06-21-2008, 09:50 AM
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#1 |
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More data!
Elois
Night Elf
Hunter
<Driven>
Uldum
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Statistical Reference Guide
INTRODUCTION:
In several of my posts people have asked for explanations of the variables that I used. I have directed them to my earlier post White Paper doll to Raid DPS multiplier (http://forums.tkasomething.com/showthread.php?t=9633), but I have never been quite satisfied with that. It is a great post for theorycrafters; it has some rather lively dialogue that addresses many concerns about using ratios and shows the development of my ideas about using ratios. However, it is a lot of material to get through, and the conclusions and uses of the data are not very obvious. That thread started out as a discussion and transformed into something much more with the discovery of Wow Webstats. It was never intended to be a reference guide for hunters wanting to understand statistics. I hope that this guide will help hunters understand my work, and will help them to build their own framework for performing statistical analysis of DPS. I have written this in the same format as a statistical dictionary that would be used for financial analysis. I have even copied a couple of definitions from Wikipedia with some links that give further information on those concepts. In real life I am a CPA and I have often used financial ratios in my work to better understand businesses. When I performed my statistical studies, my models for my work were Leo Troy’s ratios based on tax returns http://www.amazon.com/Almanac-Busine...554083-9567969, and RMA’s ratios based on bank loan applications http://www.rmahq.org/RMA/. When I did my original study I described my ratios in terms of the variables that they were derived from. I have taken a more user friendly approach in this post, and I am naming the ratios in terms of the concepts that they embody. In White Paper doll to Raid DPS multiplier, I never created a variable dictionary and never attempted to systematically explain my ratios. At the time, I did not even know which ratios were the ones to watch, it was very much a discovery process. There are many more ratios than the ones that I have listed here, and I am very open to adding more upon request. I have listed the most significant ones based on about a year of use and research. CONCEPTS Covariance -- In probability theory and statistics, covariance is the measure of how much two variables change together (as distinct from variance, which measures how much a single variable changes). If two variables tend to vary together (that is, when one of them is above its expected value, then the other variable tends to be above its expected value too), then the covariance between the two variables will be positive. On the other hand, if one of them is above its expected value and the other variable tends to be below its expected value, then the covariance between the two variables will be negative. http://en.wikipedia.org/wiki/Co-variance Proxy Variable -- In statistics, a proxy variable is something that is probably not in itself of any great interest, but from which a variable of interest can be obtained. In order for this to be the case, the proxy variable must have a close correlation, not necessarily linear or positive, with the inferred value. Per-capita GDP is often used as a proxy for measures of standard of living or quality of life. Likewise, country of origin or birthplace might be used as a proxy for race. http://en.wikipedia.org/wiki/Proxy_%28statistics%29 RATIOS Ratio Abbreviation: Armory Auto Shot Ratio Name: Armory Auto Shot Description: This is a measure of the amount of damage that the armory predicts an auto shot will do. Use: It is used in computing certain ratios, such as Auto Shot Realization and the Buffing Index. Computation: Multiply the armory DPS by armory attack speed. Ratio Abbreviation: AR Ratio Name: Auto Shot Realization Description: This ratio is a measure of how much of the amount the armory would predict auto shots would do vs. how much the hunter is actually doing with auto shots. Use: It is used to identify the effectiveness of buffing and grouping on a raid. Computation: Divide the average non-critical auto shot in a raid by the Armory Auto Shot amount. Ratio Abbreviation: AVGSHOT Ratio Name: Average damage per shot Description: This is a measure of how hard your shot hit. Use: This is used to evaluate overall DPS and locate where a problem is occurring. Low DPS can occur