Attack Rating vs Real Damage: Analysis of Defense

Preface

Long story short: Reim and Yesuurd performed some extensive PvP damage tests with different weapons and armors, Reim collected the data, and passed it on to me to try and squeeze some sense out of the numbers. These are my preliminary conclusions.

Heads up: read slowly! I want to keep this concise, so I might not explain as well as I should in certain places. I'm not saying this to insult your intelligence, but rather to insult my explaining skills!

To be perfectly frank, the numbers aren't as talkative as I'd like them to be. What I mean is: there are more inconsistencies than I would like. For example: two weapons that have almost the exact same AR, on the same defense, will have a greater variance in real damage vs two other weapons that have a greater difference in their AR. But, even though the results aren't as consistent as I'd have liked them to be (consistent enough, say, to derive a formula), I still managed to get some sense out of them.


The Meat:

- Not surprisingly, defense does not block a static amount.

Now that that's out of the way, let's get complicated! I'll cut to the chase and just tell you that damage blocked, like so many other things in Dark Souls, is subject to diminishing returns. Notice I didn't say attack rating, defense, or damage, suffer from diminishing returns, but damage blocked. This is key to understanding how damage works in Dark Souls.

There are 2 obvious factors involved when you attack someone: your weapon's attack rating (AR) and your opponent's defense. In the same way, there are 2 outcomes: damage inflicted and damage blocked. Simply: AR - damage inflicted = damage blocked. It's when you compare the damage blocked value with the defense that you notice how the game calculates damage. And what I found, is that it's the damage blocked that suffers from diminishing returns. This may seem like a backwards way of looking at things, but as you keep reading you'll understand why it makes sense.

Unfortunately this is where I couldn't get a specific formula (but do we really need to get that scientific? ). But even though we can't discuss the implications of these results specifically, we can still do it vaguely:

- The higher the AR, the higher the damage blocked. But, since damage blocked is subject to diminishing returns, all proportions maintained, the higher the AR, the higher the damage inflicted. For example: if you double the AR, the damage blocked will be less than doubled. This actually means that, contrary to almost everything else in Dark Souls, AR is actually subject to increasing returns.

- Increasing defense will not give you equal returns on damage blocked. If you triple your defense rating, you will not triple the amount of damage you block. However, depending on the weapon's AR, even though you didn't triple the damage blocked, you can still cut the damage inflicted by more than 3. This actually means that weapons with low AR are more penalized by heavier armor.


Here are some examples that will help make sense of this (from Reim's data):

- Low AR on low defense:
AR: 275
Def: 138
Damage = 184
Damage Blocked = 91

- High AR on low defense:
AR: 658
Def: 138
Damage = 528
Damage Blocked = 130

- Low AR on high defense:
AR: 275
Def: 418
Damage = 58
Damage Blocked = 217

- High AR on high defense:
AR: 658
Def: 418
Damage = 380
Damage Blocked = 278

So you can play around with the above numbers to understand what I was explaining. Notice the AR more than doubles from the first weapon to the second, but the damage blocked does not. You can also notice the defense from the first armor set (nude, actually) to the second more than triples, but again the damage blocked does not. Finally, notice how the damage of the small weapon (a mail breaker+15 @40 Str/ 40 Dex) is more than divided in 3, whereas the damage from the large weapon (Great Club+15, same stats) isn't even cut in half. This explains why you need to look at damage blocked, rather than damage inflicted, to understand how damage is calculated in Dark Souls.


Conclusion

Now, obviously, you didn't need me to tell you that more defense = less damage! But by explaining how damage works, we... lol I'll leave this part to you--I've done my part! In the mean time, this finally explains without a shadow of a doubt why elemental weapons do less damage than pure weapons: since their large ARs are split into 2 damage types, they're actually 2 small ARs which trigger 2 defenses which each have less diminishing returns on the damage blocked = more blocked.


Thanks a lot to Reim and Yesuurd for their testing!

I'm adding extra info here, because I don't want to edit the first post, and I especially don't want to make it any longer than it is!

