Combat Damage Faq -- STR, VIT, DEF, & ATK explainedFollow

I have finished my FAQ on combat damage. Please let me know how to improve it. I also give permission to post this FAQ on ffxi.allakhazam.com.

 
Damage FAQ 
By BugPop 
res1exu4@verizon.net 
 
http://mysite.verizon.net/res1exu4/ 
 
================================================================================ 
Table of Contents/version History 
================================================================================ 
 
1.  Introduction 
2.  Basics 
3.  Battle Damage (The part you want) 
4.  Calculating STR, VIT, ATK, and DEF.  (The part you won’t like) 
 
A.  Calculating Z values 
B.  Z Tables 
C.  Legal Information 
D.  Contact/Donation (Gil please) information 
 
v. 0.51 (13 OCT 2004) 
A few clarifications made to stat descriptions and added personal web 
page including charts, tables and a combat damage calculator.  I plan on 
revising this to be much easier to use based on feedback I have recieved from 
various people.  Please let me know how I can improve (besides adding data for 
dex, abilities, and weaponskills info).  I have come up with a formula which 
simulates the damage curve which can account for the use dex, agi, eva, and acc 
in the game but I still have some work cut out for me.  I'll post more when 
I am reasonably sure it's good. 
 
v. 0.5 (23 SEPT 2004) 
I have included everything needed to determine combat damage.  One will have to  
come up with some values by experimentation with various mobs.  I still wish to  
come up with a damage curve that simulates actual accumulated data.  I have a  
few theories but it’s not yet complete.  I am hoping that in time that I will  
either be able to get enough data to extract the pattern, or that someone else  
will figure it out. 
 
================================================================================ 
1.  INTRODUCTION 
================================================================================ 
 
I’ve been interested for some time about how stats influence the final damage  
equation.  I have been working on the formula for some time now and I have an  
equation that accurately predicts the minimum and maximum damage using STR, VIT, 
ATTACK and DEFENSE.  I wanted to be able to come up with a universal damage  
equation (involving DEX, AGI, ACC, and EVA as well) but that is proving to be a  
challenging task. 
 
Currently the equation is only useful for determining the minimum and maximum  
values of damage.  I have been working on several modifications to the equation  
so that it more accurately resembles the calculated curve from the raw data.  It 
looks promising, but I likely need to collect more data. 
 
I took a class called Civil and Environmental Systems Engineering recently at  
the University.  For part of the course we learned to use simulations to model  
the behavior of a system.  Using a continuous uniform distribution curves,  
normal distribution curves, and/or exponential distribution curves, one can  
accurately determine the behavior of a system. 
 
It occurred to me that FFXI was utilizing various distribution curves to govern  
the success and fail rates of the system.  It’s a simulated world governed by  
simulated laws that are determined by the laws of probability.  One can see it  
in synthesis, combat, and even in NM spawn times. 
 
I will be using a normal distribution curve as part of the formula for  
determining min and max values.  It is the use of this function that makes  
easier to understand the roles of ATTACK, STR, DEFENSE, and VIT.  I have  
included brief instructions how to use the normal distribution curve as well as  
some Z tables at the end of this FAQ.  Even if you know nothing of statistics,  
just follow the instructions and you will be fine. 
 
================================================================================ 
2.  BASICS (You ought to know these) 
================================================================================ 
 
STR – Every 2 points add +1 ATTACK and +1 DAMAGE INFLICTED 
DEX – Affects Hit%, Critical Hit% 
VIT – Every 2 points add +1 DEFENSE and -1 DAMAGE RECIEVED 
AGI – Affects EVA, Ranged ACC, Block%, Parry% 
INT – Increases magical attack, decreases magical damage recieved 
MND – Increases magical healing, increases magical defense 
 
ATTACK = 8 + STR/2 + SKILL = Affects damage output, Hit% 
DEFENSE = 8 + VIT/2 + LEVEL = Affects damage received, EVA? 
 
(Without gear, food, status effects, job abilities, or job traits.) 
 
