Curse

Frozen Ele · May 06, 2011, 08:24 PM // 20:24

Quote:

Originally Posted by Mouse at Large

This is soooooo impressive

However, and I apologise if I have missed it, another factor that might be taken into consideration is the total damage dealt.

Let me explain - if you are running a water ele for snaring, then you are, in effect, lessening your teams damage output as (in general) the direct damage from the spell is small. Therefore, the TOTAL damage dealt during the snare/DoTAoE event is potentially less (by some unquantified amount) than say two DoTAoEs which may not hit so many targets due to scatter, but over their duration will provide more total damage than a snare/DoTAoE combo.

This may never be amenable to the sort of analysis carried out in this thread, as there would probably have to be too many assumptions made re. the variables, but it's a thought

Thanks for the compliment

. You’re post is very interesting because I never really though about that scenario (or similar ones). Looking at (DoTAoE + Snare) vs. (2 DoTAoEs), it depends on the damage of the DoTAoE. Here’s a basic look at the general scenario of (less DoTAoE with snare) vs. (more DoTAoE with no snare):

Because of the assumptions made, you can actually input the raw damage values for each variable. (see variables and assumptions below). An important note is that EAoE can never be less than 1, so if the right hand of the equation is less than 1, you know that bringing the snare (regardless of whether it’s “happenstance” or “guaranteed”) will always be more beneficial than bringing the additional AoE.

For example, if I want to know whether I should bring Firestorm and Maelstrom or Firestorm and Deep Freeze, all in Hard Mode:

Right-Hand of the Equations: 1 + 25/35 – 80/(2.39*35) = 0.7579
Since 0.7882 < 1, bringing Deep Freeze, even if I don’t know if it will be “happenstance” or “guaranteed,” will be better than bringing Maelstrom.

On the flip side, if I want to know whether I should bring Firestorm and Maelstrom or Maelstrom and Deep Freeze, all in Hard Mode:

Right-Hand of the Equations: 1 + 35/25 – 80/(2.39*25) = 1.0611
Looking at this value, I should do Maelstrom + Deep Freeze regardless if Deep Freeze is “happenstance” or “guaranteed,” because the AoE efficiency either at this AoE size is greater than 1.0611

Remember to be careful with all calculations: if the snare can provide more hits than the AoE has, you can’t use the efficiency values, etc. listed in the table, but rather insert in the maximum hits of the AoE in for H(snare) in the EAoE equation to calculate efficiency.

New Variables:

Some of the assumptions that were made include:

All AoE has the same radius of effect.
The same foes were hit (same armor)
All AoE is independent; all cast at the same time or at completely different times so that scatter doesn’t affect H0.

Frozen Ele · May 06, 2011, 09:02 PM // 21:02

Quote:

Originally Posted by Jeydra

I thought I showed that it is possible, even easy, to get monsters to stay in AoE without a snare ... aka. your empirically derived times for monsters running out of AoE are inaccurate ...

First off - the values I derived are averages, you just looked at one instance of one particular AoE against one mob in one region with one specific team set-up.

Second off - we've been though how these screens don't prove anything. In terms of my values, the fact that you've got minions in there confounds any potential from Meteor Shower. Reversely, this don't prove anything about minions because (1) they're too variable and (2) their action is confounded with Meteor Shower's.

Quote:

Originally Posted by Jeydra

Recharge is no argument against relying on KDs as your pseudo-snares.

Recharge matters if you can't guarantee the KD will coincide with AoE. If you can guarantee that they'll happen at the same time (or roughly the same time), then you're right. The problem with KD's is all about timing. If you're more than 0.58 seconds late (after the foes have started moving) on average, the KD will have no effect (not increase AoE efficiency at all). If you're more than 0.32 seconds early (before foes have started scattering) for a 2 second KD or 0.75 seconds early for a 3 second KD on average, snaring will be better. On top of all this, there's no real way to time when the KD should be placed because of natural variance in when the foes start moving, so snaring is better because you can cast snares well in advance.

If you can't even guarantee that your KD will coincide with AoE at least even a little bit, then recharge destroys any potential the KD would have.

Quote:

Originally Posted by Jeydra

As for minion bodyblocking, if you're good with controlling aggro it's simple enough to get the monsters to latch onto minions.

Minions, etc. have the potential to do well, but then at the same time, the potential to do nothing at all. Yes, while you can exercise different agro techniques and whatnot to make minions effective, on average, snaring is better (especially with the absence of such tenchinques). All-in-all we're looking at the effect of minions and the like on AoE, not the effects of agro on minions.

