Home > Age of Conan, Combat Mechanics > Hit amount as a function of DPS

Hit amount as a function of DPS

(This post is a kind of continuation of my post about combat mechanics from a few weeks ago.)

Well, here’s at least one thing that makes sense. I measured the amount of damage done by an unarmed white hit (i.e. while having nothing in my main hand) — an ‘up’ attack to be precise, though it seems that other directions hit for the same amount anyway. The theory here is supposed to be that the amount of damage done is computed as

damage = DPS · animation_length,      (*)

where DPS is the DPS number from your Attributes/General tab, and consists of your weapon damage plus the DPS coming from strength (or dexterity, depending on your weapon) and combat rating. I varied my DPS by swapping some gear around, and I also did the tests with several classes. To my considerable surprise, all the measurements match up perfectly:

We see that all the measurements lie on the same straight line; the slope of this line is the animation length of our unarmed ‘up’ attack. It must be equally long regardless of your class, since the measurements of different classes all lie on the same line.

As often with this sort of testing, we are slightly hampered by the fact that damage is rounded to the nearest integer in our combat log, even though the game internally works with non-integer amounts. (The DPS as shown in the Attributes/General tab is similarly rounded to one digit after the decimal point, but this isn’t a problem as we can compute the exact value by ourselves from combat rating and strength.) For example, at 132.2 DPS (actually more like 132.2295; coming from 1.0 weapon damage + 4803 combat rating) our hits were shown as being 164 points, so the real amount must have been somewhere between 163.5 and 164.5. And the animation length must therefore have been somewhere between 163.5/132.2 = 1.236 sec and 164.5/132.2 = 1.244 sec.

So we don’t know exactly what the animation length is, but we at least found a lower and an upper bound on it. Other measurements from the chart above give us slightly different bounds. The highest lower bound I could find was 1.24107, and the lowest upper bound I could find was 1.24154; between these two, we have estimated the length of this particular animation with an accuracy of less than half a millisecond!

So as we can see, the formula (*) above isn’t some sort of approximation; it’s the real thing. For any of the measurements shown on my chart, you can take any animation length from the range [1.24107, 1.24154] that we’ve just established, multiply it by DPS and round the result to the nearest integer, and you get exactly the amount of damage that really appeared in my combat log. (Of course, if we made more measurements at still different values of DPS, we could perhaps narrow down the range of possible animation lengths still further. But the current range is already very narrow.)

These measurements also demonstrate that when the tooltip says you got 1.0 weapon DPS from your unarmed main hand, it isn’t joking. If you subtract 1.0 from the DPS in all my measurements, you can no longer explain the amount of damage done in each hit with a linear function of the form DPS · animation_length — you’d have to add a constant term to it.

Defensive stance

Among other classes, my tests in the previous section included two soldiers (guardian and DT) in neutral stance. But what happens if we switch to defensive stance instead? The tooltip on defensive stance says, among other things, “−10% damage multiplier”. This multiplier seems to affect nothing more or less than the DPS value shown in the Attributes/General tab; in other words, the formula for DPS is actually

DPS = (weapon_damage + combat_rating / 36.6) · damage_multiplier.

By default, the damage multiplier is 1 (or 100%), but there might be various buffs or debuffs that modify it. Switching from neutral to defensive stance brings your damage multiplier to 0.9 (or 90%), due to the −10% damage multiplier on defensive stance. If there are several things affecting your damage multiplier, they stack additively rather than multiplicatively. For example, the death penalty debuff includes −1% damage multiplier; together with defensive stance this brings your damage multiplier down to 100% − 10% − 1% = 89% = 0.89, and not to (100% − 10%) · (100% − 1%) = 0.90 · 0.99 = 0.891.

So, here are some measurements of hits made in defensive stance. For the x-coordinate, we used the DPS as shown in the GUI during defensive stance, so it’s already been multiplied by the 0.9 damage multiplier.