 
================================================================================ 
3.  BATTLE DAMAGE  
================================================================================ 
 
DAM = the damage of your weapon 
 
BON = Attribute Bonus = (STR-VIT)/2 
 
CBR = Combat Ratio = (ATTACK-DEFENSE)/ATTACK = 1-(DEF/ATK) 
 
SIG = Sigma = DAM/6 
 
***The following values require the use of the Z tables, see parts A & B*** 
 
                  Zmin = Z[CBR] 
 
                  Zmax = Zmin+4 
 
   ************************************************* 
   *                                               * 
   *   MINIMUM_DAMAGE = DAM + BON + SIG*(Zmin)     * 
   *                                               * 
   *   MAXIMUM_DAMAGE = DAM + BON + SIG*(Zmin+4)*  * 
   *                                               * 
   ************************************************* 
 
*Why +4?  Examining the range of values (excluding critical hits and     dodges) 
will reveal that the range of any damage curve is equal to     2/3*DAM or 4*SIG. 
 
 
WHAT HAPPENS WHEN MOBS DEFENSE IS HIGHER THAN PLAYER’S ATTACK??? 
 
ATTACK is an important attribute to keep as high as possible when leveling.  If  
you are fighting a mob with High Defense, your damage curve is in the toilet.  A 
mob has “high defense” when its DEFENSE is higher than your ATTACK.   In this  
situation your CBR is now negative and there are no negative values on the  
chart. 
 
{THIS PART MAY NOT BE CORRECT AS WRITTEN, I NEED TO CHECK MY NOTES} 
To Fix this, you temporarily remove the negative sign to compute Zmin.  Then  
once Zmin is determined, affix the negative sign to Zmin.  This causes your Zmin 
to effectively become Zmax and Zmin = Zmax – 4. 
{IT HAS BEEN LEFT HERE IN CASE IT'S CORRECT} 
 
================================================================================ 
4.  Calculating enemy VIT and DEFENSE (or STR, ATTACK, and WEAPON DAMAGE) 
================================================================================ 
 
STEP 1 - Obtain Damage Values – Read this - Important 
Decide on a mob type to concentrate on.  Record the damage values and note the  
critical hits and the times you only hit for half damage and be sure to record  
the misses too.  Avoid using any spells or abilities that would contaminate your 
data.  If your opponent uses an ability that affects your one of your  
attributes, make note of which values are affected which values are not.  Record 
the experience earned after defeating the enemy so you can determine its level. 
 
Check out http://www.geocities.com/bside_ffxi/index.html to determine the level  
of your opponent. 
 
Since attributes increase as levels go up, and attributes vary among different  
jobs, use only data for a specific job and level.  Try to obtain data for at  
least 30 solid hits (not counting critical hits or dodged values), but more  
might make you feel more comfortable with your results.  30 is a “magic number”  
in the sense that it takes 30 observations to get the shape of the curve and  
obtaining more will not significantly alter its form.   
 
If your weapon does a lot of damage, it may be useful to obtain more data.   
Although you have the shape of the curve, the range of your damage values is  
large.  It may require more data to ensure you have found your minimum and  
maximum damage value. 
 
 
STEP 2 - Sort Data 
Enter all the data in one column in a spreadsheet and sort it. 
 
 
STEP 3 - Determine Frequency 
Frequency = the number of times a value occurs in the data set. 
If all you want to do is calculate the mobs VIT and DEFENSE go to step 6 
 
 
STEP 4 – Determine Relative Frequency 
                         Number of times the value occurs 
Relative Frequency = ---------------------------------------- 
                      Number of observations in the data set 
Relative frequency is useful when determining multiple sets of data. 
 
