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Miscellaneous Maths/Testing II

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  • LeviticusLeviticus Member Posts: 159 ✭✭✭ - Distinguished
    Attached are my numbers for limb damage. With/Without means with level 3 knuckles, without level 3 knuckles. Still trying to find someone with around 4500 health so I can see the breakpoint in health ranges. Now just to figure out how much to set kick and how much to set punch for svo limbcounter. Any help would be awesome
  • SenaSena Member Posts: 3,757 @@ - Legendary Achaean
    I'm still not sure. Someone who knows more about limb damage would be more helpful.


    In other news, testing the effects of armour on denizen damage isn't as simple as I expected. I figured that if a denizen dealt X damage, armour would reduce the damage by Y% of X, with Y being equal to some percentage of the armour stat. Instead, it seems more likely that the denizen deals X±Y, and armour only reduces X, except that doesn't quite fit perfectly.

    For example, I've been testing with the King Stag. Damage ranges from 459 to 741 (600±23.5% fits perfectly, but that could be a coincidence) with no armour/resistance. With roughly 21% armour (it's not possible to see actual stats any more, as far as I know, so 21% isn't exact), damage ranges from 394 to 670. It's possible that those aren't the actual limits (and I'll continue testing to be sure), but the sample sizes are high enough that it's unlikely.

    If it was reducing the total damage, then I'm not sure how to account for the lower end being reduced by so much more than the higher end. On the other hand, if it is something like 600±23.5% or 459+(0 to 282) with armour only applying to the base (the 600 or 459), the higher end is being reduced slightly more than the lower end.

    It could be explained by the damage being 459+(0 to 282) with armour applying to both the base and random portions at different rates (~14% reduction to the base and ~2% reduction to the random portion). But that seems unlikely.
  • ErnamErnam Member Posts: 2,416 ✭✭✭✭✭ - Grand Achaean
    edited January 2015

    I'm extremely knowledgeable regarding limb damage, its equations, and solving for them.

    If you want to team up and solve for some of the equations, PM me or msg me in game.  If you bring the data, I'll bring the maff skills, and we can get this done without me paying 900cr to class hop twice.


    One thing I would like to FIRMLY dispel is the concept of "break points" (aka: magic numbers).  There are no fixed "break points", until you plug in all applicable variables (meaning that the "break points" are different for every person, vs every person, per weapon, per attack type).  Some systems (like SVO) use "breakpoints", or in some cases, linear (incorrect) equations that solve for break points based on max health.  These are thumb-rules that do end up being accurate within a certain range (usually centered around 4000-5000 health) but can and often do result in being "one hit off", which is exactly one too many in either direction IMO.

    For BMs, you can use Manda (which is 100% accurate).  I'm planning on doing monk (next time I have a trans Tekura character) and am currently in the process of doing the new knight equations.


    "Our lives are not our own. We are bound to others, past and present. And by each crime and every kindness, we birth our future."


          Manda  |  Godzilla  |  SLC
      1. AustereAustere TennesseeMember Posts: 1,958 @@ - Legendary Achaean
        Sena said:
        Does anyone have a list of what the armour stats were when you could still see the unreduced values (like fullplate was 90/90 instead of 51/51, for example)?
        @Sena:
        I thought I had scale too, but it looks like I missed it, sorry:

        a suit of polished field plate armour  Cutting%   43;  Blunt%   46
        a suit of steel chain mail                    Cutting%   60;  Blunt%   50
        a suit of ring mail                               Cutting%   43;  Blunt%   30
        Sena
      2. TaelTael Member Posts: 1,197 @ - Epic Achaean
        edited January 2015
        Ernam said:
        There are no fixed "break points"
        It's been a while since I was magi, but don't magi use fixed break points for staffstrike (one might even say, magical fixed break points)? I remember it as always being 4 hits, for every person I fought, though I might be misremembering.
      3. JosoulJosoul Member Posts: 131 ✭✭✭ - Distinguished
        Austere said:
        Sena said:
        Does anyone have a list of what the armour stats were when you could still see the unreduced values (like fullplate was 90/90 instead of 51/51, for example)?
        @Sena:
        I thought I had scale too, but it looks like I missed it, sorry:

        a suit of polished field plate armour  Cutting%   43;  Blunt%   46
        a suit of steel chain mail                    Cutting%   60;  Blunt%   50
        a suit of ring mail                               Cutting%   43;  Blunt%   30
        Adding the rest: (cutting/blunt %)
        leather: 25/20
        splint: 56/33
        scale: 50/45

        and shields just because:
        buckler: 5/5
        banded: 15/15
        kite: 13/24
        cavalry: 8/8
        tower: 20/34
        SenaAustere
      4. ErnamErnam Member Posts: 2,416 ✭✭✭✭✭ - Grand Achaean
        Tael said:
        Ernam said:
        There are no fixed "break points"
        It's been a while since I was magi, but don't magi use fixed break points for staffstrike (one might even say, magical fixed break points)? I remember it as always being 4 hits, for every person I fought, though I might be misremembering.

        I'm fairly certain that that is not true, however I was specifically referring to Tekura in that post.

        "Our lives are not our own. We are bound to others, past and present. And by each crime and every kindness, we birth our future."


              Manda  |  Godzilla  |  SLC
            Tael
          1. NimNim Member Posts: 2,015 @@ - Legendary Achaean
            I believe what @Ernam means is that the concept of X HP requiring Y hits is a result of some more complicated formula, rather than how the game mechanic itself works.

            Magi staffstrikes probably just do heavily proportionate damage, possibly even outright doing 25% damage or something like that (probably a bit more, since Achaea seems to have issues with rounding things). I think I remember rumors that seemingly simple limb breaks that usually require four attacks sometimes required a fifth for outliers, as well.

            From what little I know of limb damage, it definitely looked like it worked similar to ordinary damage, with attacks having a proportionate and a fixed damage value. That, or limb HP was calculated in some way based off of actual HP (or perhaps just level and constitution).

            Unfortunately, I never gathered nearly enough data to get close to figuring out the exact values. Even with limb probing, there's not a lot of granularity to figure things out without just testing nearly every HP value you can.
          2. TharvisTharvis The Land of Beer and Chocolate!Member Posts: 3,107 @@ - Legendary Achaean
            staffstrike earth/fire/water seems to do 22.25% limb damage with staffstrike air doing 11.125% limb damage (I could be a little bit off here, don't shoot me)
            Aurora says, "Tharvis, why are you always breaking things?!"
            Artemis says, "You are so high maintenance, Tharvis, gosh."
            Tecton says, "It's still your fault, Tharvis."

          3. ErnamErnam Member Posts: 2,416 ✭✭✭✭✭ - Grand Achaean

            @Nim it's a bit more complex than that (limb damage equations are rarely linear) - but yes that's the basic idea.  My equations do not focus on number of hits (although that's easy to derive), they track the actual amount of limb damage (in hitpoints) each limb has taken.  There are more applications for this than simply dividing that out for number of hits required to break - and for blademasters and monks specifically, it allows you to reliably switch between different attack types and stances without messing up a sloppy "hit count", without losing a single bit of accuracy.

            "Our lives are not our own. We are bound to others, past and present. And by each crime and every kindness, we birth our future."


                  Manda  |  Godzilla  |  SLC
                Nim
              1. EldEld Member Posts: 3,946 @@ - Legendary Achaean
                Sena said:
                I'm still not sure. Someone who knows more about limb damage would be more helpful.


                In other news, testing the effects of armour on denizen damage isn't as simple as I expected. I figured that if a denizen dealt X damage, armour would reduce the damage by Y% of X, with Y being equal to some percentage of the armour stat. Instead, it seems more likely that the denizen deals X±Y, and armour only reduces X, except that doesn't quite fit perfectly.

                For example, I've been testing with the King Stag. Damage ranges from 459 to 741 (600±23.5% fits perfectly, but that could be a coincidence) with no armour/resistance. With roughly 21% armour (it's not possible to see actual stats any more, as far as I know, so 21% isn't exact), damage ranges from 394 to 670. It's possible that those aren't the actual limits (and I'll continue testing to be sure), but the sample sizes are high enough that it's unlikely.

                If it was reducing the total damage, then I'm not sure how to account for the lower end being reduced by so much more than the higher end. On the other hand, if it is something like 600±23.5% or 459+(0 to 282) with armour only applying to the base (the 600 or 459), the higher end is being reduced slightly more than the lower end.