because of a low rate of fire, low average damage of a shot, or low pet damage. Computation: Divide your total damage from shots by the number of all shots taken. Ratio Abbreviation: Buff Ratio Name: Buffing Index Description: This ratio is a measure of how much of the amount the armory would predict auto shots would do vs. how much the hunter is actually doing with auto shots. Unlike AR it takes into consideration armor penetration of the hunter. Use: It is used to identify the effectiveness of buffing and grouping on a raid. Computation: Reduce the average non-critical auto shot by dividing it by 1+ % damage increase from armor penetration and divide that result by Armory Auto Shot amount. Ratio Abbreviation: Clip Ratio Name: Clipping Index Description: This ratio measures how many auto shots that could have been fired are not fired. Use: It is a measure of the effectiveness of a shot rotation. Computation: It is calculated by dividing the total auto shots fired by the number of auto shots that the armory would predict would be fired. The formula is as follows: (total auto shots fired) / (Time in combat/attack speed) Ratio Abbreviation: CShot Ratio Name: Clipping from Shots Description: This ratio measures how many auto shots that could have been fired are not fired, during times in which the hunter was firing. It excludes times in which the hunter was bandaging, removing a Naj’entus spine, was in Morogrim Tidewalker’s watery grave, etc. . . Use: It is a measure of the effectiveness of a shot rotation. Computation: It is calculated by dividing the total auto shots fired by the number of auto shots that the armory would predict would be fired. A big problem with computing this ratio is identifying the time in combat spent attacking. Doing this requires access to detailed combat logs. The formula is as follows (total auto shots fired) / (Time in combat spent attacking /attack speed) Ratio Abbreviation: CR Ratio Name: Cheeky Realization Description: This ratio is the percentage of the damage that a hunter is doing Use: It is a measure of the overall performance of a hunter Computation: Divide the raid DPS of the hunter by the DPS that Cheeky’s spreadsheet would predict that they would do. This ratio does not consider buffs. Ratio Abbreviation: CR with buffs Ratio Name: Cheeky Realization including buffs Description: This ratio is the percentage of the damage that a hunter is doing Use: It is a measure of the overall performance of a hunter Computation: Divide the raid DPS of the hunter by the DPS that Cheeky’s spreadsheet would predict that they would do. Buffs and raid grouping are taken into consideration in this computation. Ratio Abbreviation: CR no pet Ratio Name: Cheeky Realization without pet Description: This ratio is the percentage of the damage that a hunter is doing Use: It is a measure of the overall performance of a hunter Computation: Divide the raid DPS of the hunter, excluding pet, by the DPS that Cheeky’s spreadsheet would predict that they would do, excluding pet. This ratio does not consider buffs. Ratio Abbreviation: NRADPS Ratio Name: Normalized Raid to Armory DPS. Description: This is like RADPS except that the time in combat has been “Normalized.” Wow Webstats computes time differently than some damage meters. If you are using Recap or Damage Meters this ratio will be the one for you to use. WWS does not count time that you spend out of combat when it computes your DPS, Recap and Damage Meters do count that time. Use: It is a measure of the overall performance of a hunter. Computation: It is computed just the same as RADPS; the only difference is in how I arrived at the numbers used in my tables. Divide the hunters DPS does to hostile targets (don’t include shatter at Gruuls, etc…) in a raid by their armory tooltip DPS when they have no buffs in the armory. Ratio Abbreviation: NRADPS w/o Pet Ratio Name: Normalized Raid to Armory DPS Without Pet Description: This is like RADPS w/o Pet except that the time in combat has been “Normalized.” Wow Webstats computes time differently than some damage meters. If you are using Recap or Damage Meters this ratio will be the one for you to use. WWS does not count time that you spend out of combat when it computes your DPS, Recap and Damage Meters do count that time. This ratio compares the hunter’s DPS without their pet to their armory DPS. Use: It is a measure of the overall performance of a hunter, excluding their pet. Computation: Subtract pet DPS from raid DPS, divide the product by armory tooltip DPS. Ratio Abbreviation: Pet % Ratio Name: Pet % of damage Description: This is a measure of the damage that a pet does in relation to the hunter’s damage. Use: It is used to measure the effectiveness of a hunter in utilizing their pet and how effective their spec is in producing pet damage. Computation: Add up all of the damage done by the pet, including kill command, and divide it by the total damage done by the hunter (including the pet). Ratio Abbreviation: QBuff Ratio Name: Quick Buffing Index Description: This ratio is a measure of how much of the amount the armory would predict auto shots would do vs. how much the hunter is actually doing with auto shots. Use: It is used to identify the effectiveness of buffing and grouping on a raid. It is less accurate than Autoshot Realization or the Buffing Index, but it is easier and quicker to compute. It relies heavily on co-variance to produce meaningful results. Computation: Divide the average non-critical auto shot in a raid by the Armory DPS amount. Ratio Abbreviation: RADPS Ratio Name: Raid to Armory DPS. Also called “White Paper Doll to DPS Multiplier” and “Raid to Tooltip Ratio.” Description: This ratio compares the DPS that a hunter puts out in a raid with the DPS they could be expected to put out based on their gear. The tool tip is not a “true” DPS measure, it is really a proxy variable. It does not take into consideration many factors that can impact DPS, for example crit rating, shot rotation and spec. However, tooltip is sufficiently covariant with “true” DPS that it can produce meaningful results when used as a proxy variable. Use: It is a measure of the overall performance of a hunter. Computation: Divide the hunters DPS does to hostile targets (don’t include shatter at Gruuls, etc…) in a raid by their armory tooltip DPS when they have no buffs in the armory. Ratio Abbreviation: RADPS w/o Pet Ratio Name: Raid to Armory DPS Without Pet Description: This ratio compares the hunter’s DPS without their pet to their armory DPS. Use: It is a measure of the overall performance of a hunter, excluding their pet. Computation: Subtract pet DPS from raid DPS, divide the product by armory tooltip DPS. Ratio Abbreviation: ROF Ratio Name: Rate of Fire Description: This is a measure of how fast a hunter fires. It is the inverse of Time Per Shot Use: It is a measure of the effectiveness of a hunter’s shot rotation. Computation: It is calculated by dividing the number of all shots taken by the time in combat. Ratio Abbreviation: SAR Ratio Name: Specials to auto ratio Description: This ratio measures the use of special shots. It compares special shots used to auto shots. Use: It is used to analyze the effectiveness of shot rotations in producing high rates of fire. Computation: Add up all of the special shots taken, and divide by the number of auto shots taken. Ratio Abbreviation: Time Per Shot Ratio Name: Time Per Shot Description: This is a measure of how long it takes to fire a shot. Use: It is a measure of the effectiveness of a hunter’s shot rotation. Computation: It is calculated by dividing the total time in combat by the number of all shots taken. Last edited by Elois; 06-27-2008 at 04:09 AM. |
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06-21-2008, 09:50 AM
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#2 |
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More data!
Elois
Night Elf
Hunter
<Driven>
Uldum
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Code:
GRUUL
Time
DPS w/o Armory RADPS per
Shatter DPS RADPS w/o Pet shot
B Top 1/3 993 334 2.98 2.35 1.41
Middle 1/3 871 340 2.57 2.10 1.40
Bottom 1/3 727 334 2.18 1.86 1.56
M Top 1/3 1,035 283 3.67 3.02 1.54
Middle 1/3 912 311 2.93 2.57 1.53
Bottom 1/3 696 306 2.27 2.14 1.72
S Top 1/3 995 315 3.16 2.79 1.38
Middle 1/3 833 300 2.77 2.56 1.39
Bottom 1/3 700 285 2.46 2.46 1.40
LURKER
Time Auto
DPS w/o Armory RADPS per Shot
Shatter DPS RADPS w/o Pet shot Realiz
B Top 1/3 1172 357 3.29 2.65 1.57 0.97
Middle 1/3 972 351 2.77 2.23 1.75 0.94
Bottom 1/3 834 358 2.33 1.96 1.68 0.86
M Top 1/3 1050 294 3.58 3.17 1.62 1.02
Middle 1/3 973 311 3.14 2.75 1.67 0.95
Bottom 1/3 896 357 2.51 2.41 2.37 0.78
S Top 1/3 1060 310 3.43 3.07 1.71 0.95
Middle 1/3 896 307 2.92 2.75 1.87 0.96
Bottom 1/3 632 298 2.12 2.10 1.99 0.86
GRUUL
Norm.
DPS w/o Norm. Norm. Ratio
Shatter DPS RADPS Ratio w/o pet
B Top 1/3 993 975 2.98 2.93 2.26
Middle 1/3 871 861 2.57 2.54 1.99
Bottom 1/3 727 703 2.18 2.10 1.71
M Top 1/3 1,035 1,006 3.67 3.56 2.85
Middle 1/3 912 912 2.93 2.93 2.48
Bottom 1/3 696 685 2.27 2.24 2.03
S Top 1/3 995 977 3.16 3.11 2.67
Middle 1/3 833 825 2.77 2.75 2.39
Bottom 1/3 700 700 2.46 2.46 2.32
LURKER
Norm.