 
-------------------------------------------------- 
Steps 1-4 
-------------------------------------------------- 
ELVAAN WAR23/THF11 
vs 
GOBLIN MUGGER - TOUGH – 120 EXP – Level 24 
-------------------------------------------------- 
Base stats -- STR 32, DEX 26, ATTACK 92. 
Weapon Used –- Longsword +1 -- DMG 17 
-------------------------------------------------- 
|  Step 1    |  Step 2   |  Step 3  |   Step 4   | 
-------------+-----------+----------+------------- 
|            |  Sorted   | Frequency| Relative   | 
|  Raw Data  |   Data    |          | Frequency  | 
|------------+-----------+----------+------------| 
|15  16  m   |  m(46)20  |  m   46  |  41.82%    | 
|46* m   17  |  14   20  |  14  4   |  3.64%     | 
|m   m   17  |  14   20  |  15  2   |  1.82%     | 
|m   18  20  |  14   20  |  16  7   |  6.36%     | 
|16  19  m   |  15   20  |  17  7   |  6.36%     | 
|m   m   21  |  15   21  |  18  3   |  2.73%     | 
|24  20  m   |  16   21  |  19  3   |  2.73%     | 
|14  m   m   |  16   21  |  20  23  |  20.91%    | 
|m   16  24  |  16   22  |  21  3   |  2.73%     | 
|m   20  m   |  16   22  |  22  3   |  2.73%     | 
|16  m   20  |  16   22  |  23  3   |  2.73%     | 
|24  m   m   |  16   23  |  24  3   |  2.73%     | 
|m   20  20  |  16   23  |  25  1   |  0.91%     | 
|20  m   m   |  17   23  |  26  0   |  0.00%     | 
|14  25  m   |  17   23  |  27  0   |  0.00%     | 
|20  16  20  |  17   24  |  28  0   |  0.00%     | 
|21  m   20  |  17   24  |  29  0   |  0.00%     | 
|33* m   m   |  17   24  |  30  0   |  0.00%     | 
|m   20  20  |  17   25  |  31  0   |  0.00%     | 
|m   20  22  |  17   33  |  32  0   |  0.00%     | 
|m   19  20  |  18   46  |  33* 1   |  0.91%     | 
|m   m   17  |  18       |  34  0   |  0.00%     | 
|20  22  m   |  18       |  35  0   |  0.00%     | 
|m   20  m   |  19       |  36  0   |  0.00%     | 
|14  m   m   |  19       |  37  0   |  0.00%     | 
|18  19  m   |  19       |  38  0   |  0.00%     | 
|17  m   20  |  20       |  39  0   |  0.00%     | 
|X#  m   m   |  20       |  40  0   |  0.00%     | 
|120 m   20  |  20       |  41  0   |  0.00%     | 
|    m   16  |  20       |  42  0   |  0.00%     | 
|    20  18  |  20       |  43  0   |  0.00%     | 
|    17  21  |  20       |  44  0   |  0.00%     | 
|    23  m   |  20       |  45  0   |  0.00%     | 
|    m   23  |  20       |  46* 1   |  0.91%     | 
|    17  22  |  20       |      --- |            | 
|    m   23  |  20       |      110 |            | 
|    20  X#  |  20       |          |            | 
|    16  120 |  20       |          |            | 
|    m       |  20       |          |            | 
|    20      |  20       |          |            | 
|    m       |  20       |          |            | 
|    24      |  20       |          |            | 
|    X       |  20       |          |            | 
|    120     |  20       |          |            | 
|            |           |          |            | 
-------------------------------------------------- 
*Critical Hit     
#Gob killed self with Goblin Bomb 
 
 
 
STEP 5 – Create a graphical representation of your data 
Create a histogram.  In Excel you can choose to do a COLUMN graph and specify  
the damage values as the “Category (X) axis label” or use the XY (Scatter)  
graph. 
 
------------------------------------------------------------------- 
|Histogram                                                        | 
|-----------------------------------------------------------------| 
|    |                                                            | 
|    |  42%                                                       | 
|    |  XX                                                        | 
|40% |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|35% |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|30% |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|25% |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                                                        | 
|    |  XX                       21%                              | 
|20% |  XX                       XX                               | 
|    |  XX                       XX                               | 
|    |  XX                       XX                               | 
|    |  XX                       XX                               | 
|    |  XX                       XX                               | 
|15% |  XX                       XX                               | 
|    |  XX                       XX                               | 
|    |  XX                       XX                               | 
|    |  XX                       XX                               | 
|    |  XX                       XX                               | 
|10% |  XX                       XX                               | 
|    |  XX                       XX                               | 
|    |  XX                       XX                               | 
|    |  XX                       XX                               | 
|    |  XX           6% 6%       XX                               | 
|5%  |  XX           XX XX       XX                               | 
|    |  XX     4%    XX XX       XX                               | 
|    |  XX     XX    XX XX 3% 3% XX 3% 3% 3% 3%                   | 
|    |  XX     XX 2% XX XX XX XX XX XX XX XX XX                   | 
|    |  XX     XX XX XX XX XX XX XX XX XX XX XX 1%       1%    1% | 
|----+------------------------------------------------------------| 
|    |  MISS•••14 15 16 17 18 19 20 21 22 23 24 25 26 •••33*•••46*| 
------------------------------------------------------------------- 
*Critical Hit 
 
STEP 6 – Locate the “Sample Mean,” Minimum damage value. 
The “Sample Mean” is the spike you see in the damage range of your data.  This  
is where the Z value is 0.  Normally the mean value (average value) is equal to  
sum of all damage values divided by the number of damage values.  We do not do  
this here due to other factors affecting the damage curve.  This “Sample Mean”  
is part of the equation that will help us solve our problem. 
 
