Item Search
     
BG-Wiki Search
+ Reply to Thread
Page 2 of 2 FirstFirst 1 2
Results 21 to 28 of 28
  1. #21
    BG Content
    Join Date
    Jul 2007
    Posts
    21,103
    BG Level
    10
    FFXI Server
    Lakshmi
    Blog Entries
    1

    Yes, another important thing to discover is how approaching the cRatio cap affects pDIF value. Does it shrink the distribution but keep it symmetric? Does it Ceiling it to something and then apply some second filter to create extremes (look at the upper end of Mote's data)?

    I have access to a character again, but he's starting naked and I'm still on PS2 (no parsing). I think it's unlikely that I can contribute to this discussion without access to a parser, but I might be able to check min/maxs for my hits as I level BST. I tend to basically farm EP/DC for levels and levels and levels . . . For instance, I just went from 30 to 39 in Sauromugue Champaign without getting a Herder Subligar. On Byrth I farmed Gigantobugards from either 54-56 or 55-57. I don't know, I'm just trying to think of some way I could contribute to this. xD

  2. #22
    Sea Torques
    Join Date
    Dec 2007
    Posts
    582
    BG Level
    5

    Note that due to flooring, the distribution of actual damage (not pDIF), if uniform, will be tapered at the ends, depending on whether pDIF*(base damage) is an integer or not, so you would expect the minimum and maximum to have a lower observed frequency relative to the rest of the data.

    Flooring alone doesn't explain why there are three damage values at either extreme with low observed frequencies. As suggested, there could be another random factor. If this is a uniform random variable and the "base" pDIF is also uniform random, the sum of two uniform random variables (either discrete or continuous) can be trapezoid-like, which can describe the observed pattern of frequency. If there were no rounding, it would be easier to see if this is true or not.

  3. #23
    Chram
    Join Date
    Sep 2007
    Posts
    2,526
    BG Level
    7
    FFXI Server
    Fenrir

    From Masamune's data:

    Relic Bhuj
    Predicted internal min/max: 17/24

    Data:
    Spoiler: show
    Code:
      Melee
           16:    6
           17:   27
    +      18:   40
           19:   37
     ^     20:   21
           21:   29
           22:   37
           23:   34
           24:   13


    Result: 17 matches data. Data indicates internal max is 23, not predicted 24.


    Jupiter Staff
    Predicted internal min/max: 88/122

    Spoiler: show
    Code:
      Melee
           85:    7
           86:    4
           87:   11
           88:   14
           89:   15
           90:   13
           91:   21
           92:   16
           93:   20
           94:   18
           95:   17
    +      96:   29
           97:   11
           98:   18
           99:   17
          100:   22
          101:   22
          102:   17
          103:   15
          104:   21
          105:   23
     ^    106:   20
          107:   16
          108:   20
          109:   21
          110:   13
          111:   17
          112:   18
          113:   20
          114:   21
          115:   22
          116:   27
          117:   27
          118:   20
          119:   21
          120:   18
          121:   21
          122:   17
          123:    6
          124:    5
          125:    1
          126:    1


    Difficult to judge whether data shows 87 or 88 as internal min, so may or may not match. Data shows 122 is max, which matches prediction.


    Orc Piercer
    Predicted intrinsic min/max: 116/162

    Spoiler: show
    Code:
      Melee
          114:    2
          115:    4
          116:    2
          117:    5
          118:    2
          120:    1
          121:    5
          122:    1
          123:    3
          124:    4
          125:    2
          126:    4
          127:    7
          128:    2
          129:    1
          130:    4
          131:    5
          132:    5
          133:    6
          134:    3
          135:    3
          136:    6
          137:    5
          138:    6
          139:    4
          140:    4
     ^    141:    8
          142:    4
          143:    5
          144:    5
          145:    4
          146:    3
          147:    4
          148:    4
          149:    6
          150:    3
          151:    3
    +     152:    9
          153:    2
          154:    2
          155:    5
          156:    8
          157:    4
          158:    6
          159:    3
          160:    2
          161:    1
          162:    4
          163:    2
          164:    2
          166:    1
          168:    1


    Really impossible to judge, with the data so spread out and not enough to distinguish between internal and secondary values. I would be inclined to guess 117 and 162 as the limits, which is off by one and a match, respectively.


