A Precision and Might Comparison

Discussion in 'Oracle’s Database (Guides)' started by Remander, Mar 13, 2014.

  1. Remander Steadfast Player

    REVISED 3/15/2014

    Many thanks to Sore and Shiny Mackerel for bringing more information to light, particularly the nebulous, unpublished multiplicative factor used in the precision equation. This has really changed the conversation dramatically, but I believe it’s still an important one to have. Hopefully, this will help those who are brave enough to dive into the math better understand the differences (and similarities) between precision and might in DCUO.

    This is a reposting of a thread I started in the Powers, Weapons, and Movement forum. I moved it here in order to clean it up and add to it. Additionally, I can now edit the posts over time, if changes are needed. Thanks to those who contributed to the original thread. Here is a link: https://forums.station.sony.com/dcuo/index.php?threads/a-precision-and-might-comparison.196019/

    I often see people post that precision scales better than might, so might needs a buff. Well, it’s just not as simple as that. Yes, the amount of precision in our gear has increased more through the tiers than the amount of might, but you have to look at how precision and might work, in order to have a better understanding of the impact of those changes.

    Both precision and might scale as linear functions. Going back to algebra, this can be represented as follows:

    Y = MX + B

    In this equation, B = base damage of an attack, X = the precision or might value, M = the scaling factor, and Y = the adjusted damage.

    Scared yet? Buckle up, and let's look at the scaling factors!

    For might, each point increases base damage of might attacks by 0.45% (once you hit level 30; under 30, it's 0.25%). Base damage will vary by attack. Since the damage increase is actually a percentage of base damage, base damage needs to be included in the scaling factor portion of the equation.

    If we plug the scaling factors into the function, we get:

    Adjusted might damage = [(0.0045 * base damage) * might] + base damage

    For precision, each point increases weapon or precision combo damage by 0.1 damage per second (DPS). Interestingly, there is no real base damage for a precision attack. If you have no precision, you do no precision damage. This can be confirmed by taking off all your gear and weapon and performing a precision combo, like Celestial’s Smite to cleansed Haunt. You’ll get the might damage from Smite, because even without gear there is a base might value of 572, but cleansed Haunt will just be a pretty animation without damage ticks. Additionally, there is a multiplicative factor for each precision attack. While it is possible to derive this factor from a set of accumulated damage data, it is not a value that is published anywhere in the game. We’ll just call it “m.”

    If we plug the scaling factors into the function, we get:

    Adjusted precision damage = [(0.1 * m) * precision] + 0

    To compare the two, we have to set some assumptions. Since we will soon have more standardized might cast animations, let's assume a might cast duration of 1 second. That will allow easier comparison with precision, which is actually represented as DPS, rather than a single value. We also have to consider a weapon attack or precision combo with the same animation duration of 1 second. Once we do that, we can compare the scaling of a precision attack and a might attack across a range of precision and might, respectively.

    If we set the Adjusted damage equal:

    [(0.0045 * base damage) * might] + base damage = [(0.1 * m) * precision] + 0

    Assume equal precision and might (X):

    [(0.0045 * base damage) * X] + base damage = [(0.1 * m) * X] + 0

    Simplify:

    [(0.0045 * base damage) * X] + base damage = [(0.1 * m) * X]

    (0.0045 * base damage) + (base damage / X) = 0.1 * m

    0.0045 + (1 / X) = (0.1 * m) / base damage

    0.045 + (10 / X) = m / base damage

    Set X = 4200, which is around the max current precision and might:

    0.045 + (10 / 4200) = m / base damage

    0.04738 = m / base damage

    Then, for a given base damage for a might attack, we can solve for the “m” that will give us a similar adjusted damage for a precision attack:

    m = 0.04738 * base damage

    Below is a plot of the two functions. On the X axis is the value of precision or might with a range of 200 to 5000. Your starting precision on the Brainiac ship is 200, as the item level 1 weapons are 20 DPS. I said above that might without gear is 572. With currently available gear, the max precision (including precision from weapon DPS) is roughly 4200, whereas might seems to max out a little higher at around 4300. On the Y axis is the scaled damage. I used a base might damage value of 10, and an equivalent “m” value of 0.4738 to generate this data. Adjusted might damage is represented by the red lines, and adjusted precision damage is represented by the blue lines.