Quote:

Originally Posted by Jeydra

Math can be useful in a more closely contested problem e.g. SoS vs. SoGM, but here it's simply irrelevant.

I disagree; I'm able to make a "batch-process" that can analyze hundreds (thousands if you factor in what I just posted above) of different scenarios, accurately and effectively.

Chthon · May 07, 2011, 03:06 AM // 03:06

Quote:

Originally Posted by Frozen Ele

If the number of pulses is 5, you just won't be able to exceed this value with your total hits. This means that the maximum additional hits would be:

(Total Number of Pulses - H0) = Maximum Additional Hits

You can then compared the maximum additional hits to the "guaranteed/happenstance" number of additional hits (the valeus found in the tables; calculated from the "happenstance" and "guaranteed" formulas). If the maximum number of additional hits exceeds the "guaranteed/happenstance" additional hits, use the "guaranteed/happenstance" additional hits in calculating AoE efficiency. If the maximum number of additional hits is smaller than the the "guaranteed/happenstance" additional hits, use the maximum number of additional hits to compute AoE efficiency.

For example, if I want to look at the "guaranteed" AoE efficiency of using Deep Freeze with Eruption:

Maximum number of additional hits = (5 - 2.39) = 2.61
"Guaranteed" number of additional hits = 0.76

As maximum > "guaranteed," I use "guaranteed," yielding an AoE efficiency of 131.68%.

If I wanted to look at Mind Freeze with Eruption, however, the values are:

Maximum number of additional hits = (5 - 2.39) = 2.61
"Guaranteed" number of additional hits = 3.51

As "guaranteed" > maximum, I use the maximum number of additional hits, yielding an AoE efficiency of 209.21% (versus the listed "guaranteed" AoE efficiency of 246.86%).

I'm aware of how to make the adjustment to the bottom-level figures. I was more looking for a sweeping generalization of what happens to the overall value of the various snares when you take this into account.

Frozen Ele · May 08, 2011, 04:01 PM // 16:01

Quote:

Originally Posted by LexTalionis

.

Your qualm is about induction (empirical testing) vs. deduction (mathematics). Each form of reasoning has its own advantages and disadvantages:

We often use induction (creating conclusions by looking at a group of data) when we have no choice but to look at limited evidence to draw conclusions. Induction can only ever yield probable truths, never certain truths, as there may be an exception to the induced pattern lurking around the corner to invalidate your conclusion. For example, just because it has rained for the past five days doesn’t mean it will rain again tomorrow. We can try to grapple with the problem of induction by using statistics (confidence intervals, hypothesis testing, etc.), but even then, we’re never 100% sure (a confidence interval with a 100% confidence interval would have a margin of error that extends to infinity).

Deduction (combination of axioms and logic to produce a conclusion), however, allows us to deduce conclusions with absolute certainty given that our axioms/assumptions themselves are correct and that the logic is valid.

Within context of this investigation (noun, “a searching inquiry for ascertaining facts”), I chose deduction for a number of reasons. Foremost, it allows a “batch process” of sorts, allowing us to examine potentially thousands of cases quickly and accurately, whereas using induction to test each would require too much time to be of any use (we’re talkin’ years in magnitude). Additionally, the axioms/assumptions are not unreasonable (hitting the same number of foes, etc., sidestepping any problems by using averages), yielding conclusions of absolute certainty and therefore bypassing the “problem of induction” and induction’s only-ever probable truths.

All-in-all, this investigation is to allow people to make more informed choices. It’s not about the actual percentages, but comparing them to decide what’s best for your team. If you believe that any of the sections need fixing, write the section with the amendments and I’ll look into it.

Quote:

Originally Posted by LexTalionis

Please consider the combination of Binding Chains + Anguished was Lingwah + Ghostly Haste and/or Weapon of Quickening ... Consider snare efficiency versus Churning Earth (Hard Mode) and Meteor Shower.

I’ve looked at the different cases you requested, but I’ll warn you – if you’re still not a fan of deduction, turn back now.