Now, here’s an odd thing: the measurements in defensive stance still all fall on a straight line — but it isn’t the same line as in neutral stance (or on non-soldier classes for whom stances don’t apply at all). For example, in the previous section we saw that when our DPS was 132.2 (in neutral stance), our hits were for 164 points. Switching to defensive stance brings our DPS down to 119.0, which is good, as this really is 90% of 132.2 (rounded to one digit after the decimal point). But if you now plug this DPS into our formula (*), and use the same animation length that we established in the previous section (around 1.241 sec), you’d expect the resulting hit to be around 147.7 points. So the combat log, where things are rounded to the nearest integer, should show us hitting for 148 points; but it actually turned out that we were hitting for 150 points.

This anomaly, where our hits in defensive stance are slightly stronger than we expected, was present in all my measurements in defensive stance, both on my guardian and my DT. I’m not sure how to explain it. One way is to imagine that although the GUI (in the Attributes / General) tab shows our DPS exactly as we would expect it given a −10% damage multiplier, it’s actually lying to us and the game actually uses a slightly higher DPS when calculating how much we’re hitting for. It’s as if, instead of having 90% as much DPS as in neutral stance, we actually had around 91.6% or 91.7% as much; i.e. as if the damage multiplier stat on defensive stance was not −10%, but around −8.3% or −8.4%. But this idea, that the GUI shows one thing but internally the game uses a completely different amount when calculating damage, seems a bit too bizarre and improbable to me.

Another explanation that comes to mind is that animation length is different in defensive stance than in neutral. We can calculate bounds on animation length from our measurements in defensive stance, just like we did in the previous section for neutral stance. The result is that the animation length in defensive stance should be between 1.26395 and 1.26463 seconds — about 0.02 sec longer than in neutral stance. Now, this doesn’t strike me as completely implausible; after all, the character’s hands etc. are in a slightly different position in defensive stance than they are in neutral, so it might require a slightly longer animation to perform the hit.

I tried to test this explanation in the following way. If each hit is 0.02 seconds longer in defensive stance than in neutral, then a sequence of 100 hits should be about 2 seconds longer. The combat log shows the timestamp of each hit to within 1 second, so we can perform 101 hits and compute the difference between the timestamp of the first and the 101st hit to estimate the total duration of 100 hits. We’d expect this duration to be around 124 or 126 seconds, since we’ve seen above that the animation length should be around 1.24 or 1.26 seconds. What actually turned out is that the duration of 100 hits was slightly longer — around 134 seconds — which suggests that there’s a small gap of about 0.1 seconds between each hit and the next. I doubt there’s any way to avoid this gap, since it was there even though I always pressed the button for the next attack before the current attack was finished.

If we repeat this several times, the duration of 100 hits will not be exactly the same each time; this is probably partly because it depends on where within that one whole second our first hit fell, and partly because the tiny gaps between hits are perhaps not all equally long. If we want to compare the results for neutral and for defensive stance, we’ll have to assume that the gaps are on average equally long in both stances. Under this assumption, a sequence of 100 hits should still take about 2 sec longer in defensive stance than in neutral (if it’s true that the animation length in defensive stance is 0.02 sec longer than in neutral). But is that really the case? I repeated this test 100 times in each stance and the following chart shows how often I got which duration:

As we can see, the durations in defensive stance aren’t really 2 seconds longer than in neutral stance. On average they are about 0.58 sec longer; I’m not sure if this difference is just a random statistical artefact (I did a t-test and it clearly showed that the difference is statistically significant) or if it really suggests some underlying difference in animation length, but in any case, the difference isn’t big enough to explain the anomaly in the amount we hit for.

So, to sum it up, I don’t have any good explanation for why the hits in defensive stance are stronger than you’d expect. Either the game is lying and using one damage multiplier in the GUI but a different damage multiplier when computing the actual damage of your hits; or the animation is longer in defensive stance but the uncontrollable gaps between hits are shorter and so cover up this increase in length; or there might be some other explanation altogether.

  1. January 26, 2013 at 23:38

    that was the most boring thing I have read …ever

    • January 27, 2013 at 00:05

      Muahahaha ๐Ÿ˜› *rubs hands evilly*

    January 28, 2013 at 20:29

    Thanks for posting on the economy of defensive stance (that it isn’t as bad as the description in AoC puts it).

  3. Sapiento
    January 29, 2013 at 07:31

    Or perhaps -10% dmg modifier applies only to some part of damage output and another part stays the same? This would result with less than overall 10% dps reduction in def stance.

