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Mar 10, 2010, 02:07 AM // 02:07
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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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Symbolic and Graphical Investigation of the Efficiency of Water Magic Snares
NOTE: All charts, values, and equations are up to date. If there's a part doesn't make sense, please let me know!
TABLE OF CONTENTS Post 2: Introduction Post 3: Parameters & Standards/Settings Post 4: Charts Post 5: Variables Post 6: “By Round” Equations Post 7: Graphical Examples Post 8: Convergence Equations Post 9: Proofs of the Convergence Equations Post 10: Mesmer Fast Casting vs. Elementalist Higher Attributes Post 11: Conclusions Post 12: FAQ Post 13: Outdated Work Last edited by Frozen Ele; Dec 31, 2010 at 11:55 PM // 23:55.. |
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Mar 10, 2010, 02:08 AM // 02:08
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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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Introduction
INTRODUCTION
This thread is an exploration and evaluation of water magic snares, both solo and in combination. By combination, I mean a chain of snares; casting one and then another snare. The primary point of evaluation is the efficiency of each snare, or the percent of time that a snare is active/affecting a foe. In assessing the efficiency, equations were created to symbolically derive the efficiency, both “by round” and convergence. By “by round,” I mean the time of recharge of the snare – or combination of snares; “by round” is the time it takes to be able to cast a snare, or two, until it has recharged. Convergence would be when the number of “rounds” (time it take to cast the same snare set) approaches infinity. Thus, with the equations of efficiency, one can find the percent of time active of a snare or combination of snares both over a definite period, or over an infinite interval. In this thread, the equations of efficiency and the convergence values are presented, as well as a few graphical representations of the equations. NOTE: The equations presented in this study generally work for water magic 9 or more. Below 9 water, Equation Set #1 still holds, as well as the Signle Snare Equations, but Equation Set #2 doesn't always hold (the coefficient of 2 on Set #2 might become 3 or greater, depending on how far below 9 water magic you have). Also, this study includes investigation on damage output (DPS), energy management (EPS), and the amount of time one would spent casting for sinlge snares and combinations of two snares. Equations for representing DPS, EPS, and percent of time casting were generated, for both "by round" and convergent use. I have decided to only focus on single snares and a combination of two snares. Focusing on combinations of three snares or more would explode the scope of this investigation - in a combination of two snares, there are only two different orders of snares, whereas in a combination of three, there are six different orders of casting the snares. With that being said the purpose of the study is as follows: To present a comprehensive method (be it referencing tables, or using equations) to compare the efficiency, damage output, energy management, and percent of time casting of both single snares and combinations of two snares. Just a few notes before we move on (not in any particular order): The highest level of math involved is calculus, although the majority is algebra. The calculus used is lower-level calculus (L’Hospital’s Rule) and the equations and tables are still usable without understanding calculus. I’ve had the majority of the math done for a while now, but have been too lazy to get around to actually type it up and present it, and have only typed up so much. The scratch work and work to derive the “by round” equations are not posted, nor typed, but if enough people would like to see that work, I’d be up for scanning and posting it. 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. If you haven’t figured out already, each section in the table of contents is its own post, that way it’s easier to find the section you’re looking for. I am assuming that anyone who reads this understands what a water magic snare is. If you don’t, look here. I might end up updating sections here and there, so stay tuned. Last edited by Frozen Ele; Jun 14, 2010 at 12:52 AM // 00:52.. |
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Mar 10, 2010, 02:09 AM // 02:09
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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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Parameters & standards/settings
PARAMETERS & STANDARDS/SETTINGS
In this investigation, I assumed a few things/used certain settings (in no particular order):
Last edited by Frozen Ele; Jun 14, 2010 at 12:53 AM // 00:53.. |
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Mar 10, 2010, 02:09 AM // 02:09
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Jungle Guide
Join Date: Jul 2009
Guild: Mirror of Reason [SNOW]
Profession: E/N
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Charts
CHARTS
Convergence Chart Here is the chart for both a single hex and a chain of two hexes for convergence efficiency, DPS, EPS, and percent of time casting. By convergence, I mean the efficiency, etc. if you were to keep casting the snare or snare combination continuously for a while. With snare combinations and these convergence values, it doesn't matter which of the two snares is cast first, so long as they are cast in the proper sequence - which is indicated by the reference equation - and for a significant amount of time. On the other hand, if only casting a few "rounds" of the snare(s) (indicated by the round time in this chart - ex. casting the Deep Freeze + Ice Spikes snare sequence for 34 seconds would be two rounds), refer to the "By Round" Chart (below this chart). Quick note: if the efficiency is over 100%, it suggests that there is an overlap in the duration of the snare(s); when the snare is cast again, or the second is cast, the duration from the first hex has not expired yet (I can explain this more thoroughly). What this means is that there can be “human error”; the caster doesn’t have to count seconds as much to maximize efficiency.