    Iron Ram Lance
    Predicted intrinsic min/max: 163/226

    Spoiler: show
    Code:
      Melee
          158:    1
          160:    3
          161:    3
          162:    2
          163:    3
          164:    3
          165:    9
          166:    4
          167:    2
          168:    5
          169:    9
          170:    7
    +     171:   14
          172:    8
          173:   10
          174:   10
          175:    5
          176:    5
          177:    6
          178:    7
          179:    6
          180:    6
          181:    6
          182:    7
          183:    4
          184:    8
          185:    4
          186:    5
          187:    7
          188:    7
          189:    6
          190:    6
          191:    6
          192:    4
          193:    6
          194:    4
          195:    2
          196:    7
     ^    197:    5
          198:   10
          199:    6
          200:    9
          201:    6
          202:    8
          203:    5
          204:    5
          205:    5
          206:    5
          207:    9
          208:    6
          209:   10
          210:    7
          211:    8
          212:    7
          213:   10
          214:    6
          215:    6
          216:    5
          217:    4
          218:    4
          219:    7
          220:    9
          221:    6
          222:    7
          223:    6
          224:    8
          225:    2
          226:    7
          227:    7
          228:    3
          229:    2
          230:    2
          231:    1
          232:    2
          233:    2


    Again insufficient data to be sure of distinctions. I would guess 165 and 227, which is a point or two off from predictions.


    Erlking's Kheten
    Predicted intrinsic min/max: 209/290

    Spoiler: show
    Code:
      Melee
          203:    3
          204:    3
          205:    1
          206:    4
          207:    7
          208:    6
          209:    7
          210:    2
          211:    5
          212:    3
          213:    8
          214:    6
          215:   11
          216:    7
          217:    2
          218:    5
          219:    5
          220:    9
          221:    5
          222:    8
          223:    1
          224:    7
          225:    6
          226:    2
          227:    5
          228:    7
          229:    7
          230:    5
          231:   12
          232:    2
          233:    4
          234:    8
          235:    8
          236:    9
          237:    6
          238:    9
          239:    7
          240:    6
          241:    5
          242:    5
          243:    7
          244:    4
          245:   10
          246:   10
          247:    9
          248:    4
          249:    5
          250:    4
          251:   11
          252:    7
     ^    253:    4
          254:    5
          255:    7
          256:   10
          257:    6
          258:    3
          259:    5
          260:    8
          261:    7
          262:    8
          263:   11
          264:   11
          265:   12
          266:    8
          267:    8
          268:   11
          269:    9
          270:    4
          271:    6
          272:    5
          273:    7
          274:    9
          275:    3
          276:    7
          277:    6
          278:    6
          279:    7
          280:    8
          281:    9
          282:    6
          283:    7
          284:    9
    +     285:   13
          286:    3
          287:    8
          288:    7
          289:    9
          290:    9
          291:    2
          292:    5
          293:    3
          294:    5
          295:    2
          296:    2
          297:    3
          298:    2
          299:    1


    Same as the others two that have such a large damage spread. Guess would be 207/290, which is off by two for min and matches prediction for max.



    Even with rather insufficient data, it's interesting to see that the tail effects occur on every sample, and that the length of the tails is proportional to the range of damage values.
    Code:
    Weapon Rank    Range (internal)    Min Tail   Max Tail   % Range (min)   % Range (max)
    0              7                   1          1          14%             14%
    3              36                  2          4          6%              11%
    5              46                  3          4          7%              9%
    7              63                  6          6          10%             10%
    10             84                  4          9          5%              10%
    Looks like a tendancy to reach ~10% of the internal range.

    So at this point I'm fairly certain that there are two separate formulas being applied together here. It's still possible it's some sort of bell curve formula (it would have to be mostly flat with sharp dropoffs at either end), but that seems overly complicated to implement in fixed-point math.