    • January 29, 2013 at 11:12

      True, that would work. For example, if approx. 84% of the damage in neutral stance is subject to change when you switch to defensive, and the remaining 16% remains unchanged, this would explain our observations (because 90% * 84% + 16% = 91.6%, which is approximately the amount we were hitting in defensive stance relative to neutral stance).

      But I can’t think of anything in the game that would encourage us to expect this kind of mechanic. For example, what would this division into 84% and 16% be based on? It cannot be e.g. stats on gear vs. innate attributes, because the defensive/neutral ratio of approx. ~91.6% occurs in all my measurements regardless of how much or how little gear I wore (or what my innate strength was — 200 on DT vs. 210 on guardian).

      This explanation also doesn’t change the fact that the DPS as shown in the GUI during defensive stance shows the entire original DPS (from neutral stance) multiplied by 0.9, not just a part of it.

  4. longtail-aoc
    January 31, 2013 at 19:59

    Is it possible that some feats are not subject to the -10% defensive stance penalty? For example, let us consider fully spec’d Sustained Rage of +15%.

    Neutral: 1.15
    Defensive -10% on everything: 1.15 * 0.9 = 1.035
    Defensive -10% does not affect Sustained Rage: 0.9 + 0.15 = 1.05

    • January 31, 2013 at 20:13

      Well, the 1.0 DPS from bare hands is not affected by weapon damage bonuses (which is what Sustained Rage gives you).

  5. Askii
    February 19, 2013 at 11:51

    About the 84% idea:
    I did some testing on crits recently where a similar number popped up. (warning: this will be a lengthy post).
    I noticed that in your last game mechanics post, you said that not only is there no inherent +50% for crits, also Crit Dmg Rating only boosts crit dmg by about 4/5 of what it says.

    Wanting to know more about this, I wrote down non-crit dmg, crit dmg, and critical dmg rating (CDR) for various combinations of gear, perks and buffs (on a conq with no feat points spent, attacking guild city strawman unarmed). The results:

    Non-Crits: {191,191,191,191,191,191,191,191,207,160,160,160,179,179,179,179, 37,37,212,212,212}
    Crits: {206,209,226,215,223,229,212,232,250,187,182,167,190,196,212,206, 42,37,231,238,257}
    CDR: {329,395,787,541,721,867,475,933,925,729,583,191,264,410,802,656,604,66,387,533,925}

    Assuming the formula works like this:
    Crit_Dmg = Base_Dmg * (1 + WEIGHT * Crit_Multiplier)
    Crit_Multiplier = (CDR/36.6)/100

    I now did the same upper/lower bound calculation you did, and came up with those bounds for the WEIGHT parameter: [0.8257, 0.8431]

    Conspicuously close to .84 …
    Not sure what causes this…maybe the strawman has an inherent Critigation Amount (with a Critigation Chance of 100%), or maybe the devs modified the bonus damage from crits in this way for balancing purposes. Or maybe it’s something completely different.

    • February 19, 2013 at 12:04

      Very interesting! I’ve got some measurements on critical hits from the same experiments that were the basis for the first chart in this post, but I didn’t get around to analyzing them yet. I’ll take a look and see if the same 84% figure shows up there as well.

      I guess the Critigation Amount could be a possible explanation, though I’d be surprised to see it on a straw dummy — when the devs introduced the critigation mechanic, they emphasized that mobs don’t have critigation (only players do), so I wouldn’t expect it on a straw dummy either.

      About the inherent +50% bonus for crits, my impression was that it’s certainly not there for unarmed hits, but there might be something of that sort on armed hits – but those experiments were really preliminary and will need some more investigation some day when I get around to it. (The problem with armed hits is of course the variance, which means you need a lot of hits – and crits – to estimate the mean hit amount decently.)

  6. TheFollower
    February 22, 2013 at 19:36

    “thereโ€™s a small gap of about 0.1 seconds between each hit and the next”

    From my experience, this gap simply is your latency. Each time you hit something, you need to wait for the server to give your client the damage done (well, all hit consequences like damage, hit or miss, etc.).
    This is something very easy to notice when you have a big latency. Mine is around constant 300ms (I live very far away from the server). I made a test spamming Fires of Ghenna. It should be 2s per shot but I really loose 0.3s on each shot (46s to cast 20 FoG instead of 40s).