First, for the new players, definition of AR:

AR = Attack Rating. This is the number you see on the stats screen, which is an indicator of your weapon's damage potential. It is the sum of all the weapon's attack stats (base damage + scaling bonuses, for physical, magical, and elemental damage). Many people make the mistake of referring to this number as "damage"--it is not. Attack Rating is the number the game uses in order to calculate how much damage your attack will do, once all of your opponent's defenses have been factored in. Note that it is possible to do higher damage than the weapon's AR number, and it is also possible for multiple weapons of the same AR to do different amounts of damage. For these reasons, AR should not be taken at face value. It is not an absolutely reliable measure of a weapon's capabilities (not to mention other factors such as moveset, speed, range, etc., are much more important than AR.)


Also, a theory to be considered:

It is my assumption that AR, before defenses are factored in, is subject to a hidden modifier that the game uses to either inflate or deflate its value, according to weapon and attack used. This multiplier is used, more obviously, to differentiate the amount of damage a weapon will do with an R1 attack or an R2 attack (or any of the other attacks in its moveset!). But, less obviously, I think this modifier is also used to differentiate attack values between different weapons. Because of this modifier, two weapons with the exact same AR could have different damage values. Rather than unbalance weapons, this would actually have been implemented to balance the damage between weapons to compensate for moveset differences (especially: variance in attack speeds).

Adding to the resources thread.

It must be really dramatically increased at some range or depending on a factor I cant see because, as a tested example, my +15 iaito with its 410 ar hits for 190 or so in both hands through 307 slash defense where my +15 great scythe in both hands hit the same guy for 417.

Thanks BLA1NE for making sense of the data. It seemed pretty random to me when Yesu and I were collecting it. That's interesting about the diminishing returns - it's best to have all your AR in one stat, as lower AR is punished more heavily.

If you guys want to spreadsheet for the damage done, here it is.

It is data for 17 weapons, 4 upgrades (+15 and all elementals) against 3 different armors. It might help you decide which way you want to go for upgrade paths.

Give Yesu a +1 somewhere guys. He created a special build to help me damage test, and spent hours with me to do it - we even had to redo the entire thing because we messed up.

I think when def vs AR is calculated one thing people often ignore is the type of attack. For example, if someone has high elemental resistance but low thrusting defence than it is clear that the damage being done will lean more towards the fact that he was just stabbed by a rapier rather than assuming lightening actually did anything.

If you hit someone with a regular only weapon than it is going to do different amounts of damage than if you hit them with a thrusting weapon, depending on their defence.

^That's why I had to keep my explanation basic. When you hit someone, you don't see damage as X physical and X elemental, you only see the sum. This makes it practically impossible to figure out how much comes from either until I figure out more precisely how one is calculated. So I can't really be more specific than I am at the moment.

Also, the physical defense ratings were confusing me too. I didn't spend much time looking at them to try and make sense of them, but that should probably be the next step. What I mean is, armors have 4 physical defense ratings: "physical", "strike", "slash", "thrust". What does the "physical" defense stand for when you're being hit by a slashing weapon, for example? And it didn't strike me as just a figurative number, either, since it wasn't something as obvious as an average. So is physical damage calculated according to "physical" defense and the defense for the attack type applied?

There's a lot of questions that need answering... Gonna have to be one at a time!


@Reim: Seems I was up late last night and gave my ratings for the day early... But I'll get you and Yesu when I can!

For some reason I always assumed "slashing" was "regular"...

I looked quickly through the armor page of the wiki, though, and the phys defense isn't an average on most of them.

Thanks for your help! I'd rep you too, but I'm spent for the day...

That wasn't part of the data Reim and Yesu collected, but there was 1 weapon in there that threw me for a loop for a second! lol, the Demon Great Axe did more damage on 138 defense than its attack was rated for... Until I realized it said 2H, which accounts for the increased damage output.

It's highly possible that you're right about the different 2H modifiers for different weapons. It's also possible that there are different modifiers for elemental weapons, but I think it would just seem that way because of the 2-defenses issue rather than an actual different modifier.