In our case in the Histogram in step 5, our spike shows that our mean value is  
20.  If your spike is at a damage value but the next damage value seems to be  
part of that spike, consider it to be the average of the two values.  For  
instance if our spike had at 20 damage - 17% and at 21 damage - 9%) we would  
consider our “Sample Mean” to be 20.5. 
 
We’re not looking at damage values from critical hits or ones that were reduced  
by some skill.  If you forgot which ones were critical hits, they generally tend 
to be the outliers to the right of the curve and the damage- 
reduced hits would be the outliers on the left side of the curve.  The range of  
your curve (the  
width) should not be greater than 4*SIG (rounded).  It is possible to have a  
critical hit in the damage curve.  Usually it’s due to a mob benefiting from its 
damage reducing skill when you hit it with a critical hit. 
 
By observation, we see that our Minimum Value = 14 
 
 
STEP 7 – Make calculations – 
 
For reference, here is the equation to find minimum damage. 
   MINIMUM_DAMAGE = DAM + BON + SIG*(Zmin)   
 
 
PART 1 – Determine VIT (or STR) 
We determined our SAMPLE_MEAN to be 20, since here our Z value is 0, then we can 
calculate VIT easily. 
   SAMPLE_MEAN = DAM + BON + SIG*(0) = WEAPON_DAMAGE + (STR-VIT)/2 
 
Do some Algebra... 
   VIT = 2*(WEAPON_DAMAGE – SAMPLE_MEAN) + STR 
 
As for our example, WEAPON_DAMAGE = 17, STR = 32, SAMPLE_MEAN = 20 
   VIT = 2 * (17 – 20) + 32 = 2 * (-6) + 32 = 26 
 
In case you’re trying to determine STR 
   STR = VIT – 2*(WEAPON_DAMAGE – SAMPLE_MEAN) 
 
 
PART 2 – Determine DEFENSE (or ATTACK) 
Using the values we already know 
   MINIMUM_DAMAGE = DAM + BON + SIG*(Zmin) 
 
      DAM + BON = SAMPLE_MEAN, SIG = DAM/6 
 
   Zmin = 6*(MINIMUM_DAMAGE – SAMPLE_MEAN)/(DAM) 
 
   Zmin = 6*(14 – 20)/17 = 6*(-6)/17 = -36/17 = -2.1176 
 
Take this Z value and convert it into the CBR.  First go to the Z table and find 
the row for -2.1, and then find the column with for .01 and .02.  You can  
interpolate if you wish or just round to .02. 
 
---------------------------------------------------------------------------- 
        0      0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09 
---------------------------------------------------------------------------- 
-2.9 | 0.0019 0.0019 0.0020 0.0021 0.0021 0.0022 0.0023 0.0023 0.0024 0.0025 
-2.8 | 0.0026 0.0026 0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 
-2.7 | 0.0035 0.0036 0.0037 0.0038 0.0039 0.0040 0.0041 0.0043 0.0044 0.0045 
-2.6 | 0.0047 0.0048 0.0049 0.0051 0.0052 0.0054 0.0055 0.0057 0.0059 0.0060 
-2.5 | 0.0062 0.0064 0.0066 0.0068 0.0069 0.0071 0.0073 0.0075 0.0078 0.0080 
-2.4 | 0.0082 0.0084 0.0087 0.0089 0.0091 0.0094 0.0096 0.0099 0.0102 0.0104 
-2.3 | 0.0107 0.0110 0.0113 0.0116 0.0119 0.0122 0.0125 0.0129 0.0132 0.0136 
-2.2 | 0.0139 0.0143 0.0146 0.0150 0.0154 0.0158 0.0162 0.0166 0.0170 0.0174 
-2.1 | 0.0179 0.0183 0.0188 0.0192 0.0197 0.0202 0.0207 0.0212 0.0217 0.0222 
-2.0 | 0.0228 0.0233 0.0239 0.0244 0.0250 0.0256 0.0262 0.0268 0.0274 0.0281 
 
Examining the table reveals our CBR to be between 0.0183 and 0.0188 
 
Linear interpolation 
I am only including it if you really want to do it.  You probably will see more  
benefit from using it when your Z value is closer to 0. 
 
