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    Combat Damage FAQ by BugPop

    Version: 0.5 | Updated: 09/23/04 | Printable Version | Search Guide | Bookmark Guide

    Damage FAQ
    By BugPop
    res1exu4@verizon.net
    
    ================================================================================
    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.  Z Tables
    B.  Legal Information
    C.  Contact/Donation (Gil please) information
    
    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
    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
    
    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.
    
    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.
    
    
    ================================================================================
    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
    
    
    ================================================================================
    B.  Legal Information
    ================================================================================
    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.
    
    ================================================================================
    C.  Contact Information
    ================================================================================
    I can be contacted at res1exu4@verizon.net
    
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