  4. #24

    Quote Originally Posted by Masamune View Post
    I'm not sure to understand why you interested in frequency, i thought only max and min observable dmg are relevant :s

    Sended you my parses + excel file @ your email Mote.
    Precisely, these tests show that max and min are not enough. They give a correct idea of what you are punching for on average for non- critical hits only, but for crit it's not correct, if anything the average is about

    ( (min+max)/2+max)/2

    So if you want to compare X or Y gear when critical hits come to play, the older comparisons based on (min+max)/2 are systematically underestimating critical hit damage : (min+max)/2 is pretty much the minimum observed damage for crit, which can have an impact especially for low pdif situation, for exemple, where crit damage is huge compared to normal hits.

  5. #25
    Chram
    Join Date
    Sep 2007
    Posts
    2,526
    BG Level
    7
    FFXI Server
    Fenrir

    Ok, to get a better handle on the pDiff spread I went back to 1-h weapons. Have accumulated 1800+ swings on Azoth, Behemoth Knife and Behemoth Knife +1 (so ~1300 non-crit, 400 crit) [was gonna add a couple more, but already taking a long time]. Since we know exactly what the cRatio cap is for them, I can get a better sense of what the pDiff is doing around the distribution.

    First, collection of all the data:

    Behemoth Knife
    Spoiler: show


    Code:
    Melee Damage
    Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
    Motenten             172110  100.00 %    1823/96   95.00 %    65/103    84.73    441   110/132  124.73   24.19 %
    Normal hits graph:
    http://img704.imageshack.us/i/bknorm.png/

    Crit graph:
    http://img51.imageshack.us/i/bkcrits.png/


    Code:
    Motenten
      Melee
           65:    3
           66:   12
           67:   22
           68:   34
           69:   30
           70:   39
           71:   37
           72:   32
           73:   41
           74:   42
           75:   36
           76:   43
           77:   32
           78:   37
           79:   38
           80:   42
           81:   33
           82:   29
           83:   34
           84:   38
           85:   34
     ^     86:   40
           87:   44
           88:   44
    +      89:   57
           90:   41
           91:   43
           92:   42
           93:   42
           94:   47
           95:   38
           96:   40
           97:   38
           98:   50
           99:   47
          100:   40
          101:   20
          102:   13
          103:    8
      Melee Crits
          110:    2
          111:    5
          112:    9
          113:   10
          114:    9
          115:   14
          116:   13
          117:   16
          118:   10
          119:   11
          120:   19
          121:   13
          122:   11
          123:   12
          124:    6
          125:   13
          126:   40
    +^    127:   42
          128:   39
          129:   38
          130:   33
          131:   41
          132:   35



    Behemoth Knife +1
    Spoiler: show


    Code:
    Melee Damage
    Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
    Motenten             171219  100.00 %    1765/91   95.10 %    67/107    87.23    421   112/135  128.24   23.85 %
    Normal hits graph:
    http://img51.imageshack.us/i/bk1norm.png/

    Crit graph:
    http://img193.imageshack.us/i/bk1crits.png/

    Code:
    Motenten
      Melee
           67:    6
           68:   13
           69:   23
           70:   33
           71:   30
           72:   49
           73:   32
           74:   32
           75:   23
           76:   35
           77:   39
           78:   44
           79:   30
           80:   41
           81:   29
           82:   28
           83:   30
           84:   25
           85:   34
           86:   37
           87:   35
     ^     88:   39
           89:   38
           90:   37
           91:   44
           92:   43
           93:   36
           94:   42
           95:   51
           96:   44
           97:   36
           98:   44
           99:   40
          100:   40
    +     101:   52
          102:   40
          103:   24
          104:   16
          105:   19
          106:    9
          107:    2
      Melee Crits
          112:    1
          113:    2
          114:    5
          115:    4
          116:    9
          117:   13
          118:   11
          119:   10
          120:    4
          121:   14
          122:    8
          123:   10
          124:    8
          125:   16
          126:    9
          127:   14
          128:   13
    +     129:   47
     ^    130:   31
          131:   43
          132:   38
          133:   35
          134:   38
          135:   38