It's worth testing, yes. This is related to this topic, but it can be tested completely separately, since it should (I hope...) be a straightforward multiplier.

Also, now that I think of it, it could help shed more light into the defenses issue. If you test only regular weapons and find that they have a simple multiplier (like you said, straightsword 1H x 1.95 = 2H), then test elemental weapons, and we assume the multiplier remained the same, but the final damage was different, that would tell us how much the defense is worth.

Great thread guys. Would also love to know more about the 2hd damage modifiers. I had noticed that my beloved balder side sword did great damage with 2hd thrust attacks (possibly because of both a 2hd damage and some sort of bonus to thrust attacks per its description) but the science behind it escapes me.

Wow I just read the Data!!! although Blaine wanted it to be a bit more percise maybe, I am very happy about the outcome, thanks to Blaine for crunching and to reim for letting me
be part of this really at the same time for all his work, I was just a sandbag on this lol.

If there are any more tests we can think of I would be more than glad to help.

+1 to both of you for your work.

I was horsing around with my fire balder side sword +10. While a 2HD thrust does do more damage than a 1HD R2 thrust, the difference did not seem to be huge. On the hollows in the parish, it was only about 70 points difference. Both, however, do a lot more damage than a regular R1 slash attack, so the fact that it is a "strong" R2 attack seems to be the big driver, not whether it's 1hd or 2hd.

BLA1NE wrote:That wasn't part of the data Reim and Yesu collected, but there was 1 weapon in there that threw me for a loop for a second! lol, the Demon Great Axe did more damage on 138 defense than its attack was rated for... Until I realized it said 2H, which accounts for the increased damage output.

It's highly possible that you're right about the different 2H modifiers for different weapons. It's also possible that there are different modifiers for elemental weapons, but I think it would just seem that way because of the 2-defenses issue rather than an actual different modifier.

It's worth testing, yes. This is related to this topic, but it can be tested completely separately, since it should (I hope...) be a straightforward multiplier.

Also, now that I think of it, it could help shed more light into the defenses issue. If you test only regular weapons and find that they have a simple multiplier (like you said, straightsword 1H x 1.95 = 2H), then test elemental weapons, and we assume the multiplier remained the same, but the final damage was different, that would tell us how much the defense is worth.

So when are we testing this? I am up for it.

Me too, I'm down for some additional testing.

First, we should figure out what question we want to answer, then. That way we can decide what data will best help up answer that question.

Ok, here's a strange event I noticed earlier.

I have been using the Manserpent Greatsword for PvP. At +14, It was hitting most people for around 150-200 damage. Most people run around in heavy armor, so it could be armor, until I tried using a BKGA. At +5, it's AR (base + scaling, I assume?) is around 10 more then the Greatsword. Hitting someone I had JUST invaded with the different weapons, showed a MASSIVE difference. The Sword dealt around 200 damage, the Axe dealt over 500 (!) damage,

I am completely at a loss for this massive difference.

So...What happens if you have an elemental weapon, that does say, slashing damage. Does the elemental go through slashing and lightning, or is it that the physical part goes through slashing, and the elemental goes through lightning?

@Shkar

Was this 500+ damage an isolated hit, or was every hit that strong? And how many people did you invade with the BKGA? If the BKGA is consistently hitting for 500+ on many opponents, and the MSGS was hitting for 200, then I do find it hard to explain such a large difference if their attack ratings are as close as you say they are...

@Tolvo:

Good question... That could be the next thing we test; different attack types on armor, and split attack weapons of different types also.

BLA1NE wrote:@Shkar

Was this 500+ damage an isolated hit, or was every hit that strong? And how many people did you invade with the BKGA? If the BKGA is consistently hitting for 500+ on many opponents, and the MSGS was hitting for 200, then I do find it hard to explain such a large difference if their attack ratings are as close as you say they are...

I realized I forgot to carry the one, so it was actually about a 110 difference (~500 to ~615). I didn't use the axe for long, but most hits seemed to do about 500 from my memory.