DPS w/o Norm. Norm. Ratio
Shatter DPS RADPS Ratio w/o pet
B Top 1/3 1172 955 3.29 2.68 2.16
Middle 1/3 972 752 2.77 2.14 1.72
Bottom 1/3 834 661 2.33 1.85 1.55
M Top 1/3 1050 830 3.58 2.83 2.50
Middle 1/3 973 816 3.14 2.65 2.32
Bottom 1/3 896 502 2.51 1.40 1.35
S Top 1/3 1060 831 3.43 2.69 2.41
Middle 1/3 896 690 2.92 2.24 2.10
Bottom 1/3 632 527 2.12 1.77 1.75
GRUUL
Crit Hit Ratin AP
B Top 1/3 24.5% 100 1,600
Middle 1/3 26.2% 132 1,697
Bottom 1/3 24.3% 118 1,650
M Top 1/3 27.1% 52 1,577
Middle 1/3 27.2% 105 2,056
Bottom 1/3 25.0% 109 1,836
S Top 1/3 35.3% 103 2,112
Middle 1/3 32.2% 92 1,917
Bottom 1/3 30.8% 154 1,762
LURKER
Crit Hit Ratin AP
B Top 1/3 28.3% 108 1,797
Middle 1/3 26.2% 113 1,772
Bottom 1/3 25.7% 125 1,776
M Top 1/3 26.2% 40 1522
Middle 1/3 30.3% 73.5 1913
Bottom 1/3 25.6% 102 2229
S Top 1/3 34.3% 108 2,033
Middle 1/3 32.8% 96 2,031
Bottom 1/3 33.2% 98 1,794
GRUUL
Auto % Steady % Arcane %Multi % Aimed % Serpent%
B Top 1/3 34% 28% 4% 4% 1% 4%
Middle 1/3 37% 32% 4% 2% 1%
Bottom 1/3 36% 28% 9% 5% 0% 2%
M Top 1/3 35% 25% 7% 7% 1%
Middle 1/3 38% 17% 15% 12%
Bottom 1/3 41% 27% 14% 11% 2%
S Top 1/3 36% 27% 11% 8%
Middle 1/3 39% 24% 13% 12%
Bottom 1/3 39% 36% 18% 4% 0% 0%
LURKER
Auto % Steady % Arcane %Multi % Aimed % Serpent%
B Top 1/3 36% 26% 7% 5%
Middle 1/3 34% 29% 7% 4% 1%
Bottom 1/3 37% 30% 7% 5%
M Top 1/3 39% 27% 10% 6% 0% 0%
Middle 1/3 37% 20% 14% 11%
Bottom 1/3 42% 37% 14% 0% 0% 0%
S Top 1/3 36% 28% 13% 9%
Middle 1/3 36% 32% 15% 9%
Bottom 1/3 45% 21% 14% 15% 2%
GRUUL
Pet % shatter %
B Top 1/3 27% 3%
Middle 1/3 24% 4%
Bottom 1/3 18% 5%
M Top 1/3 22% 3%
Middle 1/3 15% 4%
Bottom 1/3 6% 4%
S Top 1/3 14% 3%
Middle 1/3 9% 6%
Bottom 1/3 0% 6%
LURKER
Pet % shatter %
B Top 1/3 24%
Middle 1/3 24%
Bottom 1/3 19%
M Top 1/3 13%
Middle 1/3 14%
Bottom 1/3 4%
S Top 1/3 12%
Middle 1/3 10%
Bottom 1/3 2%
GRUUL
Shots Shots Shots Shots Shots Special
per min per min per min per min per min shots to
auto steady arcane multi aimed autoshot
B Top 1/3 21.4 17.2 2.5 1.7 0.1 1.0
Middle 1/3 22.1 18.7 1.9 0.7 0.0 1.0
Bottom 1/3 18.7 14.7 3.3 2.0 0.0 1.1
M Top 1/3 18.3 13.7 4.1 2.8 0.1 1.1
Middle 1/3 19.3 8.7 7.1 4.3 0.1 1.0
Bottom 1/3 17.0 10.6 5.1 2.3 0.1 1.1
S Top 1/3 19.1 14.9 5.8 3.8 0.0 1.3
Middle 1/3 19.2 11.9 7.8 4.4 0.0 1.3
Bottom 1/3 18.8 15.0 7.4 1.5 0.0 1.3
LURKER
Shots Shots Shots Shots Shots Special
per min per min per min per min per min shots to
auto steady arcane multi aimed autoshot
B Top 1/3 19.7 14.3 3.0 1.8 0.0 1.0
Middle 1/3 16.9 14.3 2.6 1.1 0.0 1.1
Bottom 1/3 17.3 13.8 3.8 1.4 0.0 1.1
M Top 1/3 16.0 12.7 6.0 2.4 0.0 1.3
Middle 1/3 17.0 10.4 6.1 3.8 0.0 1.2