Binding Chains + Anguished was Lingwah + Ghostly Haste and/or Weapon of Quickening

With the combined effects of all four skills, there’s a 90% slow-down with a “snare” efficiency of 53.2%. Since the duration of the “snare” is less than 5.8 seconds, the “guaranteed” AoE efficiency in HM is less than that of Water 90% snares (5.8 seconds is the average cut-off time for the “nearby” range, 7.7 seconds for “in the area”). The “guaranteed” efficiency for the “adjacent” range would be the same as Water 90% snares, as the duration of the Rit snare is greater than 3.9 seconds (although in terms of casting, there’s really no room for error and I’m guessing that the efficiency – 246.86% - won’t be reached often; it runs into the same problem that 3 sec KD’s run into for “guaranteed” efficiency). If using the cast -> drop -> recast -> etc. chain, then the AoE efficiency is the same as the 90% water snares.

In terms of “happenstance” AoE efficiency, the average HM efficiency would be 120.39% because of the snare efficiency of 53.2%. This means that Water snares are better (average “happenstance” of 149.18%) and even that running with a “guaranteed” cripple (50% slow-down) would be better than this 90% slow-down.

Snare vs. Churning Earth

The big difference between the snares and Churning Earth is that Churning Earth itself is DoTAoE. So while you can cast the snare before the other AoE actually starts and be fine, if you cast Churning Earth before the AoE, Churning Earth will cause scatter, potentially reducing the efficiency of other AoE.

With “guaranteed,” Churning Earth only knocks down moving foes. If you manage to land a KD during that time, Churning Earth will provide two additional hits, yielding a maximum “guaranteed” HM AoE efficiency of 177.80% (which is still lower than Water snarings’ average “guaranteed” efficiency).

Because foes will only be knocked down while moving in Churning Earth’s AoE range and Churning Earth has one hit per second, we can look at the normal escape time as a continuous uniform probability distribution to calculate the average “guaranteed” efficiency. In other words, Churning Earth’s hit could occur anytime during the 0.39 seconds the foes are moving through it or up to 0.61 seconds before this time; there’s a 39% probability the hit will occur to cause KD (39% probability for the two additional hits). As such, the average “guaranteed” efficiency for Churning Earth turns out to be 130.34%, which is less than Water snares’ “happenstance” average, proving Water snares to be better regardless of whether the Water snares are “guaranteed” or “happenstance.”

As for “happenstance” AoE efficiency, Churning Earth is only 12.12% efficient, so the average “happenstance” HM AoE efficiency is 103.06%, proving Water Magic is superior to Churning Earth.

Snare vs. Meteor Shower

Meteor Shower is similar to Churning Earth in that it has the potential to decrease other AoEs’ efficiency if used as a preemptive measure, whereas Water Magic snaring does not have this effect.

For the “guaranteed” efficiency, it’s also similar to Churning Earth. Meteor Shower’s maximum “guaranteed” HM AoE efficiency of 177.80% (which is still lower than Water snarings’ average “guaranteed” efficiency). We can also approach Meteor Shower’s average “guaranteed” efficiency by using a continuous uniform probability distribution. Meteor Shower’s KD is unconditional, but only occurs every three seconds and only increases AoE efficiency if the foes are within Meteor Shower’s “adjacent” range when it hits. While the foes are stationary in the AoE, there is a 2/3rds chance of the KD, which would yield an average additional hit of one. There is a 13% chance (0.39/3) that the KD will hit while the foes are moving, yielding an additional hit value of two. Reconciling these two probabilities, Meteor Shower will have an average “additional hit” value of 0.9267, yielding an average “guaranteed” efficiency of 136.05%. This efficiency is less than Water snares’ “happenstance” average, proving Water snares to be better regardless of whether the Water snares are “guaranteed” or “happenstance.”

As for “happenstance” AoE efficiency, Meteor Shower’s KDs are only 9.23% efficient, so the average “happenstance” HM AoE efficiency is 102.26%, proving Water Magic is superior to Meteor Shower.

Frozen Ele · May 08, 2011, 04:18 PM // 16:18

Quote:

Originally Posted by Chthon

I'm aware of how to make the adjustment to the bottom-level figures. I was more looking for a sweeping generalization of what happens to the overall value of the various snares when you take this into account.

The 5-pulse restriction only affects 90% snares. I'll look at quantifying the new averages sometime this week.

Quote:

Originally Posted by Jeydra

Why don't you try nuking mobs with Firestorm the same way I did in those screenshots, and see how fast they run out? Or try with Meteor Shower, for that matter. Then post screenshots.

There is no way snaring is better than "bodyblocking", which is a terrible term for using minions as your pseudosnare. Proof: there are no SCs which use water snares without a tank to keep monsters in AoE.