    [IMG]

    Pretty close, eh? What if we increase the base damage of the might attack from 10 to 15, but leave the “m” value the same?

    [IMG]

    You can see that the adjusted damage function now grows at a faster pace with might than precision. We can then do the opposite and keep base might damage at 10, but increase “m” to 0.6738.

    [IMG]

    You can see that precision now edges out might, as both stats grow. So, really, for any given attack, the value of the base might damage or the “m” factor will determine how well attack damage will scale with the respective stat. Without extensively testing different attacks and different powersets over a range of precision and might values, it’s impossible to provide definitive comparative data; however, one could assume that the intent, at least, of the Dev team is to try and balance these types of attacks as well as possible. Hopefully, you can appreciate how complicated this task truly is.

    So, the obvious question is why do precision-based powersets seem more powerful than might-based powersets in game? The answer is power. All might damage costs power. The only precision damage that costs power directly is Earth aftershocking, but that's another discussion. :( Weapon damage is free. Precision combo damage is free after the initial might cast, though there is some associated cost (see the second post in this thread). Because precision-based powersets tend to have greater proportion of damage originating from precision than might, they can focus on magnifying that free precision damage. Might-based powersets don't have that luxury. They can use weapon attacks, but the majority of their damage potential will always come from might casts that cost power.

    If might-based powersets are inherently less power-efficient, what's the best way for them to compete? They can't just stack precision. Their strength is in might. On the other hand, if they go full might and rarely use their weapon, they basically need a dedicated troller to feed them power. In my experience, the best approach is actually to go for more of a balance between might and precision while incorporating potent weapon combos, rather than simple range taps, into each rotation. This conserves power, so that you can have a steady stream of might damage, while putting at least some emphasis on precision to enhance the damage of your weapon combos. That's how I ran Rem, when he was Electricity.

    Of course, there are other variables that play into damage output, and those need to be taken into consideration. Base damage, “m” value, and attack duration will differ between might casts, precision combos, as well as the various weapon attacks. Some powersets have might or precision buffs. Some have critical attack buffs. Some can set up power interactions (PIs) to enhance damage. There are critical damage buffs from ability casts. Some powersets have more burst damage, whereas others rely more on damage over time (DoT). There are trinkets. These all need to be considered, as well. For instance, Nature is a might-based powerset with a 45% precision buff. That allows a Nature player to shift the balance more toward full might, because they can make up for a lower precision with Carnage. You could also carry a precision trinket to buff weapon attacks, so you can push more might.

    The TL;DR take home message is that it's not as simple as saying, "hey, let's buff might." You just need to find the best method for your setup to make the most of it.
    • Like x 16
  2. Remander Steadfast Player

    I decided to get on the test server and look into base damage numbers for the 2 most used Celestial combos and compare them to some weapon attacks.

    I took off all my gear, and equipped an IL 1 20 DPS Bow I picked up from one of the PDs (Bow was Rem's original weapon, so I went with that). Keep in mind, it's just 20 DPS. No added prec (or might, for that matter), so when I looked at my stats, no prec was even listed. That 20 DPS should equate to 200 prec. To confirm the role of weapon DPS in prec combos, I actually tried ScH without the weapon. I got the might tick from Smite, but nothing after that. No prec = no combo damage. So, 200 prec for both weapon attacks and combos. My might was 572. I only speced 5 SP for SS flight (regular flight is too slow), the first 2 Bow slots (crit bonus, though I didn't record crits, and +4 Vit), Impact Arrow, and Trick Shots. I did not FRAPS, so my durations are best estimates by stop-watch.

    Bow Impact Arrow: 23-33 dmg, avg 28; ~1 sec duration

    Arrow Storm: 5-8 dmg x 4, avg 28 total; ~1 sec duration

    Long Draw: 24-34 dmg, avg 28; ~1.5 sec duration :p

    Smite: 86-112, avg 100 --->
    into cleansed Haunt: 20-24 x 1, 10-12 x 2, avg 44 total; ~3.8 sec duration, 190 power for total combo

    Retribution: 80-112, avg 100 --->
    into cleansed Wither: 59-66 x 1, 26-33 x 2, avg 123 total; ~3.8 sec duration, 285 power for total combo

    So, looking at the differences, the might damage ticks for both Smite and Retribution were equal, but Retribution costs 50% more power. The prec damage from cHaunt was lower than expected at 44 with cWither having more prec damage at 123. Total average damage for ScH was 144; for RcW, 223. That actually amounts to a little over 50% increase in damage, which closely matches the difference in power cost. Essentially, you are spending the extra power on prec damage, rather than might damage.