“By Round” Chart Coming soon! Last edited by Frozen Ele; Apr 07, 2011 at 12:35 AM // 00:35.. |
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Mar 10, 2010, 02:10 AM // 02:10
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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
VARIABLES
Here’s the list of variables used in the following equations: 
Last edited by Frozen Ele; Apr 24, 2010 at 01:10 AM // 01:10.. |
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Mar 10, 2010, 02:10 AM // 02:10
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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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“By round” equations
“BY ROUND” EQUATIONS
These are the “by round” equations. For a single hex, the “by round” equation is:  The following equations are for snare combinations. Notice that there are limits on each equation, so depending on which chain of hex you’re looking at, the equation you’ll use will vary. The variance depends on whether you can cast the second snare twice while waiting for the first to recharge. Here’s the implications of each set: (#1) This is the most commonly used equation set, where the second snare is cast during the “cool-down” time for the first snare (the time where the snare is not affecting a foe and is recharging; gap between the end of the duration of the snare and until it has recharged), but because of the length of the recharge of the second snare and the shortness of the cool-down for the first, the second snare can only be cast once before the first snare can be cast again. Effectively, this means that one is alternating between two snares: snare one, then snare two, then snare one, etc. (#2) This is where the recharge of the second snare is shorter than the cool-down for the first, so that the second snare can be cast twice while waiting for the first snare to finish recharging. What this means is that the first snare is cast, then the second is cast, the second is cast again, the first snare is cast, etc.  NOTE: The equations presented in this study generally work for water magic 9 or more. Below 9 water, Equation Set #1 still holds, as well, as the Signle Snare Equations, but Equation Set #2 doesn't always hold (the coefficient of 2 on Set #2 might become 3 or greater, depending on how far below 9 water magic you have). Last edited by Frozen Ele; Apr 06, 2011 at 02:52 AM // 02:52.. |
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Mar 10, 2010, 02:11 AM // 02:11
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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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Graphical examples
GRAPHICAL EXAMPLES
The following are some examples of the efficiencies of snare combinations over time. Each example, follows a different equation set: Shard Storm + Ice Spikes is from set #1 and Ice Prison + Frozen Burst is from set #2. Notice how the efficiency is slightly larger when you use the snare with the shorter cast time first, but as the time goes to infinity, they will converge to the same number. (This is because the ratio between the time active and total time will be greater, because the total time is increased less) Shard Storm + Ice Spikes:  Frozen Burst + Ice Prison: 
Last edited by Frozen Ele; Apr 06, 2011 at 03:39 AM // 03:39.. |
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Mar 10, 2010, 02:12 AM // 02:12
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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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Convergance equations
CONVERGANCE EQUATIONS
These are the convergence equations, which is the optimal efficiency should someone keep casting the combination of snares for infinity. For a single hex used repeatedly, the efficiency, DPS, etc. values are listed in the chart above, but here's the convergence equation:  The following equations only deal with the convergent efficiencies, etc. of a chain of hexes. The convergence efficiencies, etc. for all combinations of two hexes are listed in the above chart, so one might not find this section to be too helpful, aside from how I derived the efficiencies, etc. Each convergence equation corresponds to one of the “by round” equation sets from above:  NOTE: The equations presented in this study generally work for water magic 9 or more. Below 9 water, Equation Set #1 still holds, as well, as the Signle Snare Equations, but Equation Set #2 doesn't always hold (the coefficient of 2 on Set #2 might become 3 or greater, depending on how far below 9 water magic you have). Last edited by Frozen Ele; Apr 06, 2011 at 02:49 AM // 02:49.. |
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Mar 10, 2010, 02:12 AM // 02:12
