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 Elois 01/19/09 1:22 PM

Statistical Reference Guide for hunters

FORWARD:

This was originally posted at TKASomething. I have found it to be an excellent reference guide, and very useful for understanding my own DPS performance, the performance of other hunters, and raid configurations. I have left it in its original formatting.

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 (White Paper doll to Raid DPS multiplier - TKA Something), 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 The Risk Management Association.

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.
Covariance - Wikipedia, the free encyclopedia

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.
Proxy (statistics) - Wikipedia, the free encyclopedia

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 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 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 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 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.

LINK TO A STATISICAL CALCULATOR THAT COMPUTES THESE RATIOS

http://tkasomething.com/statcalc.xls

 Elois 01/19/09 1:24 PM

EXAMPLE OF A STATISTICAL STUDY

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%```

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