    How does the prec damage from combos compare to weapon attacks? If you separate out the prec portions of the combos, the durations are ~3 sec apiece. The initial might cast is ~0.8 sec (presumably that will increase with the proposed changes). In 3 sec, cHaunt did 44 damage, and cWither did 123. I could smoothly get off 3 each of Impact Arrow or Arrow Storm in that amount of time for a total of 84 damage. Interestingly, I could do more damage following Smite with either weapon attack than cHaunt. The damage from cWither is a little over 45% more damage than the weapon attacks, though. Of course, I can clip ScH and RcW after the first tick of prec damage and still get the last 2 ticks. That saves me about ~1.8 sec of animation time, making the clipped combo ~2 sec.

    Then, I looked at HB Solar Flame combo, which can be clipped at ~1 sec. Charged Blast avg damage = 17 and Solar Flame avg damage = 35, for a total average of 52. In a little over 3 sec, I could get off 2 Solar Flame combos clipped with Smite for a total average damage of 304 (keeping in mind, the 2nd Smite registered damage before the animation completes) and a power cost of 380. That's about 36% more damage than RcW and over twice the damage of ScH.

    If you do a rough DPS calculation, though, you find that ScH clipped comes out at ~72 DPS, RcW clipped at ~111 DPS, and Solar Flame clipped with Smite at ~101 DPS. Power costs per second (clipped ScH and RcW only take ~2 sec, where SF/Smite takes ~1.5 sec) are roughly 95, 143, and 152, respectively. So, DPS for a clipped weapon combo, in this case HB Solar Flame, is actually fairly close in DPS to RcW and only a little less power-efficient.

    I speced to Sorcery to try out another HB clip with Condemn. Condemn has a ~24% higher power cost than Smite at 235, but the average damage is about 30% higher at 130. It took me ~1.5 sec from initiation of Charged Blast to when I could clip the tail of Condemn. Total average damage was 182, for a DPS of ~121. That’s actually better than RcW, but again for a little worse power efficiency (RcW at ~143 power/sec and SF/Condemn at ~157 power/sec).

    I know this is a wall of text, but I hope it helps in understanding some of the nuts and bolts of a precision combo powerset, like Celestial.
    • Like x 7
  3. Remander Steadfast Player

  4. Sore Steadfast Player

    MIGHT
    X = Might
    Y = Damage
    BASE = Range of base damage values the attack can do

    Start with the forumula we know...
    Y = (1 + 0.0045*X) * BASE

    That's not in standard format, so let's expand...
    Y = BASE + BASE*0.0045*X

    Let's re-order...
    Y = (BASE*0.0045)X + (BASE)

    Now we're in standard format, let's identify what the slope and y-intercept is....
    M = Slope
    B = zero-intercept
    Y = MX + B <----standard format
    Y = (BASE*0.0045)X + (BASE)
    M = (BASE * 0.0045)
    B = (BASE)

    That means two interesting things. One, base damage and y-intercept are the same. BASE DAMAGE mathematically means this is the damage you will do at zero might (not counting damage mitigation and armor penetration). Of course that's a base range and not just a singular value. From our best guesses, that range is simply hand-picked by the devs.

    The more interesting thing is that the slope of might damage is not constant. The higher the base damage of an attack, the steeper the slope. As your might increases, your burst damage increases at a greater rate than your DoTs do. I wonder how many people that comes as a surprise to. But don't let that get the better of you. That means the DoT as a proportion of Might is worse than the Burst as a proportion of Might. However, the proportion of the DoT to the Burst will stay relative with each other. If the DoT started by doing 1/4th of the damage of the Burst, it will always do 1/4th the damage of the burst. If you do 1/4th the damage then you increase at 1/4th the rate.

