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May 01, 2011, 02:50 AM // 02:50
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#1 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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An Investigation of Water Magic Snares’ Ability to Increase AoE
Abstract (Summary)
This thread quantifies the increase of damage-over-time AoE (AoEDoT; just referred to as “AoE” throughout) efficiency by using snares. In Hard Mode, the average AoE efficiency of using a water snare is 168.36%. Knowing that the AoE will coincide with the duration of the water snare (“guaranteed”), the average efficiency is 187.54%. Casting AoE without knowing if the water snare is in effect or not (“happenstance”), the efficiency is 149.18%. Compared to other traditional snares (cripple, knockdowns, body-blocking with minions), the average AoE efficiency is greater with water snares than any other measure. In other words, water snares are the best method to increase AoE efficiency by increasing the number of hits foe(s) will take. Other methods to increase AoE efficiency, however, include increasing the damage per hit and the number of foes hit, both of which largely do not apply to snares. This thread also provides:
Last edited by Frozen Ele; May 01, 2011 at 03:46 AM // 03:46.. |
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May 01, 2011, 02:53 AM // 02:53
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#2 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Table of Contents
Post 1: Abstract (Summary) Post 2: Table of Contents Post 3: Introduction Post 4: Parameters Post 5: Variables Post 6: AoE Efficiency Post 7: Additional Hits and Hits Without Snaring Post 8: Guaranteed vs. Happenstance Post 9: Guaranteed Post 10: Happenstance Post 11: Snares vs. Cripple/Knockdowns/Minions (Body-Blocking) Post 12: Conclusions Post 13: Equations Catalog Post 14: FAQ Post 15: Outdated Work Post 16: Extra Space Last edited by Frozen Ele; May 01, 2011 at 03:39 AM // 03:39.. |
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May 01, 2011, 02:55 AM // 02:55
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#3 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Introduction
We all know snaring makes AoE (area of effect skills, especially damage-over-time ones) more efficient; it slows down foes, making them take longer to leave the area. The questions remains, however, exactly how much does snaring increase AoE efficiency and can we quantify this increase? These questions frame this investigation and answers to both will be explored. This study is an extension of the “Symbolic and Graphical Investigation of the Efficiency of Water Magic Snares” and as such, there are some common elements:
Constructive feedback/criticism is always welcome; if I made a mistake, let me know. After I modify/fix a section, I’ll post with the critic’s suggestion in quotes, saying what section I modified. This investigation was done, to be honest, for me; when I did this investigation, I didn’t have the original intention of posting my findings, but decided that other people might be interested/benefit from it. As such, I have no problem removing any of the material, so if there are plenty of trolls, I will delete my posts. I don’t expect this to happen, but I want to give a fair warning. Last edited by Frozen Ele; May 01, 2011 at 03:43 AM // 03:43.. |
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May 01, 2011, 02:58 AM // 02:58
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#4 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Parameters and Assumptions
In this investigation, I assumed a few things/used certain settings (in no particular order):
Last edited by Frozen Ele; May 01, 2011 at 03:39 AM // 03:39.. |
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May 01, 2011, 02:59 AM // 02:59
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#5 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Variables
Here’s a list of all of the variables used in the study and a brief description of each:  There should be a hyperlink to my previous investigation with the first variable. The hyperlink is here. Last edited by Frozen Ele; May 01, 2011 at 03:39 AM // 03:39.. |
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May 01, 2011, 02:59 AM // 02:59
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#6 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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AoE Efficiency
Three factors affect AoE efficiency: the number of foes hit, the number of hits (how many ticks/packets of damage dealt), and the damage per hit. Multiplying these factors yields the total damage of the snare:  The problem with this method is that each foe can have a different armor value or be hit a different number of times, causing the damage per hit and the number of hits to differ by foe. Thus, we can look at the total damage of a snare as the sum of the damage dealt (number of hits times damage per hit) to each foe:  Whichever method you choose to evaluate AoE damage depends on the assumptions you want to make and that you’re comfortable making. Regardless of the method, AoE efficiency can be expressed as the actual damage the AoE deals over the theoretical maximum it can do:  -OR-  Snares primarily affect the number of hits. Aside from the damage dealt from the snare, the snare doesn’t increase the damage per hit. As for the number of foes hit, using snares with initial agro can help to control enemy movement and ball them better, however, this usually requires another mechanism to fully achieve (i.e. minions, EVAS, etc. to deter the foes). Because snaring can’t usually increase the number of foes hit alone, its potential ability to improve this factor will be ignored. Since the number of foes and damage dealt per hit remains constant, the number of assumptions required to use former method to assess AoE efficiency decreases. The only assumption remaining is that this method assumes the foes will all be hit the same number of times (the foes are at the same location within the AoE). This assumption can be sidestepped by using average values: the average hits for foes within AoE at a given AoE range size. The AoE efficiency from a snare can be expressed as the AoE efficiency with the snare over the AoE efficiency without the snare:  We can simplify this result to:  This result has powerful implications:
Last edited by Frozen Ele; May 01, 2011 at 03:40 AM // 03:40.. |
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May 01, 2011, 03:00 AM // 03:00
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#7 | ||||||||||||||||||||||||
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Additional Hits and Hits Without Snaring
Now that the AoE efficiency increase has been isolated to two variables, we can examine these more closely: Hits Without Snaring The average number of times an AoE skill will hit a foe varies based off the AoE size (“adjacent,” “nearby,” “in the area”), mode difficulty, and the location of the foe(s) within the AoE. The empirically derived hits without snaring are:
Additional Hits Snaring increases hits by causing foes to move slower. By moving slower, the time it takes them to escape the AoE range increases, allowing the AoE to hit more times. As such, the additional hits gained from snaring depend on how many times slower the foe is moving than normal, the normal amount of time to leave AoE, and the time per hit. We can express the number of times slower than normal the foe is moving as:  The empirically derived normal AoE escape times are:
Multiplying the number of times slower and the normal AoE escape time yields the total time that a foe will take to leave the AoE under the snare. To get to the additional hits caused by the snare, we’re only interested in the additional time the foe stays in AoE, so from this total time, we must subtract out the time that it would normally take the foe to leave AoE. Thus, the additional time the foe is in AoE is:  Taking advantage of the time per hit, we can convert the additional time into additional hits:  Almost all AoE have a period of one second (one second per hit) although there is the occasional Meteor Shower (three seconds per hit). Ignoring the rare cases like Meteor Shower, the additional time will equal the additional hits:  Substituting this general expression for the additional hits into the AoE efficiency equation yields:  All components of this equation have been flushed out except for one parameter, P. P will be explored in the next post. Last edited by Frozen Ele; May 01, 2011 at 03:20 AM // 03:20.. |
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May 01, 2011, 03:00 AM // 03:00
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#8 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Guaranteed vs. Happenstance
P is the slow-down percentage that the foe experiences. This value could be the actual percentage listed in the skill description or it could be an average percentage based off the efficiency of the snare. How do we know when to use each? Guaranteed If we can guarantee that the AoE will be active while the snare is up, we know exactly what percentage the foe will be moving at – the percentage listed in the skill description:  This usually means that we’re timing our snares and making sure that they coincide with the AoE, either by calling or micro-ing. Here, we know when exactly the AoE will be cast to we can ensure overlap between the snare and AoE. Examples include: using a snare to call AoE, micro-ing heroes to use AoE/snare at the right time, etc. Happenstance Sometimes, however, we don’t know exactly when the AoE will be cast or where it might even be coming from. If this is the case, then sometimes the snare will be up when AoE is up and sometimes not. We can arrive at the average slow-down percentage by multiplying the percentage listed in the skill description by the efficiency of the snare (percent of time the snare is active):  This usually means that we’re not timing AoE or micro-ing, but letting our teammates and possible other allies act by their own pace and cast the AoE whenever. Now that we’ve grappled with all of the variables affecting AoE efficiency, we can calculate the AoE efficiency with a snare active: Last edited by Frozen Ele; May 01, 2011 at 03:22 AM // 03:22.. |
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May 01, 2011, 03:01 AM // 03:01
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#9 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Guaranteed
***From these charts, the average “guaranteed” additional hits is 2.30 and the average “guaranteed” AoE efficiency is 187.54%.*** Remember, here we know that the AoE will be cast while the snare is up; we can guarantee the snare’s effect. General efficiency equation: Being “guaranteed,” we know: So the “guaranteed” equation for AoE efficiency becomes:  As such, the equation for the additional hits becomes:  Here’s the chart for the “guaranteed” additional hits while a single snare or snare combination is in effect:
Here’s the chart for the “guaranteed” AoE efficiency values while a single snare or snare combination is in effect:
Last edited by Frozen Ele; May 01, 2011 at 03:49 AM // 03:49.. |
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May 01, 2011, 03:02 AM // 03:02
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#10 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Happenstance
***From these charts, the average “happenstance” additional hits is 1.29 and the average “happenstance” AoE efficiency is 149.18%.*** Remember, here we don’t know that the AoE will be cast while the snare is up; the snare’s effect is happenstance. General efficiency equation: Being “happenstance,” we know: So the “happenstance” equation for AoE efficiency becomes:  As such, the equation for the additional hits becomes:  Here’s the chart for the “happenstance” additional hits while a single snare or snare combination is in effect:
Here’s the chart for the “happenstance” AoE efficiency values while a single snare or snare combination is in effect:
Last edited by Frozen Ele; May 01, 2011 at 03:48 AM // 03:48.. |
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May 01, 2011, 03:02 AM // 03:02
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#11 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Snares vs. Cripple/Knockdowns/Minions (Body-Blocking)