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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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Proofs of the convergence equations
PROOFS OF THE CONVERGENCE EQUATIONS
The following are the proofs from how the convergence equations are derived from the “by round” equations. This is the only section with calculus involved and is a crucial section, so one might want to not read it in the interests of time. Single Snare:  Snare Combination: 
Last edited by Frozen Ele; Apr 06, 2011 at 02:46 AM // 02:46.. |
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Mar 10, 2010, 02:13 AM // 02:13
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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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Mesmer Fast Casting vs. Elementalist Higher Attributes
Mesmer Fast Casting vs. Elementalist Higher Attributes
Quote:
It’s important to remember that the maximum rank a mesmer could have in water magic (void of other skills or factors – such as Glyph of Elemental Power, etc.) would be 12. The following is a table comparing the efficiencies of an elementalist casting the snare (rank 15 water magic) compared to a mesmer casting it (rank 12 water magic, rank 15 fast casting):
Out of all of the sinlge snares, the only snare that could be cast better as a mesmer than as an elementalist was Deep Freeze, primarily because it has a set duration. All other snares cast by a mesmer would have a decrease in efficiency anywhere between 4.44% to 22.22%. As such, for a single snare, it is normally more efficient for an elementalist to cast it rather than a mesmer. There are only one instance out of the fourty-four different dual snare combinations in which a mesmer casting the combination would be better than an elementalist casting the combination, which is when a mesmer is casting Deep Freeze and Frozen Burst. On average, a mesmer will cast water magic snare (or combination) with a decrease of efficiency of over 10%, causing elementalists to be more efficient at casting water magic snares than mesmers. Last edited by Frozen Ele; Apr 06, 2011 at 01:09 AM // 01:09.. Reason: Type-o |
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Mar 10, 2010, 02:13 AM // 02:13
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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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Conclusions
CONCLUSIONS
Just a few final notes and highlights from this investigation: (1) Winter’s Embrace has the worst efficiency of all the snares. (2) Any combination of two snares, when executed correctly, has an efficiency of over 75%, many with an efficiency near 100% (3) If not casting your chain of snares for infinity, it’s more efficient to cast the one with the shorter cast time first (reference the “by round” equations and the graphical examples). (4) There are certain casting patterns to maximize the efficiency of a combination of snares (reference "by round" equations). (5) Some hex combinations actually allow for human error to still have 100% efficiency (reference charts). (6) Elementalists are more efficient at casting water magic snares than mesmers. Last edited by Frozen Ele; Mar 13, 2010 at 09:52 PM // 21:52.. Reason: Type-o |
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Mar 10, 2010, 02:14 AM // 02:14
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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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Faq
FAQ
Place for questions and answers, in no particular order: Quote:
The reason for providing the equations, and not just the charts, is so one can go back through and insert whatever rank of water magic he/she is using and find the efficiency for his/her particular build. Once again, I tailored this investigation towards what I use, but did not prevent anyone else from using in the equations with what they use. Quote:
Quote:
Yes, as time continues Mind Freeze [E] will become less effective, but I side-stepped the matter of energy within this investigation and is a limitation on any snare combos with Mind Freeze [E]. Quote:
For other skills like Echo and Arcane Echo, the recharge could fundamentally be "zero" for the first few round(s) and then it would be the normal value, meaning you'd have to treat those first n number of rounds distinctly from the continuing rounds. The values one is plugging into the equations just need to be modified to reflect the changes to the skills and if need be, separate rounds to evaluate separately. Quote:
Reflecting on this, I should have titled the investigation: "Symbolic and Graphical Investigation of the Efficiency of Snares" with a specific focus on water magic snares. I will go ahead and churn out the single snare efficiencies of the earth snares. If enough people want, I can expand this to also include single mesmer snares, and then combinations of mesmer snares, combinations of earth snares, and then combinations of earth and water snares, water and mesmer snares, and earth and mesmer snares. Quote:
Quote:
For an example, if you wanted to experimentally derive the "convergence" 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 for all 54 total combinations (an average trial time of 200-300 seconds - since you have to perform each combination ~10 times sequentially to reach the "convergence" efficiency), it would take about 56.8 to 85.2 millenniums. Last edited by Frozen Ele; Apr 06, 2011 at 03:10 AM // 03:10.. Reason: Type-os |
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Mar 10, 2010, 02:14 AM // 02:14
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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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Outdated Work
OUTDATED WORK
This section holds the old charts, equations, and graphs before certain skill updates. You can use this section to see how much snaring, and this thread, has changed since March 9th, 2010. Pre-April 23rd, 2010 Charts Pre-Skill Balance on May 21st, 2010 (Changed Fast Casting) Pre-Skill Balance on December 9th, 2010 (Changed Freezing Gust) Pre-Clean-Up on April 5th, 2011 Last edited by Frozen Ele; Apr 07, 2011 at 12:23 AM // 00:23.. |
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Mar 10, 2010, 02:53 AM // 02:53
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#14 |
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Ascalonian Squire
Join Date: Aug 2009
Guild: Currently a Free Agent
Profession: Rt/
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Very impressive, but WAY too much work imo. How long did all of this take you? I feel like you could have cured cancer or HIV or someting
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Mar 10, 2010, 03:10 AM // 03:10
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#15 |
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Desert Nomad
Join Date: Mar 2008
Location: Sacramento, CA
Guild: Geezers
Profession: R/
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Or you could just kill the guy.
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Mar 10, 2010, 03:40 AM // 03:40
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#16 |
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Forge Runner
Join Date: Jan 2007
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I appreciate the work you put into this, but... ah well, who am I kidding. It's a game. I went into battle a few times with water snares and let them do the work for me while enjoying them attempt to chase after me. Quite enjoyable.
But hey, if this is your thing, to analyze all this data and enjoy it, more power to ya, honestly. |
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Mar 10, 2010, 04:41 AM // 04:41
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#17 |
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Departed from Tyria
Join Date: May 2007
Guild: Clan Dethryche [dth]
Profession: R/
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I am going to have fun looking through all of this and the math you went through when I wake up tomorrow morning.
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Mar 10, 2010, 05:30 AM // 05:30
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#18 |
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Forge Runner
Join Date: Apr 2008
Location: Canada
Profession: E/
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Very interesting, it looks like you've put quite a bit of time into this and now you can at least say someone else found your findings worthwhile
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Mar 10, 2010, 06:48 AM // 06:48
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#19 |
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Krytan Explorer
Join Date: Dec 2008
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very nice work, so did any of it change your strategy while using water hexes? ah do you think then that there would be much differences if someone were to play fast cast mesmer?
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Mar 10, 2010, 10:26 AM // 10:26
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#20 |
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Ascalonian Squire
Join Date: Oct 2009
Location: Euro
Guild: [YUM]
Profession: N/
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Congratulations on getting a masters degree in Water magic ^^ Impressive thread, very usefull and helpfull. Its amazing how some people set their mind to something and expand the existing borders to clarify stuff. Good work
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