Bottom 1/3 11.4 9.9 3.8 0.1 0.0 1.2
S Top 1/3 15.4 11.8 4.7 3.2 0.1 1.3
Middle 1/3 13.8 10.9 4.6 2.9 0.0 1.4
Bottom 1/3 15.6 6.8 4.1 4.0 0.0 1.0
GRUUL
Avg Avg Avg Avg Avg Avg
norm norm norm norm norm norm
auto steady arcane multi aimed serpent
B Top 1/3 682 691 862 762 137
Middle 1/3 652 664 742 741 142
Bottom 1/3 639 662 707 783 148
M Top 1/3 782 790 841 907 1510
Middle 1/3 794 796 879 1029 1217 153
Bottom 1/3 715 751 846 960 1335
S Top 1/3 754 748 827 858
Middle 1/3 723 749 837 844
Bottom 1/3 634 703 839 779 0 0
LURKER
Avg Avg Avg Avg Avg Avg
norm norm norm norm norm norm
auto steady arcane multi aimed serpent
B Top 1/3 736 732 731 873
Middle 1/3 700 704 744 843 1,055
Bottom 1/3 648 661 711 740
M Top 1/3 752 738 831 880 0 0
Middle 1/3 779 787 836 946
Bottom 1/3 723 733 847 908 0 0
S Top 1/3 752 763 826 853
Middle 1/3 739 751 837 932
Bottom 1/3 657 663 665 835
GRUUL
Damage
Total Mana Damage without
Mana per per pet per
Used sec mana mana
B Top 1/3 13,936 51.1 18.7 13.5
Middle 1/3 12,794 45.5 19.2 14.7
Bottom 1/3 13,903 50.2 14.3 11.5
M Top 1/3 16,403 60.3 16.3 12.7
Middle 1/3 17,371 63.4 14.0 11.9
Bottom 1/3 13,561 50.0 13.3 12.3
S Top 1/3 18,340 66.8 14.3 12.3
Middle 1/3 18,963 71.7 12.4 11.3
Bottom 1/3 14,810 62.8 11.9 11.9
LURKER
Damage
Total Mana Damage without
Mana per per pet per
Used sec mana mana
B Top 1/3 18,123 46.0 20.1 15.1
Middle 1/3 18,701 41.6 17.8 13.5
Bottom 1/3 21,583 46.7 15.6 12.4
M Top 1/3 21,775 57.0 15.1 13.2
Middle 1/3 25,823 60.0 13.4 11.6
Bottom 1/3 15,755 33.4 13.4 12.9
S Top 1/3 19,023 54.6 14.5 12.8
Middle 1/3 20,648 50.8 14.0 13.0
Bottom 1/3 22,675 46.3 11.1 11.0
LURKER Only, no data for Gruul
Time
Clippingper
Index Shot
B Top 1/3 0.70 1.57
Middle 1/3 0.60 1.75
Bottom 1/3 0.61 1.68
M Top 1/3 0.67 1.62
Middle 1/3 0.74 1.67
Bottom 1/3 0.50 2.37
S Top 1/3 0.66 1.71
Middle 1/3 0.58 1.87
Bottom 1/3 0.67 1.99
GRUUL
% of shot
damage % of shot
from damage
normal from
shots crits
B Top 1/3 57% 43%
Middle 1/3 56% 44%
Bottom 1/3 59% 41%
M Top 1/3 51% 49%
Middle 1/3 54% 46%
Bottom 1/3 57% 43%
S Top 1/3 47% 53%
Middle 1/3 48% 52%
Bottom 1/3 42% 58%
LURKER
% of shot
damage % of shot
from damage
normal from
shots crits
B Top 1/3 52% 48%
Middle 1/3 55% 45%
Bottom 1/3 56% 44%
M Top 1/3 37% 63%
Middle 1/3 50% 50%
Bottom 1/3 52% 48%
S Top 1/3 39% 61%
Middle 1/3 40% 60%
Bottom 1/3 48% 52%
Last edited by Elois; 06-21-2008 at 09:58 AM. |
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06-21-2008, 09:51 AM
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#3 |
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More data!
