage, then it will do more damage over time than an item that only adds X% crit.

If the equipment would a less than X% of your current damage, but adds X% crit, then that will end up doing more damage than the item that only adds X% of your damage.


Hope that makes sense to ya'll

Rule - Heavens Tear

A tiered breakdown for dmg range vs crit range would be an ideal here so that the balance could be struck.

Yourmom - Lost City

Fleuri - Sanctuary wrote: »

Also, you should maybe keep in mind: most skills do a different amount of damage than your magic attack.

Also, does ring damage get counted in "weapon damage" which gets used for calculating some skill damage?

Anyways... when you have a good critical chance, increasing your critical chance has diminishing returns, and when you have a high attack, increasing your attack has diminishing returns. Ideally, you need to be finding a balance.

That's why I said I was doing this considering hell venom scarab as the skill I was using for my math. It uses base mag atk + 100% of weapon damage, so its a pretty basic one.

I don't think that ring damage counts towards "weapon damage". At least I didn't count it there. I think it just goes towards your matk, but I could be wrong, I just guessed.

As far as balance goes, I think that finding rings your own level with crit on them is all the balance you really need. The attack from the ring should be enough to keep you in decent range, while the crit % is always good.

Solandri - Heavens Tear

Asterelle - Sanctuary wrote: »

You are assuming the TT90 weapon is unrefined and unsocketed and you are not including the equipment mag damage from the rings.
TT90 mag sword at a modest +4 refinement is +86 dam bringing the average dam of the sword to 917.

Well, the basis of my statement was that the vast majority of players are not level 90. You can dress up the TT90 weapon as much as you want, they still can't use it. b:chuckle

Anyway, my point was to simplify the math so anyone can plug in their numbers and see relatively quickly which one is more advantageous. A lot of the messy stuff in that formula cancels out when you calculate a before/after ratio. I just did the +21 atk vs. +2% crit case as an example for others to follow.

Asterelle - Sanctuary_1381265973

Solandri - Heavens Tear wrote: »

Well, the basis of my statement was that the vast majority of players are not level 90. You can dress up the TT90 weapon as much as you want, they still can't use it. b:chuckle

Pfft, newbs. b:chuckle

starman17

took the words right outta ma mouth Ast, right outta ma mouth.

Calliope - Heavens Tear

Rule - Heavens Tear wrote: »

A tiered breakdown for dmg range vs crit range would be an ideal here so that the balance could be struck.

Indeed. +21 magic attack is a lot cheaper than +2% crit at level 78, that only gets more true at 88, where your +mAtk adds are bigger. Let's find the balance point.

Here's a sample full int Wizard at lvl 90 (I went with yourmom's weapon upgrades, so hh90 glaive +6, two g6 mAtk stones), with normal rings:

http://pwcalc.ru/pwi/?char=dbd6d7e05efba483

Skill will be Heaven Stone Rain, for obvious reasons. That's base magic plus 200% of weapon damage plus 4804.0.

I'll edit this post once I figure out how much mAtk it takes to equal +4% crit.

edit: I tried 100 mAtk to start, and that was awfully close. Here are some numbers!

6995.5 = avg base magic

1099 = avg wep

13,997.5 = avg stone rain dmg (no crit)

with 2% crit, 14,277.45 is avg.

With 6%, 14,837.35 is avg.

let's see what happens when we add +100 magic attack (** or *** rings with lots of +21 and +18 mAtk)

7523.5 = avg base magic

(wep is still the same, unless rings are added in there. If so, gotta redo the whole thing)

14525.5 = avg stone rain damage with +100 mAtk (no crit)

14,816.01 = avg damage with 2% crit and +100 mAtk

Almost the same. So at level 90, +1% crit is worth more than +25 magic attack, but not much more (aside from spke damage utility).

edit again: I just noticed that yourmom said +1% crit is roughly equal to +28 mAtk. Lemme try that.

edit3: +28 is too much, its closer to +26 as far as I can tell. I'd like the full formulas, though. Oh, and I'm forgetting about masteries!

AndromedaB - Sanctuary

crit is better in 2 situations


if ur attack is pretty high already (due to refines and stuffz)
if u pvp because lets say +69 mattack will increace my pvp dmg by around 5
while 1 more % crit will help me 1shot ppl thugh you really cant count on a 4% crit rate...

Yourmom - Lost City

Calliope - Heavens Tear wrote: »

edit again: I just noticed that yourmom said +1% crit is roughly equal to +28 mAtk. Lemme try that.

What I meant by that, was that the 1% crit modifier on a ring happens at about the same frequency as the +28 magic attack modifier. I didn't know they were even similar damage

Shamino - Sanctuary

The major issue of doing this sort of math is its heavily dependent on your initial values of both Magic Attack and Crit rate.

To demonstrate this ill grab a hypothetical character with 10% crit and 2000 damage and one with 1% crit and 2000 damage. The first character will have an average damage of (90*2000 + 10*4000)/100 = 2200 damage on average, the second character will have an average damage of (99*2000 + 1*4000)/100 = 2020 damage on average. Adding a +1% crit to both characters gives 2220 and 2040 damage respectively numerically the same change but based as a percentage of the previous normal damage the 1% crit on the character with the low crit % had the largest effect. To emulate this crit % increase the 10% character needs a +18.2 magic damage increase the lower character needs a +19.8 magic damage increase.

A high crit rate character with low damage is going to get way more average damage from +damage than +crit rate.

A low crit rate, high damage character will recieve better average results from the crit rate.

However this isnt actually addressing the main reason why people want crit rate in the first place which is for 1 shots (only midly) but more commonly for 2-3 crit chains which take people out fast. Archers use this to take out classes whos heiros would normally stand up against normal attacks and even single crits but chains of 2-3 crits will tick and then kill the character. Raw DPS is only a consideration for PVE combat for PvP its all about the spike damage you can get in 10 seconds (which is 2-3 skills for most characters) which means by chaining crits (if your lucky and have a high % crit) you can quickly take down even a very high HP character.

Haiz - Lost City

To put it into simple terms.

In HH and PvP where damage is low and reduced, +matk is better because you get a bigger percent increase.

In PvE against normal mobs crit can help more because if you are doing 6k a shot and you increase it by 100, not much effect. You doing 6k though and you increase your chance of doing 12k there's a big effect. If you are doing 1k though and you increase damage by 100 to make it 1.1k, big increase. If you are doing 1k and you increase crit to have a chance of doing 2k, not very worth it.

Higher your damage is the better crit is. Killing people in PvP we all want crit for spike damage, this is for most damage over time.

Rule - Heavens Tear

ick. Dmg reduction changing the value of the different DPS. Maybe there is no good answer. Maybe Crit for TW\PK and Matt for instances. Closest thing that makes sense so far seems to be about 26 Matt = %1 crit at around lev 8x...ballparking it some.