    This lead me to the conclusion that your real dps depends on your latency. On my demo with my main pve rotation (lots of instant casts), my dps drops by 20% compared to what someone with 50ms would get. DPS is kinda proportional to the animation time but the latency is a constant. The more insta casts you spam, the more time you loose because of lag. Demos suffer a lot from this whereas rangers (long cast times) get less penalty.

    From the data you shared (0.1s gap), I’m pretty sure you have around 100ms latency ^^

    • February 22, 2013 at 20:34

      True, my latency is usually around 100 ms. I guess I was hoping that if I press the button for the next hit before the previous hit is over, this would get sent to the server immediately and it would start the next hit as soon as the previous one is done, without waiting for the information about the end of the previous hit to reach my client.

  7. Askii
    March 15, 2013 at 13:12

    Did some more testing on the crit thingy …
    I did several tests, this time armed (dual wielding 1HE):
    Stats: DPS=381.3, CritRating=652, CritDamageRating=1039
    (Crit_Multiplier = CritDamageRating/36.6 = 28.39%)
    1. The DoT of the Bloodbath VII combo does constant damage
    non-crit: 208
    crit: 370
    gain: 77.88%
    (the gain value means the crit value is gain% higher than the non-crit value, e.g. 370 = 1.7788 * 208)
    This is almost perfectly consistent with the developer-announced formula (crit = non_crit * (1 + 0.5 + Crit_Multiplier))

    However, when I tested combos and whitehits, things look rather weird:

    Combo: Bloody Hack V (+274 finisher dps, 1k hits, value here is average damage)
    non-crit: 311.03
    crit: 509.81
    gain: 63.91%

    Now, if we assume that the +50% crit dmg modifier the devs talked about is dependent on your weapon type (as in many RPGs), and modify the formula from my last comment to:
    crit = non_crit * (1 + .84 (Weapon_Modifier + Crit_Modifier))
    and assume that Weapon_Modifier is 0 for unarmed hits, and .5 for 1HE hits, then this formula works fine for unarmed whitehits and Bloody Hack combo finishers. (.84 * (.5 + .2527)) = 0.63, which is pretty close to the observed crit gain with Bloody hack.

    But it doesn’t work for the Bloodbath DoT. And then I tested whitehits…

    Whitehit (Directon:UP, 1k hits, average values)
    non-crit: 395.05
    crit: 577.62
    Gain: 146.21%

    This isn’t consistent with any formula so far. Neither the one the devs announced, nor the 84% one I’ve used earlier.
    I get the feeling that the 84% factor we saw earlier has something to do with combo animation length. Maybe unarmed whitehits and BH V finishers have similar animation lengths, and thus a similar .84 factors, while the BB VII DoT has no animation length (being a DoT) and thus might use a factor of 1. For the whitehits, this factor would be .61.
    Or maybe the formula is still wrong. I am, once again, lost. ๐Ÿ˜›
    (btw; if anyone wants the combat logs for their own analysis, send an ingame mail to Askii on Crom)

  8. April 29, 2013 at 18:22

    I recently started to map out all stats on a spreadsheet so I can tinker with numbers (put an extra few points in one field to see the resultant dribble down). I came across various issues that one would not think of at first when trying to track down discrepencies. You, m’lday, have gone in to great detail (at least to a math’s ignoramii such as myself) and hit upon the stance part.

    One of the things I have yet to properly test is Guild City/BK bonuses. I’m not sure where they come in to the equations. As I said, I’m still testing my self and have yet to get to that part =)

    And another part are the bonuses we choose when we complete the destiny quest. I also noted one of my toons, when I stripped all of them down to their bare bum, actually had an extra point in two base stats (I could not remember which two exactly), but this lead me to think the coices MAY have had something to do with it. And again, I have no idea where those choices come in to play and at what time.

    Keep up the good work. I just lost 3 hours of late night sleep to your website!