So far, we’ve been able to quantify the AoE efficiency with a snare, ~149% for happenstance and ~188% for guaranteed, averaging to ~168% between the two. How does this AoE efficiency compare to the use of other “traditional snares,” like cripple, knockdown, and to an extent, minions? Cripple The glaring problem with cripple is its slow-down percentage; it’s only 50%. A 66% snare can cause the foe to move about three times slower, but crippling the foe only yields two times slower. With this decreased percentage, crippling the foes will result in a significantly lower AoE efficiency. Assuming a 100% efficient cripple (it’s guaranteed the foes will be crippled with the AoE is in effect; the “guaranteed” AoE efficiency), the average AoE efficiency against Hard Mode foes is 122.20%. This “guaranteed” efficiency is drastically lower than either of snaring’s average efficiencies; snaring’s “happenstance” efficiency is greater than crippled’s “guaranteed” efficiency. Knockdowns Knockdowns have the ability to completely immobilize a foe for a standard time of two seconds. This means that there is a 100% slow-down percentage for two seconds. If placed perfectly when the foes begin to move, knockdowns will trap foes in the AoE for an additional two seconds, translating to an average AoE efficiency of 177.80%. This is knockdowns’ average “guaranteed” AoE efficiency. Comparing this to snaring’s average “guaranteed” AoE efficiency (187.54%), we see that between a guaranteed knockdown and guaranteed snare, snaring is better. In terms of “happenstance” efficiency, most knockdowns, especially Elementalist ones, have such a long recharge that their efficiency becomes extremely low. For example, Meteor is only 6.25% efficient and Earthquake is only 11.11% efficient. Therefore, using happenstance knockdowns to increase AoE efficiency will yield poor results. The average “happenstance” AoE efficiency for Meteor is 101.48% and 102.77% for Earthquake. Such efficiencies pale in comparison to snaring’s 149.18%. Minions (Body-Blocking) Spirits, pets, and minions have the ability to body-block, increasing AoE efficiency by prevent foes from moving. The primary use of body-blocking in PvE is minions. The AoE efficiency increase from minions is incredibly difficult to quantify precisely and accurately because of the variability in the efficiency increase. If there are too few minions, too many foes, foes too spread out, etc., then minions cannot adequately body-block. Additionally, you can’t control minion movement. Minions can body-block the wrong foes (you’re using AoE on the casters when all of the minions are surrounded around the melee, etc.), yielding no efficiency increase. Because snares are controllable and reliable, they are better suited to increase AoE efficiency. Last edited by Frozen Ele; May 01, 2011 at 03:40 AM // 03:40.. |
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May 01, 2011, 03:03 AM // 03:03
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#12 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Conclusions
Here are some highlights of the investigation:
Last edited by Frozen Ele; May 01, 2011 at 03:29 AM // 03:29.. |
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May 01, 2011, 03:03 AM // 03:03
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#13 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Equations Catalog
These are the equations used in the study: General Equations:  “Guaranteed” Equations: “Happenstance” Equations: Here are other equations that relate to this investigation, though I decided not to include them in the body of the study:  Last edited by Frozen Ele; May 01, 2011 at 03:33 AM // 03:33.. |
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May 01, 2011, 03:04 AM // 03:04
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#14 | ||
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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FAQ
Place for questions and answers, in no particular order: Quote:
Quote:
For an example, if you wanted to experimentally derive the efficiency percentages for all single and snare combinations and be 99% confident that all of the experimental efficiencies were within 0.01% of the true efficiencies, you'd have to perform about 166 million trials for each snare combination. Doing this will take millenniums. Last edited by Frozen Ele; May 01, 2011 at 03:34 AM // 03:34.. |
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May 01, 2011, 03:04 AM // 03:04
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#15 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Outdated Work
If I change any aspects of this investigation, the older work will be posted here so you can see how the study has progressed. Last edited by Frozen Ele; May 01, 2011 at 03:34 AM // 03:34.. |
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May 01, 2011, 03:05 AM // 03:05
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#16 |
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Extra Space
Last edited by Frozen Ele; May 01, 2011 at 03:35 AM // 03:35.. |
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May 01, 2011, 04:26 AM // 04:26
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#17 |
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Krytan Explorer
Join Date: Nov 2010
Guild: Social Darwinism [SaD]
Profession: A/W
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Dude, I don't even like doing this stuff for REAL data, why are you doing this for GW?
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May 01, 2011, 04:55 AM // 04:55
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#18 | |
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Krytan Explorer
Join Date: Sep 2010
Location: Home
Guild: En Caligne Veritas [DARK]
Profession: R/Rt
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Quote:
But my head hurts just looking at the formula.... |
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May 01, 2011, 05:00 AM // 05:00
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#19 |
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Academy Page
Join Date: Dec 2007
Location: Smalltownville USA
Guild: OWEN
Profession: D/A
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O.o
So snares are good...Right? |
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May 01, 2011, 05:00 AM // 05:00
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#20 |
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Krytan Explorer
Join Date: Oct 2007
Guild: Jay To Much [SrE]
Profession: Me/N
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What grade did you get for this lab report? And did your professor give you any witty remarks?
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