                It could be explained by the damage being 459+(0 to 282) with armour applying to both the base and random portions at different rates (~14% reduction to the base and ~2% reduction to the random portion). But that seems unlikely.
                Well, if those are the true limits, then there has to be some scaling to the variable portion, since the ranges with and without armour are different (282 without and 275 with). The only way I see to get the armour only applying to the base, with the variable portion unaffected, would be if the true range of damage values with armour were 6 points larger, and you were missing a few outliers. If, for example, the damage without armour ranges from 459 to 741, and with armour ranges from 391 to 673 (so 3 points extra on either end of the armoured range), you could have 600*(1-.11333) +/- 141, but a reduction of 11.3333% bears no particular relation to the nominal 21%.

                If you have all of the individual damage values stored (rather than just the max and min), it might be interesting to histogram them and see if the distribution looks pretty uniform or peaked around some central value, and maybe try fitting them with a simple Gaussian. Or even just skip the histograms and compare the first few moments of the distributions (mean, variance, skewness) with and without armour.
              2. EldEld Member Posts: 3,946 @@ - Legendary Achaean
                Eld said:
                Sena said:
                I'm still not sure. Someone who knows more about limb damage would be more helpful.


                In other news, testing the effects of armour on denizen damage isn't as simple as I expected. I figured that if a denizen dealt X damage, armour would reduce the damage by Y% of X, with Y being equal to some percentage of the armour stat. Instead, it seems more likely that the denizen deals X±Y, and armour only reduces X, except that doesn't quite fit perfectly.

                For example, I've been testing with the King Stag. Damage ranges from 459 to 741 (600±23.5% fits perfectly, but that could be a coincidence) with no armour/resistance. With roughly 21% armour (it's not possible to see actual stats any more, as far as I know, so 21% isn't exact), damage ranges from 394 to 670. It's possible that those aren't the actual limits (and I'll continue testing to be sure), but the sample sizes are high enough that it's unlikely.

                If it was reducing the total damage, then I'm not sure how to account for the lower end being reduced by so much more than the higher end. On the other hand, if it is something like 600±23.5% or 459+(0 to 282) with armour only applying to the base (the 600 or 459), the higher end is being reduced slightly more than the lower end.

                It could be explained by the damage being 459+(0 to 282) with armour applying to both the base and random portions at different rates (~14% reduction to the base and ~2% reduction to the random portion). But that seems unlikely.
                Well, if those are the true limits, then there has to be some scaling to the variable portion, since the ranges with and without armour are different (282 without and 275 with). The only way I see to get the armour only applying to the base, with the variable portion unaffected, would be if the true range of damage values with armour were 6 points larger, and you were missing a few outliers. If, for example, the damage without armour ranges from 459 to 741, and with armour ranges from 391 to 673 (so 3 points extra on either end of the armoured range), you could have 600*(1-.11333) +/- 141, but a reduction of 11.3333% bears no particular relation to the nominal 21%.

                If you have all of the individual damage values stored (rather than just the max and min), it might be interesting to histogram them and see if the distribution looks pretty uniform or peaked around some central value, and maybe try fitting them with a simple Gaussian. Or even just skip the histograms and compare the first few moments of the distributions (mean, variance, skewness) with and without armour.
                Also, the King Stag has multiple attacks: I assume you're just testing with one? From a little quick collection, looking only at his goring attack (which I'm guessing is cutting damage, but not sure), and in dragon (so level 2 cutting/blunt resistance, whatever that means), in 43 attacks, I got an average of 462 with a standard deviation of 53. The distribution looks pretty consistent with a Gaussian, but it's too small a sample to conclude much along those lines from.
              3. SenaSena Member Posts: 3,757 @@ - Legendary Achaean
                Both attacks are blunt, and seem to do the same damage. I was tracking them separately at first, and after 500+ attacks they had the same min/max and nearly the same average, with and without armour.
              4. SenaSena Member Posts: 3,757 @@ - Legendary Achaean
                As for the distribution, 735 unarmoured attacks:


                1042 attacks with 38 armour (21% in the current display, ringmail+cavalry):


                Seems uniform enough to me.
                Eld
              5. EldEld Member Posts: 3,946 @@ - Legendary Achaean
                Yup, sure does. And it would indeed be surprising if those ranges weren't correct. In that case, I don't see any way for the variable part to be unaffected, or for both to be reduced by the same percentage. Out of curiosity, though, what are the percentages for the mail and the shield individually?
              6. SenaSena Member Posts: 3,757 @@ - Legendary Achaean
                Ringmail is 24/17 cutting/blunt (actual stats are 43/30), cavalry is 4/4 (8/8).