    Azoth
    Spoiler: show


    Code:
    Melee Damage
    Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
    Motenten             196713  100.00 %   1909/108   94.65 %    72/114    92.91    437   121/144  137.19   22.89 %
    Normal hits graph:
    http://img193.imageshack.us/i/azothnorm.png/

    Crit graphs:
    http://img704.imageshack.us/i/azothcritlow.png/
    http://img15.imageshack.us/i/azothcrithigh.png/

    Code:
    Motenten
      Melee
           72:    9
           73:   20
           74:   26
           75:   36
           76:   31
           77:   37
           78:   46
           79:   29
           80:   24
           81:   35
           82:   37
           83:   21
           84:   32
           85:   47
           86:   39
           87:   37
           88:   31
           89:   36
           90:   42
           91:   45
           92:   35
     ^     93:   46
           94:   40
           95:   41
           96:   46
           97:   48
    +      98:   51
           99:   43
          100:   29
          101:   46
          102:   39
          103:   42
          104:   37
          105:   33
          106:   28
          107:   32
          108:   45
          109:   45
          110:   36
          111:   22
          112:   19
          113:    8
          114:    1
      Melee Crits
          121:    1
          122:    3
          123:    4
          124:    3
          125:    7
          126:    9
          127:   13
          128:    9
          129:   14
          130:   12
          131:   14
          132:    8
          133:   12
          134:   12
          135:    8
          136:   17
          137:    8
    +     138:   52
     ^    139:   44
          140:   36
          141:   38
          142:   43
          143:   33
          144:   37






    The outermost points on the internal pDiff range are affected by rounding/truncation of pDiff values that don't stretch across all possible results for that number. (EG: 2.4 pDiff for BK+1 (d43) is 103.2; therefore, compared to any value below that, 103 only has a 20% chance of getting hit, and thus have a lower frequency than other internal pDiff results, even though it's not entirely part of the 'tail'.) As such, it's somewhat difficult to exactly judge the cutoff points between internal and tail distributions. Still, the following appear to be fairly accurate:

    Internal estimates:

    Code:
    Wp    Min Max Min p1  Min p2  Max p1  Max p2
    BK:   68  100 1.6190  1.6429  2.3810  2.4048
    BK+1  69  103 1.6047  1.6279  2.3853  2.4186
    Azoth 74  110 1.6087  1.6304  2.3913  2.4130
    Min range: 1.6190-1.6279
    Max range: 2.3913-2.4048

    Min?: -0.375
    Max?: +0.40

    Note regarding BK+1 -- Max has to be just barely over the threshhold into 103. It's more solidly 102, but the overall range implies that 103 is just slightly part of the internal set.

    Internal pDiff range thus appears to be -0.375 to +0.400.

    There also seems to be a general upwards slope within the internal range itself. Looking at the trend lines on second-order polynomials, they are either very slightly curved or nearly flat, but generally trending up.


    Regarding 3-part formula:

    Araelus felt that the three-part formula failed because the R^2 value for the middle section was always extremely low (he couldn't get it above 0.03). That, however, is *not* a flaw in the idea. We don't -want- the middle section to have a high R^2. R^2 near 1 means that there's a positive correlation between the X values and the Y values. However our chart is damage vs frequency; for the most part we expect frequency to remain constant regardless of damage value. If it had a high R^2 that would mean that we would expect to have higher frequencies at higher damage values. A 0 R^2 means that we get the same frequency regardless of damage done.

    If I use a 3-part equation, Soboro, Azoth, BK and BK +1 all allow for strong correlation results for the tail slopes, and a slightly upward sloping (linear) trend of the main section, all of which pretty well match the results seen by Araelus.

    On the other hand, if I break the center equation up into segments for under cRatio and over cRatio, we see another distinct difference, where the frequencies for damages over cRatio are notably higher than the ones below cRatio. Both segments tend to have fairly flat linear trend lines. Trend lines tend to average about 33/40 (BK+1) to 35/42 (BK). As an average distribution, that's roughly a 45/55 split.



    Speculation on tail calculation:

    Assume that it's a flat random spread from 0 to 0.1. How much of that spread generates a new point? For BK+1, 0.0232, or about 1/4. Max non-crit is 107. 108 would be reached at 2.51, or about half a unit past 107. Therefore 107 occupies about 1/8 of the possible bonus range.