   (y(x1) – y(x2))/(x1-x2) = (y(x) – (y(x2))/(x – x2) 
 
   Find x 
 
   x = (y(x) – (y(x2))* (x1-x2)/ (y(x1) – y(x2)) + x2 
 
   y(x1)=-2.11, y(x2)=-2.12, y(x) = -2.1176, x1=0.0183, x2=0.0188 
 
   x = (-2.1176 – (-2.12))*(0.0183-0.0188)/(-2.11-(-2.12))+ 0.0188 
   x = (.0024)*(-.0005)/0.01+0.0188 = -0.0000012/0.01 + 0.0188 
     = -.00012+.0188 = 0.01868 
 
   CBR = (ATTACK – DEFENSE)/ATTACK 
 
Here is the formula for determining Defense. 
   DEFENSE = ATTACK*(1-CBR) 
 
   DEFENSE = 92 * (1-0.01868) = 92*.98132 = 90.28 
 
Note: I believe that def on enemies will always be ~±0.25.  The Attack and  
Defense values you see in your screen are always rounded down.  When you raise  
STR by 1, ATTACK increases by 0.5.  The same is true for VIT.  If your ATTACK is 
equal to the DEF of the opponent, you will get a value of 0.  Getting a 0 on the 
Distribution curve will be the same as –INFINITY.  Since that can’t happen, it  
would seem that mobs have an extra 0.25 def to ensure that doesn’t happen. 
 
In case you are looking for the formula for determining attack. 
   ATTACK = DEFENSE/(1-CBR) 
 
 
================================================================================ 
A.  Calculating Z values 
================================================================================ 
 
  _________________________________________________________________________ 
 |                                                                         | 
 | Normal Distribution Curve                                               | 
 |_________________________________________________________________________| 
 |                                                                         | 
 |                                                                         | 
 |                                                                         | 
 |                                  _.#---------------------------[0.5000] | 
 |                              _.¡||º|º||¡._                              | 
 |                            .¡|º¯   |   ¯º|¡.                            | 
 |                          #|º¯      |      ¯º|#-----------------[0.8413] | 
 |                        .|º         |         ||.                        | 
 |                      ¡|º           |         | º|¡  [0.9772]            | 
 |                    .|º             |         |   º|.   |                | 
 |                 .¡|º               |         |     º|¡.|     [0.9987]   | 
 |             _.¡#º¯                 |         |       ¯º#¡._      |      | 
 |        _..¡|ºº¯                    |         |         |¯ºº|¡.._ |      | 
 |__...¡#ººº¯                         |         |         |     ¯ººº#¡...__| 
 |-+----+----+----+----+----+----+----+----+----+----+----+----+----+----+-| 
 |                                                                         | 
 |     -3        -2        -1         0         1         2         3      | 
 |_________________________________________________________________________| 
 
 
CBR is a number between 0 and 1 and each CBR value has a corresponding Z value  
on a normal distribution curve.   
 
Find Z using your CBR.  (I will use 0.0505 for this example) 
1.	Look in the chart below to find the number that is closest to your CBR. 
2.	Add the number on the far left side to the number directly above in the 
margin. 
 
                                Add this number to the first number (-1.76). 
                                                    | 
---------------------------------------------------------------------------- 
        0      0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09 
---------------------------------------------------------------------------- 
-1.9 | 0.0287 0.0294 0.0301 0.0307 0.0314 0.0322    ^   0.0336 0.0344 0.0351 
-1.8 | 0.0359 0.0367 0.0375 0.0384 0.0392 0.0401    |   0.0418 0.0427 0.0436 
-1.7 |< --First record this number –(-1.7)-------0.0505 0.0516 0.0526 0.0537 
-1.6 | 0.0548 0.0559 0.0571 0.0582 0.0594 0.0606 0.0618 0.0630 0.0643 0.0655 
---------------------------------------------------------------------------- 
 
3.	This number is your Z[min] value, -1.76. 
 
 
================================================================================ 
B.  Z Tables 
================================================================================ 
 