    PRECISION
    We know DPS is a stat on your weapon.
    We know 10 precision adds 1 DPS to your weapon

    X = Weapon DPS + 0.1*PRECISION = EffDPS
    Y = Damage

    We didn't know the equation, so we needed to take take two samples to discover the slope. The slope is the change of Y divided by the change of X. That's the change of DAMAGE divided by the change of EffectiveDPS. So first we grab a bunch of samples at one EffeciveDPS, taking not of the MAX and MIN damage an attack could do. Then we repeat that test at another EffectiveDPS. We calculate the slope in both scenarios just in case the slope is different depending on the damage done. In the case of might, we know that is the case...so why not.

    MAX M = (MAX Y2 - MAX Y1)/(X2-X1)
    MAX M = (MAX DAMAGE2 - MAX DAMAGE1)/(EffDPS2 - EffDPS1)

    MIN M = (MIN Y2- MIN Y1)/(X2-X1)
    MIN M = (MIN DAMAGE2 - MIN DAMAGE1)/(EffDPS2 - EffDPS1)

    I don't have the numbers from our tests, but we did find the slope values to be different (no surprise).

    Once we had the slope, we solved for the B (Y-intercept or base damage) taking the standard formula and plugging in the slope from that last calculation (repeating for MIN/MAX), and the values from one of our samples for X and Y.

    Y = MX + B
    (MIN Y1) = (MIN Y2 - MIN Y1)/(X2 - X1)(X1) + B
    (MAX Y1) = (MAX Y2 - MAX Y1)/(X2 - X1)(X1) + B

    Then we solve for B
    MIN B = (MIN Y1) - (MIN Y2 - MIN Y1)/(X2 - X1)(X1)
    MAX B = (MAX Y1) - (MAX Y2 - MAX Y1)/(X2 - X1)(X1)

    In other words...
    MIN B = (MIN DAMAGE1) - (MIN DAMAGE2 - MIN DAMAGE1)/(EffDPS2 - EffDPS1)(EffDPS1)
    MAX B = (MAX DAMAGE1) - (MAX DAMAGE2 - MAX DAMAGE1)/(EffDPS2 - EffDPS1)(EffDPS1)

    What we discovered is that B (the y-intercept) was always zero or very close to it. We assume that's because of the effect of rounding on the numbers we initially collected. We concluded that B = 0. It kind of makes sense. If precision damage is meant to be measure in (damage-per-second) then at zero DPS, you get zero damage. Keep in mind for might damage, B was the base damage for the attack. This means precision attacks don't scale off of base damage. They do scale differently.

    The formula for precision damage is simply...
    Y = MX + 0, or
    Y = MX

    Y = DAMAGE
    X = EFFECTIVE DPS
    If B is base damage assigned to the attack and that is zero, how do weapon attacks differ? Well, that's where M comes in. The weapon attack must be assigned a value in some way to differentiate them. The weapon attack is assigned a value for M. Precision attacks are not assigned base damage, they are assigned multiplicative factors.

    M = a range of multiplicative factors assigned to the attack

    That means an attack like tap melee is assigned a range of values that serve as the slope of the equation, e.g. 0.336 - 0.504. We also learned from the devs that the range of values isn't exactly hand-picked. Spord spilled the beans when talking aout the damage ranges for the precision combos with Celestial. There is a middle value that they choose, e.g. 0.42 and the range is +/- 20% of that value. We've also discovered some exceptions to that variance where some attacks are +/- 10% of that variance (shield has a few of those). Further testing has verified these calculations.

    That is why it's incorrect to say precision scales additively and might scales multiplicatively. They both multiply. In the case of Might, the rate of increase is scaled off your might and the base damage of the attack. In the case of Precision, it's scaled off your effective DPS and a factor assigned to the attack.

    Now to what the OP might be trying to say. For Precision, more DPS means all your precision-based attacks scale proportionately. For powers, more Might means your high-base attacks scale at a better proportion than your low-base attacks. But even still, it does invalidate the equations initially presented and the graph.
    • Like x 10
  5. TrueOlympus New Player

    Ugh, Would people call me stupid if I ask for the general consensus of the thread to be put into 3 or less sentences of explanation
    • Like x 7
  6. Sore Steadfast Player

    1) The nature of precision scaling was misrepresented (no offense intended)
    2) You cannot analyze the scaling of precision/might in general
    3) You can only analyze the scaling of precision/might for specific rotations against specific counts of enemies
    • Like x 6
  7. Remander Steadfast Player

    Sore, I really appreciate you, one of the prominent number crunchers in the game, joining the conversation. I hadn't seen anyone lay out anything like this, so I thought I'd give it a go.