                Also, it seems I didn't have the full unarmoured range. After another 565 attacks (for a total of 1300), I have 7 instances of 745 damage. That doesn't help make anything clearer.

                Rather than just get another thousand or so attacks to be extra sure I have the complete ranges (or try and get every possible damage value, if there's a finite number of possibilities like with sipping, though I already have 120 different values for armoured compared to sipping's 40), I've been working on getting a runewarden alt up to a high enough level to survive the King Stag for testing, so I can try fullplate+tower.
              7. SenaSena Member Posts: 3,757 @@ - Legendary Achaean
                I was hoping that seeing the effects of high armour would make it easier, but it doesn't. It does seem to indicate that armour is most likely applying to both the base and variable portion at different rates, at least.

                The average and the max seem to scale pretty linearly with armour. The min is a lot higher than expected at 124 armour though, and therefore the range is a lot lower. It could be that for the base portion I've hit a cap on armour reduction, but haven't hit a cap on the variable portion. I guess I'll have to test more armour values.

                A summary of my data so far:
                Unarmoured: avg 593.16, min 459, max 745, range 286, attacks 1300
                38 armour (ringmail+cavalry): avg 524.76, min 394, max 670, range 276, attacks 1042
                124 armour (fullplate+tower): avg 393.96, min 316, max 484, range 168, attacks 716
              8. EldEld Member Posts: 3,946 @@ - Legendary Achaean
                I've been collecting some numbers with just resistances, which I expected to be a bit more straightforward than armour, in case they shed any light. The samples are pretty small, unfortunately (basically just sitting there until someone comes along to do the quest). I wasn't sure how you determined the damage type, so I thought I'd check with toughness to see if anything changed.


                Horkval, no toughness:
                  Attack 1 (gored): avg: 537.18, min: 417, max: 677, range: 260, attacks: 202
                  Attack 2 (trampled): avg: 529.81, min: 417, max: 677, range: 260, attacks: 184
                  Combined: avg: 533.67, min: 417, max: 677, range: 260, attacks: 386
                Horkval + toughness:
                  Attack 1: avg: 524.92, min: 380, max: 677, range: 297, attacks: 244
                  Attack 2: avg: 509.49, min: 380, max: 674, range: 294, attacks: 207
                  Combined: avg: 517.84, min: 380, max: 677, range: 297, attacks: 451
                It's interesting that I saw 380s in both of those when I hadn't seen them in the earlier ones at all, but the average doesn't look to be reduced near as much as would be expected for toughness, so I'm assuming you're right that they're both blunt.
                Both combined (assuming blunt damage):
                  Avg: 525.14, min: 380, max: 677, range: 297, attacks: 837

                That's pretty close to consistent with the damage being 600 +/- (0-150), with hork resistance reducing the 600 by 12-12.5% and leaving the variable part unchanged, but there's plenty of room for imagining patterns like that.
              9. AvtoAvto Member Posts: 101 ✭✭✭ - Distinguished
                Unarmoured: avg 593.16  - 100%
                21% armour (ringmail+cavalry): avg 524.76  - 88.5%
                55% armour (fullplate+tower): avg 393.96  - 66.5%

                If we go with  ring of magus description (Example, a magical-type attack is delivering 1000 damage: 500 of it would go through unaffected, and 500 would be reduced a certain percentage by the power of the Ring.) those tests are close to % marks.
              10. SenaSena Member Posts: 3,757 @@ - Legendary Achaean
                The Ring of the Magus description doesn't literally mean that half the damage is reduced and half is unreduced, that's just a simplified example. It's more complicated than that.