And there are no SCs that use minions. When it comes down to it, the increased controllability and reliability of snares - for reasons that I've already posted - makes them better than minions in this regard, especially as we can't assume the agro techniques, etc. that your use of minions necessitates (we're looking at the effect of minions and the like on AoE, not the effects of agro on minions).

Plutoman · May 10, 2011, 01:20 AM // 01:20

Quote:

Originally Posted by Jeydra

There is no way snaring is better than "bodyblocking", which is a terrible term for using minions as your pseudosnare. Proof: there are no SCs which use water snares without a tank to keep monsters in AoE.

In trenchway, when the nukes start falling, Deep Freeze is used to eliminate the possibility of enemies leaving the area before the EoE chain hits.

I like the math, to be sure. I only wish it was more useful, because most DoTAoE is lacking to be sure. The only ones I could see putting out a reasonable amount of damage are RoJ and Chaos Storm.

Jeydra · May 10, 2011, 04:57 AM // 04:57

*Water snares without a tank

I'm no speedclear expert, but I'll point out that not only does the current record for DoA HM FR has no Deep Freeze, if you really want / need the snare, you bring Deep Freeze @ 0 spec, so God help all Water Eles out there.

I'm debating whether or not I should make my own thread titled "why Water Magic is terrible" and post a bunch of math to prove it ...

Mouse at Large · May 10, 2011, 07:05 AM // 07:05

In all the above, I think the essential point I was trying to make above may have been missed.

What I was postulating was that the real question should be "What deals more damage - a snare + DotAoE or 2 x DotAoE?"

I'm sure it's difficult to determine as there are many variables i.e. scatter machanics (out of and back into the AoE), DoTAoE radius and overlap (if any), DoTAoE duration, number of foes affected etc. The number of assumptions made may make any detailed analysis meaningless.

However, as an empiricist, with over 5 years playtime on my ele, I'll stick with twin heats in NM and earth DoTAoE for HM for now

Haggis of Doom · May 10, 2011, 04:45 PM // 16:45

Heroes may behave differently from monsters because of player position, set tactics, monsters not abusing the hero AI etc, but I'm throwing this out here anyhow: I personally am much more afraid of a wipe due to DoTAoE if water magic hexes are being cast on my bunched up heroes than, say, minions or MS. Assuming minimal to no flagging, of course.

Plutoman · May 15, 2011, 12:37 AM // 00:37

Quote:

Originally Posted by Jeydra

*Water snares without a tank

I'm no speedclear expert, but I'll point out that not only does the current record for DoA HM FR has no Deep Freeze, if you really want / need the snare, you bring Deep Freeze @ 0 spec, so God help all Water Eles out there.

I'm debating whether or not I should make my own thread titled "why Water Magic is terrible" and post a bunch of math to prove it ...

The records run modified speed builds, farming runs use DF typically. Just like regular runs use two assassin tanks, while speed runs use an R/A with extra cons. Also, body blocking is different than a tank, bear that in a mind. A tank takes aggro prior to a group and holds it while the group spikes. Minions body block by just running up and getting in the way.

Kelvin Greyheart · May 17, 2011, 09:24 PM // 21:24

Some interesting theory crafting, though I fail to see any practical application where this would really matter outside of general pve if you or your party are bringing bad skills.

How many nukes worth bringing actually cause an appreciable amount of scatter for organized play? Skills such as Esurge, Mistrust, Wastrel's Demise, Wandering Eye, and many other potent nukes, especially those in the illusion, domination, channeling, and curses lines do not cause scatter.

Realistically it's almost exclusively elementalist spells that cause scattering with a few exceptions like Spiteful Spirit and Chaos Storm. In other words, don't bring eles for damage. Nothing we didn't already know since an elementalist's damage output is terrible anyways due to a lack of armor ignoring effects compounded with an extremely limited selection of reliable anti caster utility effects. The scatter spells just make them worse.

I'd also like to point out that there are very few snares in used in speed clears. The only one that comes to mind is deep freeze in some DoA teams, and that is only beneficial in a few spots, and isn't actually needed. Sure greater darkness spike can get a bit ugly with all of the earths, but EoE is extremely powerful. Tank and spank set ups simply don't need snares. Stuff is either body blocked (UW and some of DoA) or dies too fast for it to matter (Everything else).

For general pve this might have some use except almost all of the general pve trash doesn't consist of large enough groups or groups with enough health to really make snares that beneficial. Stuff simply dies too fast unless you feel the need to run really crappy bars. Herore's are beyond stupid in their usage of snare effects and as a result they frequently waste deep freeze on a lone mob at 20% health.