    With regard to might, you actually identified where I think a lot of the confusion was in the other thread. It's an error on my part, but not one of calculation specifically. As it happens, the formula I wrote in the OP was incorrect, but it was also not the actual formula used for the graph. I'm going to chalk that up to being a psych major, rather than a math major. ;) Here's what I wrote:

    adj dmg = (1.0045 * might) * base dmg

    I was trying to compare my formula to yours, because as I read through it, we seemed to be getting to the same conclusion. Turns out, I couldn't reproduce my own graph data with what I wrote (you can see for yourself). As it happens, the formula should have been written as:

    adj dmg = [1 + (0.0045 * might)] * base dmg

    which, when you multiply it out, is:

    adj dmg = base dmg + (0.0045 * might * base dmg)

    reorder:

    adj dmg = (base dmg * 0.0045 * might) + base dmg

    which is identical to yours:

    Y = (BASE*0.0045)X + (BASE)

    This is, in fact, the formula I used to generate the might data. You can check for yourself. I don't know where I got turned around, but I that explains the confusion. Thanks for uncovering that for me. FWIW, I called the formula multiplicative, because, unlike the precision formula I was using (we'll get to that in a moment), the base damage in the might formula was multiplied by the slope. Now, that may be a math terminology faux pas on my part, and if so, I apologize.

    I completely agree with you about the bases damages. You can tell from hitting a sparing target that there is variation, even without crits, so base must be a range of values. Great point about the effect of the base value on the might damage.

    Now, to the precision formula. I see what you're getting at, and it's actually something I started to think about, as I was collecting the information for the DPS comparisons listed in the second post. If you take off all your gear and weapon, you have no precision at all. Yet, if you punch the sparring target, you'll still do 1 damage. If you perform a Celestial combo, though, you'll get no precision damage. So, what's the base for a precision attack? If I'm reading you correctly, effective DPS sort of serves as it's own base, when it's present. Then, there is a multiplicative factor, which is the true slope, and is, unfortunately, not described anywhere. :( I was simply going by the 1 prec = 0.1 DPS that's given to us, standardizing the time to 1 sec, and operating under the assumption that each precision attack had a base damage value.

    So, if that's the case, the slope of the might function is dependent on the base damage (which was correctly stated) and the slope of the precision function is actually a nebulous value that varies with attack used. Therefore, the comparison of might and precision attacks is not nearly so cut and dry. You could have a precision attack and a might attack that end up with similar slopes or, conversely, two with very different slopes. It sounds like you have at least some of those precision slopes. Have you made any direct comparisons? I'd be interested to see them.

    Well, it was fun, while it lasted. I've been bored recently, and my mind goes to strange places, when it's bored. At least the second post has some hard, comparative data, rather than theorizing. Care to comment on that? Be gentle. :D
    • Like x 3
  8. Radium Devoted Player

    I, and many, MANY others on here have no idea what you just said.

    Heres a thumbs up for that.
    • Like x 14
  9. Radium Devoted Player

    You as well Remander, thumbs up the ying yang.
    • Like x 5
  10. shiny mackerel Committed Player

    Fist damage isn't based off DPS and has a static base damage (does 1-10 damage) assigned to it like weaponization damage. So no matter your DPS/precision, you'll always be doing 1-10 damage, and this is affected by modifiers and target defense. Because it's impossible to equip a weapon and have a 0 DPS stat, we can't 10000% confirm that 0 DPS means 0 damage. But we can test for damage at different DPS stats and plot the trend to see how weapon damage scales. Here's a completely scientific plot that shows this:

    [IMG]

    Basically, weapon damage scales linearly off DPS with a zero y-intercept. Zero y-intercept is okay because there are no weapons with 0 DPS. Each weapon move has its own slope that determines how damage scales with the DPS stat and we call this slope a bunch of different names like attack percent, damage multiplier, damage scalar etc etc. [edit] forgot you can check that 0 DPS = 0 weapon damage with celestial/light combos, as you mentioned. That pretty much confirms it.