    • April 30, 2013 at 00:24

      Well, the buildings and destiny quest decisions mostly give you small bonuses to various stats; they function pretty much the same as if you had those stats innately or on your gear.

      See some of my previous posts for examples, e.g. this one about the combat rating from Thieves’ Guild and from Weaponsmith, and this one about HP bonuses from the Keep, Battlekeep, and destiny quest rewards.

      I never bothered trying to investigate what exactly the other destiny quest rewards (i.e. other than HP) give you, and in what amounts. It would be too much work, not to mention that this stuff probably depends on your archetype anyway.

      The battlekeep buildings mostly increase your chance to resist CCs, you can see those in one of the tabs (I forget which one exactly). Between that and the AA (from the PvP side of the tree) you can get around 10% passive resistance to many CCs, IIRC.

  9. May 1, 2013 at 05:43

    Thanks heaps for those links mate. Much appreciated.

  10. June 20, 2013 at 17:05

    Does hit rating have any function on DPS other than bypassing evade rating and immunity rating on enemy (regarding combos & white hits)? Also, what would be the duration in seconds of 100 shots say taken from frenzy stance (you did a great job from normal and defensive stances)? Although, I’m not on Crom, thank you also to the Conquorer (Askii) who posted his 1HE information (great work brother!). What was very interesting, was the critical nature (every pun intended) of using Blood Bath by Conquorers in their rotation (77.88% gain in a critical for the dot!), and the outrageous gain of 146.21% for white hits. Blagatki! (Good!)

    • June 20, 2013 at 17:17

      I don’t think hit rating has any other effect than what you described. As for hits in frenzy stance, I have no idea – it’s hard to say without trying. Additionally, since my ping is different since the servers got moved to the US, I’d probably have to repeat the experiments with normal stance if I wanted to be able to compare frenzy vs normal now.

      • stiiixy
        June 21, 2013 at 00:55

        Yeah the latency makes a massive differance to you effectiveness as a tank if you have a random bunch of DPS hounds in your group. And the recent patch seems to have totally destroyed some players combos from what I hear, landing only one in three.

      • TheFollower
        June 21, 2013 at 07:39

        Just my 2 cents:
        1. The servers have not moved (yet?) to the US. That’s for sure. The chat server is dm10-nj4.ageofconan.com and the Crom server is gs013-nj4.ageofconan.com. Check it yourself (geo localisation IP), they are still in Sweden at gamehosting.com.
        2. There is more into hit rating than bypassing evade/immunity. It’s the attribute that controls glancing hits. As you probably know, a glancing hit is like the opposite of a critical hit (it’s like a critical fail). Low hit rating = a lot of glancing hits, which lowers the overall dps dramatically. Tanking with 8% hit rating or less is very dangerous for your dpsers ๐Ÿ™‚

  11. June 21, 2013 at 18:00

    Thank you ‘TheFollower’, that is what I thought….that there was a relationship between hit rating and DPS (due to glancing blows and maybe even more?). Further testing is needed, that and the speed of Frenzied moves (100 shots constant) will be tested. Even on straw dummies, there can be ‘glancing blows’ / critical fails…from what I have seen. In any event, hit rating is rarely described in its ‘power’ in places like the AoC-Is-Better-Than-TV (a favorite of mine), or other sites…for avoiding glancing blows (which are integrated into the formula for DPS). There are secrets waiting on good tests run on what the power is of this function. My guess also from what was written above, is there maybe a point at which, further increases in hit rating, are likely not worth it for ‘investment’ in pvp and pve situations for their ability to ‘eliminate’ the glancing blow factor/critical failure rate (on DPS averaged over a longer pd. of time). Something to think about. ๐Ÿ™‚

    • TheFollower
      June 22, 2013 at 07:30

      There is also a penalty when you fight higher level opponents (mobs or players). That’s why level 40 mobs can barely have a chance to ever hit a level 80 character, no matter what your evade rating his. Hit rating helps to deal with that. So it would make sense that you need a minimum hit rating to avoid misses and glancing hits, and that this minimum value depends on the level of the mobs you are fighting. This value must have been around 10% back in the old days but now we are often confronted to level 85 mobs and bosses. We need good testings to find out a good threshold.

  1. January 26, 2013 at 11:36

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