                With weaponry attacks for example, there are two parts to the damage, a health-scaling portion and a static portion. Only the static portion is reduced by armour, while the health-scaling portion is unreduced, which means that the more health health you have, the less effective armour is against weaponry attacks. In other attacks, the health-scaling portion might be reduced while the static portion is unreduced, or a certain portion of both parts might be reduced, or the entire attack might be unreducible (so it ignores armour entirely but not resistances), etc.
              11. SenaSena Member Posts: 3,757 @@ - Legendary Achaean
                Demon fortify drains floor(CurrentHealth/20) of your health (boosted by Scimitar of Yen-Sorte, so Mhaldorians take 7% more damage from it than rogues) and heals your baalzadeen for floor(CurrentHealth/20)*5.
              12. WessuxWessux ChattanoogaMember Posts: 510 ✭✭✭✭✭ - Grand Achaean
                I miss city bonuses. 
                Invest in a 9mm retirement plan.
              13. SenaSena Member Posts: 3,757 @@ - Legendary Achaean
                Do any smiths have a full listing of what they crafted and after which items they gained a rank? I'm curious to see if I can figure out exactly how forging experience works.
              14. AradorArador Member Posts: 1,693 @@ - Legendary Achaean
                edited January 2015
                Hmm, not sure where this should go. I bugged it a while back but have not heard anything. The last Bugfix Announce claimed the SETALIAS part was fixed at least, but does not seem to be. @Makarios @Tecton ;

                SETALIAS

                Here, the setalias command is still caught by retardation

                5418h, 4483m, 23630e, 17570w cexkdb setalias test1 kick carbine
                You move sluggishly into action.
                5418h, 4483m, 23630e, 17570w cexkdb
                Alias "test1" will now execute: "kick carbine"
                5418h, 4473m, 23630e, 17570w cexkdb

                QUEUE

                Here, things get weird. The QUEUE ADD command hits retardation, but if you have balance by the time it completes, the attack will go through straight away. If you do not have balance at that moment, then when it fires on balance you hit retardation again.

                5418h, 4473m, 23630e, 17570w cexkdb queue add eqbal test1
                You move sluggishly into action.
                5418h, 4473m, 23630e, 17570w cexkdb
                [System]: Added TEST1 to your eqbal queue.
                [System]: Running queued eqbal command: TEST1
                You cease holding your breath and exhale loudly.
                You leap into the air and launch a flying kick at Carbine.
                You connect!
                {Note no sluggishly into action when the queue fires}
                5418h, 4473m, 23605e, 17570w cekdb
                The Anthem shifts, protecting from electricity damage.
                5418h, 4473m, 23625e, 17570w cekdb queue add eqbal test1
                You move sluggishly into action.
                5418h, 4483m, 23625e, 17570w cekdb
                [System]: Added TEST1 to your eqbal queue.
                5418h, 4483m, 23625e, 17570w cekdb
                You have recovered balance on all limbs.
                [System]: Running queued eqbal command: TEST1
                You move sluggishly into action.
                5418h, 4483m, 23630e, 17570w cexkdb
                You leap into the air and launch a flying kick at Carbine.
                You miss.
                {But here both the QUEUE ADD and the firing of the QUEUE hit retardation}
                5418h, 4483m, 23605e, 17570w cekdb queue add eqbal test1

                SETALIAS is obviously still bugged, but I have no idea what is up with QUEUE. It should hit retardation when it fires the action, not before or both, right?

              15. ErnamErnam Member Posts: 2,416 ✭✭✭✭✭ - Grand Achaean
                Arador said:

                Here, things get weird. The QUEUE ADD command hits retardation, but if you have balance by the time it completes, the attack will go through straight away. If you do not have balance at that moment, then when it fires on balance you hit retardation again.
                [   ]
                SETALIAS is obviously still bugged, but I have no idea what is up with QUEUE. It should hit retardation when it fires the action, not before or both, right?

                I believe this is working as intended.  Queue doesn't actually enter commands into a queue if you have the specified balance.  It shows you a message but all it really does is execute the command as if you didn't use the QUEUE command.  That's why it gets delayed by retardation.  However if you're off balance, it does use the queue system (which bypasses retardation as a system command), and it's handled correctly by performing the command when you regain balance, at which point is is delayed appropriately.