---------------------------------------------------------------------------- 
        0      0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09 
---------------------------------------------------------------------------- 
-3.6 | 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 
-3.5 | 0.0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 
-3.4 | 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 
-3.3 | 0.0005 0.0005 0.0005 0.0005 0.0006 0.0006 0.0006 0.0006 0.0006 0.0007 
-3.2 | 0.0007 0.0007 0.0007 0.0008 0.0008 0.0008 0.0008 0.0009 0.0009 0.0009 
-3.1 | 0.0010 0.0010 0.0010 0.0011 0.0011 0.0011 0.0012 0.0012 0.0013 0.0013 
-3.0 | 0.0013 0.0014 0.0014 0.0015 0.0015 0.0016 0.0016 0.0017 0.0018 0.0018 
---------------------------------------------------------------------------- 
        0      0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09 
---------------------------------------------------------------------------- 
-2.9 | 0.0019 0.0019 0.0020 0.0021 0.0021 0.0022 0.0023 0.0023 0.0024 0.0025 
-2.8 | 0.0026 0.0026 0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 
-2.7 | 0.0035 0.0036 0.0037 0.0038 0.0039 0.0040 0.0041 0.0043 0.0044 0.0045 
-2.6 | 0.0047 0.0048 0.0049 0.0051 0.0052 0.0054 0.0055 0.0057 0.0059 0.0060 
-2.5 | 0.0062 0.0064 0.0066 0.0068 0.0069 0.0071 0.0073 0.0075 0.0078 0.0080 
-2.4 | 0.0082 0.0084 0.0087 0.0089 0.0091 0.0094 0.0096 0.0099 0.0102 0.0104 
-2.3 | 0.0107 0.0110 0.0113 0.0116 0.0119 0.0122 0.0125 0.0129 0.0132 0.0136 
-2.2 | 0.0139 0.0143 0.0146 0.0150 0.0154 0.0158 0.0162 0.0166 0.0170 0.0174 
-2.1 | 0.0179 0.0183 0.0188 0.0192 0.0197 0.0202 0.0207 0.0212 0.0217 0.0222 
-2.0 | 0.0228 0.0233 0.0239 0.0244 0.0250 0.0256 0.0262 0.0268 0.0274 0.0281 
---------------------------------------------------------------------------- 
        0      0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09 
---------------------------------------------------------------------------- 
-1.9 | 0.0287 0.0294 0.0301 0.0307 0.0314 0.0322 0.0329 0.0336 0.0344 0.0351 
-1.8 | 0.0359 0.0367 0.0375 0.0384 0.0392 0.0401 0.0409 0.0418 0.0427 0.0436 
-1.7 | 0.0446 0.0455 0.0465 0.0475 0.0485 0.0495 0.0505 0.0516 0.0526 0.0537 
-1.6 | 0.0548 0.0559 0.0571 0.0582 0.0594 0.0606 0.0618 0.0630 0.0643 0.0655 
-1.5 | 0.0668 0.0681 0.0694 0.0708 0.0721 0.0735 0.0749 0.0764 0.0778 0.0793 
-1.4 | 0.0808 0.0823 0.0838 0.0853 0.0869 0.0885 0.0901 0.0918 0.0934 0.0951 
-1.3 | 0.0968 0.0985 0.1003 0.1020 0.1038 0.1056 0.1075 0.1093 0.1112 0.1131 
-1.2 | 0.1151 0.1170 0.1190 0.1210 0.1230 0.1251 0.1271 0.1292 0.1314 0.1335 
-1.1 | 0.1357 0.1379 0.1401 0.1423 0.1446 0.1469 0.1492 0.1515 0.1539 0.1562 
-1.0 | 0.1587 0.1611 0.1635 0.1660 0.1685 0.1711 0.1736 0.1762 0.1788 0.1814 
---------------------------------------------------------------------------- 
        0      0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09 
---------------------------------------------------------------------------- 
-0.9 | 0.1841 0.1867 0.1894 0.1922 0.1949 0.1977 0.2005 0.2033 0.2061 0.2090 
-0.8 | 0.2119 0.2148 0.2177 0.2206 0.2236 0.2266 0.2296 0.2327 0.2358 0.2389 
-0.7 | 0.2420 0.2451 0.2483 0.2514 0.2546 0.2578 0.2611 0.2643 0.2676 0.2709 
-0.6 | 0.2743 0.2776 0.2810 0.2843 0.2877 0.2912 0.2946 0.2981 0.3015 0.3050 
-0.5 | 0.3085 0.3121 0.3156 0.3192 0.3228 0.3264 0.3300 0.3336 0.3372 0.3409 
-0.4 | 0.3446 0.3483 0.3520 0.3557 0.3594 0.3632 0.3669 0.3707 0.3745 0.3783 
-0.3 | 0.3821 0.3859 0.3897 0.3936 0.3974 0.4013 0.4052 0.4090 0.4129 0.4168 
-0.2 | 0.4207 0.4247 0.4286 0.4325 0.4364 0.4404 0.4443 0.4483 0.4522 0.4562 
-0.1 | 0.4602 0.4641 0.4681 0.4721 0.4761 0.4801 0.4840 0.4880 0.4920 0.4960 
-0.0 | 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 
---------------------------------------------------------------------------- 
 
