Damage FAQ By BugPop res1exu4@verizon.net More information about combat damage on my combat damage web page http://mysite.verizon.net/res1exu4/Damage_Chart.htm ================================================================================ 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. 0.51 (29 SEPT 2004) Minor corrections. Added link to my combat damage web page. 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, believed to increase divine magical attack. ATTACK = 8 + STR/2 + SKILL = Affects damage output, Hit% DEFENSE = 8 + VIT/2 + LEVEL = Affects damage received. (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 = DEF/ATK SIG = Sigma = DAM/6 Zmin = Z[fpart(CBR)] Zmax = Zmin+4 MINIMUM_DAMAGE = DAM + BON + SIG*(Zmin) MAXIMUM_DAMAGE = DAM + BON + SIG*(Zmin+4) *See Part A on how to calculate Z values ================================================================================ 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% | |----+------------------------------------------------------------| | | MISS14 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 ~ñ0.25. 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] | | _.­||§|§||­._ | | .­|§î | î§|­. | | #|§î | î§|#-----------------[0.8413] | | .|§ | ||. | | ­|§ | | §|­ [0.9772] | | .|§ | | §|. | | | .­|§ | | §|­.| [0.9987] | | _.­#§î | | î§#­._ | | | _..­|§§î | | ||­.._ | | |__...­#§§§î | | | §#­...__| |-+----+----+----+----+----+----+----+----+----+----+----+----+----+----+-| | | | -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 Donations can be made to: Bununyunu Fairy Server