                The reason the log looks the way it looks is because if you attempt to queue things at any time when you already have the balance, it doesn't appear to actually enter a Queue (although the message says that it does).  Things are only stored in a queue if you don't have balance specified.  When you used test1 (kick) the second time, you were off balance, so did actually enter a queue

                "Our lives are not our own. We are bound to others, past and present. And by each crime and every kindness, we birth our future."


                      Manda  |  Godzilla  |  SLC
                  1. AradorArador Member Posts: 1,693 @@ - Legendary Achaean
                    Except it hit retardation twice when I used it off balance. Please read that second kick again. I asked it to add the alias to the queue, it moved sluggishly into action, then it added the alias to the queue, then I regained balance, then it fired the alias which hit retardation again. 

                    I understand what you mean by the first, though I do not think that is consistent with how the queue appears to work. You are adding to the queue, it just fires the action immediately. While the way it handles it in the first kick does have you coming out and kicking in the same amount of time, it is a very awkward way to handle it. 

                  2. ErnamErnam Member Posts: 2,416 ✭✭✭✭✭ - Grand Achaean
                    edited January 2015
                    Arador said:
                    Except it hit retardation twice when I used it off balance. Please read that second kick again. I asked it to add the alias to the queue, it moved sluggishly into action, then it added the alias to the queue, then I regained balance, then it fired the alias which hit retardation again. 

                    I understand what you mean by the first, though I do not think that is consistent with how the queue appears to work. You are adding to the queue, it just fires the action immediately. While the way it handles it in the first kick does have you coming out and kicking in the same amount of time, it is a very awkward way to handle it. 

                    I see what you're saying, and it does appear to be hitting retardation twice (I actually didn't see the delay between the alias and the queue command in that log, I thought the queue command was immediate).  That's definitely not working as intended (99.9% sure of that at least).  Would paste-bin that and bug it with an explanation, or a link to your post here too (here).

                    edit: 
                    If that's just for demonstration, I get that, but obviously that's not very good use of queueing.  Personally, I don't think queueing should be used in retardation, at all, ever, so it's really a non-issue to me.  In all cases that I'm aware of, commands should be sent 1 second early, and one at a time, neither of which are accomplished using queueing.

                    It would be interesting if BATCH mode were extend to affect queues though, but there'd be issues in determining which queue to run first if you have items in multiple queues (although again, that'd probably be so rare that it wouldn't matter).

                    @Makarios, can we make BATCH mode make queued commands fire one at a time (in order), when set to OFF (batch mode sends curing commands all at once, non-batch mode sends them one at a time).  Could also just have queued commands automatically execute only one command at a time in queues, instead of firing them all at once (deleting everything but the last command).  Personally I don't really think we need to hard-code cookie-cutter easy-mode for retardation, but this method would still be 1-second slower on all commands than manually sending things 1 second early, so it's easiness in exchange for much slower actions.

                    "Our lives are not our own. We are bound to others, past and present. And by each crime and every kindness, we birth our future."


                          Manda  |  Godzilla  |  SLC
                      1. AradorArador Member Posts: 1,693 @@ - Legendary Achaean
                        Using a queue in retardation is obviously not the most efficient thing. You can hit faster of you anticipate balance. But that does not mean you would not want the system to work in a predictable and consistent manner.

                         It makes scripting more consistent and is a safe way to start so that combat jitters and inexperience does not have you mashing at keys because every second feels like a year to you. 

                        It lowers the barrier of entry for retardation fighting without lowering the barrier of possible efficiency for good fighters. 

                      2. ErnamErnam Member Posts: 2,416 ✭✭✭✭✭ - Grand Achaean

                        Well I think it's clearly a bug, so I'd just bug it and call it a day.  I've probably bugged 100 things with curing/queuing, and they've all been fixed.

                        "Our lives are not our own. We are bound to others, past and present. And by each crime and every kindness, we birth our future."


                              Manda  |  Godzilla  |  SLC
                          1. SenaSena Member Posts: 3,757 @@ - Legendary Achaean
                            When using queuing and/or serverside aliases with multiple commands, it can make balance times appear significantly shorter (possibly up to half a second if your alias is doing a lot).

                            Presumably because it delays output on your end of the commands being sent but not (or not as much) the serverside balance calculations.
                            Austere
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