--------------------------------------------------------------------------- 
       0      0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09 
--------------------------------------------------------------------------- 
0.0 | 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 
0.1 | 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 
0.2 | 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 
0.3 | 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517 
0.4 | 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 
0.5 | 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 
0.6 | 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 
0.7 | 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 
0.8 | 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 
0.9 | 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 
--------------------------------------------------------------------------- 
       0      0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09 
--------------------------------------------------------------------------- 
1.0 | 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 
1.1 | 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 
1.2 | 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 
1.3 | 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 
1.4 | 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 
1.5 | 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 
1.6 | 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 
1.7 | 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 
1.8 | 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 
1.9 | 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 
--------------------------------------------------------------------------- 
       0      0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09 
--------------------------------------------------------------------------- 
2.0 | 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 
2.1 | 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 
2.2 | 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 
2.3 | 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 
2.4 | 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 
2.5 | 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 
2.6 | 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 
2.7 | 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 
2.8 | 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 
2.9 | 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 
--------------------------------------------------------------------------- 
       0      0.01   0.02   0.03   0.04   0.05   0.06   0.07   0.08   0.09 
--------------------------------------------------------------------------- 
3.0 | 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 
3.1 | 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 
3.2 | 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 
3.3 | 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 
3.4 | 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998 
3.5 | 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 
3.6 | 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 
 
 
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Copyright 2004 Jacob M. Hart. 
This may be not be reproduced under any circumstances except for personal,  
private use. It may not be placed on any web site or otherwise distributed  
publicly without advance written permission. Use of this guide on any other  
web site or as a part of any public display is strictly prohibited, and a  
violation of copyright. 
 
All trademarks and copyrights contained in this document are owned by their  
respective trademark and copyright holders. 
 
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This will be in a constant state of editing
Edited, Thu Sep 23 19:25:18 2004 by Bugpop

Edited, Thu Sep 23 19:26:53 2004 by Bugpop

Edited, Thu Sep 23 19:30:02 2004 by Bugpop

Edited, Fri Sep 24 12:53:42 2004 by Bugpop

Edited, Wed Oct 13 14:57:10 2004 by Bugpop

:O
/em hands Bugpop the nobel prize.

Wow, exactly what I need to do with magic damages. Grats on that work, it's very well done and well supported by your data.

God damn! awesome work bugpop! At least someone's putting his/her school knowledge into practice lol. :) Way to go!!!

I think I speak for the majority of the posters here when I say: huh?!?

lol, I'm sure it was excellently done, but I have no idea how to read it or what I'm supposed to get out of it.

/em scratches head
This means I need more Attack+, right? ...RIGHT?

I got a 92 in prob and stat for engineering, and I understood it quite well. I could have done the same thing, but I lack the motivation. So I applaud you for your motivation and hard work.

While that is quite good, I'd suggest losing the intro to stats sidenotes.

Also, it would be nice if you used the same data to figure out Dex, Agi, and evasion.

I appreciate how you used your data to figure out mob STR, DEF, ATK, and VIT, but my guess with the DEX, AGI, and EVA missing, we could answer some very basic questions.

Ultimately, the only stat that matters is avg. damage per swipe, or even better avg damage per minute (including weapon delay). With the missing numbers, you would have a framework for deciding when to swap in +Dex or +Str gear for what mobs.

There's probably some other simple guidelines for these gear switches. Such as: If you miss more than xx% of the time, switch to +Dex gear.