    Anyways, because might and weapon damage are governed by two entirely different stats, you could never really compare the two - might vs. DPS/prec. How they "scale" is determined by the devs who figure out how much prec and how much might to put on armor, and how much DPS to give to weapons. And then how much base damage is assigned to might superpowers and how much base damage is assigned to weapon/combo superpowers. You can sort of guess why the white damage power sets have been really strong by the recent dev discussions, and by what's happened in the past with weapons (spin chop?). They mostly balance damage off unclipped animation times. When a combo power has really short clipped animation time, everything is thrown out of whack. They've got the tricky job of making combo powers worth using without making them too strong clipped, hardly worth using clipped, and so on.
    • Like x 5
  11. Sore Steadfast Player

    • Like x 3
  12. Sore Steadfast Player

    How they scale in a favorable ratio perspective is based mostly off your rotation, e.g. Your stats, dev rates of handing out stats, base damages, attack percentage, how many attacks are precision vs. might, how many targets they hit, how they split, and how many targets you're actually hitting.

    I think precision-based powers shine for two reasons. One is definitely the effect of clipping in how they balance precision damage. The other is how they pretty much give weapon finisher damage as the combo rather than needing to do a bunch of taps before getting to finisher-level damage.
    • Like x 4
  13. Remander Steadfast Player

    Thanks for joining the conversation, Shiny. While I'm a bit embarrassed about getting the whole precision scaling wrong, I still think this is an important topic to discuss. Some good info has been presented here that is helpful for understanding what it is we do when DPSing. It goes to show how much is misunderstood.
    • Like x 2
  14. 478874 Dedicated Player

    Yeah, this is a great topic, thanks for all the insights all of you.
    • Like x 1
  15. CrappyHealz New Player

    All those numbers are nice but when it all comes down to it precision powers are better than might cause of the upped power cost. Most powers are actually pretty close damage wise it just comes down to having enough power to do the damage.

    If they really wanted to bring balance they could just lower the power cost some then make some tweaks from there.

    I hate graphs and math!!!! Put the charts away and play the game lol. In game and paper are 2 different things.
    • Like x 3
  16. Remander Steadfast Player

    Completely agree about power. Stated that in the OP. It all comes down to the fact that might damage costs power, while precision damage doesn't. Precision-based powersets are, therefore, inherently more efficient. That's why might-based can't ignore precision and use of potent weapon combos.

    On the second point, to be fair, this game is totally based on math. Doesn't mean you have to like it, though. ;)
    • Like x 1
  17. Humane Committed Player

    How does this translate into the charge attacks being eliminated?
    At least until the next DLC that is. Doesn't this change things drastically until the weapon combos are implemented?
    • Like x 2
  18. Remander Steadfast Player

    Bit more about precision and power. Looking at my second post, you can see that precision damage from combos technically does have a cost. This is evidenced by ScH and RcW having the same base might damage, but the latter having a 50% higher total damage and power cost. It's still more efficient, though, because of the risk/reward design. You are paying on the front end for damage that isn't guaranteed. If you miss both of the above combos, you get the same damage, but spend more power with Retribution. If the damage were guaranteed, the power costs would, naturally, have to be set higher.
    • Like x 1
  19. Deathmike Loyal Player

    So you're saying that a power that does X base damage in a single tick will do more damage than a power that does N ticks of (X/N) base damage?
    That doesn't sound right.:eek:
    Let's plug those values in the formula to compute final damage of the two powers and see what we get:
    FinalDamagePower1 = X*0.0045*Might+X
    FinalDamagePower2 = ((X/N)*0.0045*Might+(X/N))*N = ((X*N)/N)*0.0045*Might+((X*N)/N) = X*0.0045*Might+X = FinalDamagePower1

    The two powers do the exact same damage (instead of the first power doing more damage than the second).
    Maybe you were trying to say something else and I misinterpreted.

    Deathmike out.
    • Like x 1
  20. Remander Steadfast Player

    Honestly, from playing around on test, I can tell you these ranged attacks are much faster and clippable for full damage earlier than the old charged attacks. Shiny's numbers show no drop in DPS for these attacks. IMO, they will be even easier to interweave into your rotations after this change.
    • Like x 1