    The value below 107 would expect to get the bonus range from the max 103 as well as the previous 102, so get twice as many possible points as 107. However 107 only got half of its full potential, so you'd actually expect a 4x differential between 107 and 106. 107 have 2 occurances, 106 had 9.

    There are a number of other tail points that seem to jump by factors of 2x, 4x, or 8x (though I somewhat discount the 8x as that usually means only 1 sample of the most extreme point occured, and is thus unreliable as a ratio measure).

    It's still possible that the 0.10 addition is a 5% bonus, since I don't have data on < 2.0 cRatios. If it's a 5% bonus, that appears to be applied to the cRatio to get our bonus amount. It also appears that the low end tail gets a 2.5% 'bonus'.

    Next, frequency of getting the bonus. If the 107 on the BK+1 is 1/8 of the total bonus granted from the internal point, and it got 2 samples, then the internal point passed out an extra 16 points' worth of bonus frequency values. Trend average on BK+1 is about 40. 16 points would be 40% of that. Of those, ~4 end up not changing the base value.



    Possible formulation (fair bit of guesswork):
    Random 45/55 check on whether pDiff goes low or high (55% chance of high).
    If high, calculate pDiff as range of 0 to 0.40.
    Check to see if bonus pDiff is granted. ~40% chance.
    -- Get bonus range as 5% of cRatio (0.10 at 2.0 cRatio).
    If low, calculate pDiff as range of 0 to 0.375.
    Check to see if 'bonus' pDiff is granted. ~40% chance.
    -- Get bonus range as 2.5% of cRatio (0.05 at 2.0 cRatio).
    If we're in high set, add to cRatio. If we're in low set, subtract from cRatio.
    Apply any applicable caps on pDiff range.


    Non-crit melee average/pDiff average:
    BK: 85.10 == 2.026
    BK+1: 87.23 == 2.029
    Azoth: 92.88 == 2.019

    So, the above formulation should be able to provide approximately a .025 pDiff increase over a flatfield spread.

    55% * (.4/2 + 40% * .1/2) = 0.121
    45% * (.375/2 + 40% * .05/2) = 0.088875

    0.121 - 0.088875 = 0.032125

    Or a smidge over 2.03 average pDiff. Fairly close.


    I've rewritten and refigured this a dozen times. Time to let other people pick it apart and come up with a better idea.

  6. #26
    Old Merits
    Join Date
    Aug 2007
    Posts
    1,088
    BG Level
    6
    FFXI Server
    Ragnarok

    why are you guys so certain it is a 0.4+/0.375- spread? wouldn't it make sense that it be a 20%+/- as well? Both model fits. I would think most of the stuff are multiplier cuz the number of 0.4/0.375 is just too random.

  7. #27
    Chram
    Join Date
    Sep 2007
    Posts
    2,526
    BG Level
    7
    FFXI Server
    Fenrir

    Because the range from min to max (excluding tails) is basically the same regardless of cRatio (aside from minor rounding issues). You could consider it a percentage of base damage if you like, but that's essentially what pDiff is anyway.

  8. #28

    Motenten

    I have worked on the damage formula a good while ago. The Studio Gobli formula works well for maximized damage estimation but for average characters and the mobs they fight the formula is unhelpful. I stopped working on it after it was clear people found the Studio Gobli formula more useful.

    I have arranged your data differently. See the attached graph.

Similar Threads

  1. Delay Reduction Cap Test
    By kittycatrag in forum FFXI: Everything
    Replies: 7
    Last Post: 2011-04-04, 04:18
  2. Newbie shield question: Optimal for block %, cap?
    By Kyreth in forum FFXI: Everything
    Replies: 12
    Last Post: 2007-01-19, 16:56
  3. Tests regarding delay cap
    By Nny in forum FFXI: Everything
    Replies: 32
    Last Post: 2006-08-22, 02:19
  4. Anyone trying for their Relic Weapon?
    By Epical in forum FFXI: Everything
    Replies: 5
    Last Post: 2004-08-08, 22:30