One conclusion u can already make from your work though is that if your average damage (when hit, excluding criticals) is less your weapon damage, then you should increase Str and Atk (to make sure you gain rather than lose the bonus: Dam/6*(Zmin). Note: I may be wrong here as I haven't looked closely enough to see if Avg damage goes up linearly with Str and Atk. Perhaps there is no big damage boost step up when atk > def. In which case, there is only a big payoff to increasing Str and Atk when Atk is much different (in either direction) than the mob's Def.

Basically though, the Tohit%/crit% curves are just as important as the damage curve. It would also help if your guide clarified the payoffs to increasing stats on diff enemies (diff atk to def, ratios).

Another interesting question about mobs is whether their Def is a direct function of their Vit or do some mobs have armour bonuses while others don't.

Edited, Fri Sep 24 13:01:54 2004 by GodSpiral

From what I have seen in my data

DEX - I don't like what I see. I need more data to be sure. DEX increases the frequency of the sample mean. In other words, DEX raises that spike in the damage curve. Sometimes it increases your hit%, sometimes it makes it worse.

What always seems to increase HIT% is raising ATTACK (especially if it's low). If you combine an increase in both ATK and DEX, the HIT% increase is impressive. You have to raise both to make raising DEX worthwhile.

Also if you're farming mobs, and your attack is already very high. You'll likely hit for more damage if you don't wear any +dex rings. Wearing stumbling sandals (-10 DEX, -10 AGI) I found that I had a better average damage when fighting Easy Prey's and weaker than when not wearing them using a TARU PLD25/WAR12. My HIT% was the same as when I had DEX +3.

If the mob you are fighting has high defense, go for +attack items before going for +acc and +dex items. Eat your Mithkabobs and have your whm or rdm use Dia if you want to use +acc and +dex items. It will make a difference.

I make these statements without supporting arguments. I don't have as clear picture on them as I would like. I would rather not post my data either as that would be too time consuming. But those are just my observations so far on DEX.

Edited, Fri Sep 24 13:33:24 2004 by Bugpop

O.o

conclusion in english?

i love it^^ but..



defense i believe has nothing to do with evasion.

only agi, and evasion skill or evasion +/evasion skill+ items raise evasion.

btw agi also lessens the chance to get hit by a crit^^

Bugpop, excellent analysis!

I've been meaning to try to analyze this myself, and you may have given me renewed interest. I have a couple of comments (unfortunately, statistics jargon) that I'd like you to consider, and that I plan on hopefully getting around to testing myself.

My first problem is the whole CBR equation being related to a normal distribution....if this is true (which it may be), then as the CBR approaches zero (Attack = Defense), then the Zmin will approach negative infinity. Even if you take into account a 0.25 difference, your damage will drop fast approaching this point and there is no clear transition from Att>Def to Def>Att without a huge drop off at that point if -Zmin now becomes the Zmax (which it may be, I don't know).

It looks like there are two issues at hand...one is what kind of distribution governs the range of damage (min-max), and the other is what kind of distribution governs the scatter of that data within that range?

Based on your experience with the dexterity test, it seems that the scatter of the data may fit a Beta distribution. This has a fixed min and max, but the peak of the curve is not necessarily in the middle of the range. This would be much more difficult to test for, which also kind of makes me think why it may be the case. If some distribution curves were found that heavily favored the min or max side or the range, then that would give a lot of evidence to this possibility.

As for the distribution for determining the min-max range, I think you're onto something with the difference being 4*SIG, but I think the Zmin and Zmax idea needs some tweaking. It may in fact be a normal distribution, but to make it work for att>def and def>att, the center of the distribution would need to be att=def. So perhaps Z[CBR] = Zmiddle instead of min or max. The Z function would have to be changed to go from -1 to 1 instead of from 0 to 1. Or, alternatively this could also be a Beta distribution that goes from -1 to 1.

The real key to knowing the equations are accurate and complete is if you can predict the new data range and new most likely damages based on new Att, STR, etc.

To test this, I think one would have to collect data from easy preys as well as tough or even TWTBW as long as the level is known.

[/statistical rant]

Well, I didn't mean to go on for so long, but I think you're definitely onto something here, and if I figure out anything additionally with some testing I'll let you know.

wow, you put some time into this. Thank you. Im needed to figure out VIT for my paladin. I dotn know what to invest in really. but thanks for this.