Elois
Night Elf
Hunter
<Driven>
Uldum
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I have now created a statistical calculator that you can use to compute these ratios for yourself. It is hosted at TKASomething. Click the link below to download it.
http://tkasomething.com/statcalc.xls Last edited by Elois; 07-14-2008 at 06:06 AM. |
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06-22-2008, 10:22 AM
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#4 |
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Mathmagician
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My eyes just kinda glazed over those zillions of definitions, but I'm sure it will be great for reference later. It's a year after the initial damage-tooltip ratio thread came out, and I haven't heard much about it since. Although I was excited about the work at the time, unless I'm forgetting or missed something, I thought this just kinda disappeared from the world. Have you kept up with your findings in some secluded corner I never noticed?
In any event, I stand by one assertion I made in the old thread: the D-T ratio is a prime indicator of the player's effectiveness at playing a hunter. For that reason alone, I think it's important to analyze. Granted, there are variables -- the ratio excludes crit, raid synergies and buffs/debuffs, and simply your spec/rotation. However, within a vacuum, it's a tremendously profound statement about whether you can consider yourself a good player or a bad player with good gear. Here's to hoping this thread is the indicator that somebody (Elois or maybe someone else entirely) will analyze the topic and find out something more from it. |
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06-23-2008, 03:46 AM
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#5 | |
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Venkman
Druth
Night Elf
Hunter
<Chimera>
(EU)Bronzebeard
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Thanks for posting this - haven't had time to complety go through it but i've got a question
Quote:
surely this ratio doesn't take in to account the benefits of Leader to the pack if it is only looking at the average damage of non crits? |
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06-23-2008, 04:40 AM
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#6 | |
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More data!
Elois
Night Elf
Hunter
<Driven>
Uldum
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Quote:
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06-23-2008, 04:45 AM
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#7 | |
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More data!
Elois
Night Elf
Hunter
<Driven>
Uldum
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Quote:
As the title says, this is a reference guide. It is worthwhile to read and refer to, but unlike the orginal post, I really don't get into the WHY. My findings have "resurfaced." I held off on releasing "Grades for BM hunters" until I did this post. I expected that post would generate a lot of questions, and the White Paper Doll to Raid DPS Multiplier thread would not do the job of answering them. |
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06-24-2008, 09:59 AM
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#8 | |
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Venkman
Druth
Night Elf
Hunter
<Chimera>
(EU)Bronzebeard
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Quote:
Hmm - I'm not sure how relevent your calculations for auto shot realization can be if they don't take into consideration Leader of the pack (probably the best individual group buff available to a hunter). |
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06-26-2008, 04:14 PM
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#9 | |
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More data!
Elois
Night Elf
Hunter
<Driven>
Uldum
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Quote:
They are relevant. I don't have to be 100% accurate to be useful. The ratios that banks use to assess credit worthiness are based on less accurate data than what I am using. I am only breaking my data into three groups, so I have a very wide margin for error. I rely a lot on the concept of covariance to acheive valid results. In other words, even if I don't get the right variable to use, it is closely related to the true variable, and the error is not big enough to matter. Perhaps there is another way to think of it. Cheeky is Issacc Newton who came up with the math formulas. I am the guy in the lab coat who is doing the measurements. Friction is left out of Newtons forumlas, but friction and a variety of other variables show up in lab measurements. We just hope the other variables are small enough to not matter much. |
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06-26-2008, 04:39 PM
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#10 | ||||||
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/more to come as I look at it Last edited by Olem; 06-26-2008 at 05:00 PM. |
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