Talk:The Lightning Capacitor

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Mrtcereal 06:32, 16 August 2007 (UTC)MrtcerealMrtcereal 06:32, 16 August 2007 (UTC)

I obtained this trinket in Karazhan last weekend, but I have a few points to make.

It can, and does hit for much higher than its listed damage(I assume do to it recieving a bonus from spellpower), and also is capable of critical hits(Which it seems to get VERY often). My highest hit from a lightning bolt according to my UI is 1971. Taking this into account, I believe it adds alot more damage than is listed on the page.

Mrtcereal 06:32, 16 August 2007 (UTC)MrtcerealMrtcereal 06:32, 16 August 2007 (UTC)

RE: Some points i have to make: It does no longer gain any spelldamage bonusses, thus lost some of it's power, but in the same patch (the one, where karazhan bosses were nurfed and the items were buffed, i think it was 2.1.1), the damage window was slightly increased, so the formulas have to be recalculated. I have also tried to prove that it actually uses the nature critical strike chance (for me as a scorch mage, this crit rate dramatically differs from my fire crit rate), but as this is really time consuming and a totally luck-based experiment i have not yet gathered enough data to confirm or deny it. Another point: It always hits the mob, which recieved the last crit that caused the third electrical charge and released the bolt, even though you switch the target while your spell is flying and critting while you have something different targetted. The Lightning Bolt does gain bonus damage from Stormstrike (20%) and thus allowed my Capacitor to crit for around 1500, nevertheless the capacitor without any damage increasing debuffs exceeds the theoretical damage range of 1209 - which is the theoretical max-crit value - slightly (1230, sometimes close to 1300). It can be resisted (partial and fully), i have not yet discovered wether it is affected by hit rating and/or spell penetration (which is quite hard to prove) And i suspect, that the bolt-damage is actually affected by Arcane Power (+35%), but i have to look at this closer to be sure. The Capacitor can also shoot multiple bolts at once, for example with 12 mobs around you, using Arcane Explosion while you have 2 charges and critting 4 targets it will release 2 bolts (but don't ask me how the server determines, which 2 mobs are hit :D) --Kamikaze28 08:36, 4 September 2007 (UTC)

I did the calculations and actualized the trinkets mechanics to 2.1 --Kamikaze28 11:24, 7 September 2007 (UTC)

As I am seemingly the only one working on this article, I will remove the obsolete first chapter and rearrange my own part with the current mechanic and mathcraft. I am really sure about the numbers and the logic, so please only correct / recalculate things if you really know what you're doing. -Kamikaze28 10:11, 8 September 2007 (UTC)

I believe your formula for calculating Bolt(t) was incorrect. I'm not sure how you arrived at the final formula, however to me it seems obvious the time for obtaining 3 charges would be:

h(t / c) * 3


h = Chance to Hit(Between 0 and 1)
t = Cast time
c = Crit. Strike%(Between 0 and 1)

--WMA 07:07, 10 August 2008 (UTC)

WMA, that is not how probability is calculated. If it was, if you knew the chance of something to occur you could make definitive statements about when it was to occur. For example, lets say the chance of a drop is 10%, and the time to kill the mob is 1 min. After 10mins I could say I have a 100% chance of having the item... which is obviously incorrect.

Probability is calculated by taking the chance of something NOT to occur. In my above example, I have a 90% chance (100%-10%) of the drop NOT to occur. After 10 attempts I have (.9^10)= .349 chance of NOT seeing the item. Therefore I have (1-.349)= .651 =65.1% chance of HAVING the item after 10 attempts which takes 10 mins. With 30 attempts, I would still have a 4.2% chance of NOT having the item yet.

Same kind of probability applies to  [The Lightning Capacitor]. Instead of the chance to gain an item, it's the chance to gain a charge. To figure that out, you have to calculate the chance NOT to gain a charge in a particular cast. I do not know if the formula before my edits is correct (I was the one who asked for a fact check after all) but I definitely know that {h(t / c) * 3} is incorrect. Therefore I'm reversing your edits. --Brunpal (talk) 20:10, 4 October 2008 (UTC)

Brunpal, I'm quite aware of how probability works. What I was showing in my working however was however the average time it takes the trinket to proc.

While certainly it is true that we cannot make definitive statements on something given, using your example, its chance to drop after x kills, we can however make statements regarding how often it can be expected to drop in x kills.

A drop rate of 10% means that, on average, this item should appear once every ten kills.

Certainly, the probability of obtaining the item once every ten kills is not 100% - this is entirely correct; however quite often in theorycraft it is common to work using averages when calculating the expected values or gains of a given item.

Again, my formula applied to the average time to proc; while different topics, we are both correct in our reasoning, as the two are somewhat linked, in that over a long-term statistical evaluation of a trinket, one finds it procs 1/10 times.

For further reading, I suggest you see the Law of Large Numbers:

Since the information I posted is correct, I will be changing it back to what it originally was. (Provided you have no further disagreements with my reasoning.)

Thank you.WMA (talk) 13:16, 7 October 2008 (UTC)

Wasn't sure that you knew probability. Turns out we both know it which makes it easier. I'm familiar with LLN already. "3" is not a sufficiently large enough number to use LLN. However I misunderstood what you were attempting to calculate with your statement of "time for obtaining 3 charges." It may seem pedantic but "Average time for obtaining 3 charges" is not the same as "time for obtaining 3 charges." So I think we are in agreement after all, just you didn't include the word "average" so I thought you were calculating something else.
What threw me was your statement on the main page: "Unfortunately however, due to the poor scalability of Spell Crit. relative to other stats, such as Haste and Damage, which arises from high itemization cost, the value of this trinket quickly diminishes in later content." That statement threw me because if you do the probability math, the value of the trinket increases significantly in later content. (IE The Lightning Capacitor sucks if you get it your first run in Kara. But if you are decked out in BT and Sunwell gear, this trinket is the best you can use.)
I'm not trying to defend what was there before you changed it. Like you, I couldn't figure out where Kamikaze got his formula's from. I did notice that the version of the page before I corrected the math error matches closely to the numbers you came up with. The only difference appears to be a rounding error. Perhaps it wasn't a math error, but a transcription error in his formula at the start? That page had "( 1 / ( 0.34 * 0.94 ) ) * 3 * 1.5 = 12.44117647" (which is incorrect, that equals 14.08). You have "(1.5 / 0.34) * 0.94 * 3 = 12.44" which does equal 12.44.
BTW: I encourage you to test out the spreadsheet I made in the summer to confirm we are both in agreement. Note that I also used (3*time) in the spreadsheet myself. It's not quite correct, but it's close enough to be useful. I also encourage you to compare earlier versions of the page. Regardless what exactly is wrong the example(s) on the page are a mess and very hard to follow. I would like to make that page easy to follow. As it is now, it's more confusing than helpful.--Brunpal (talk) 03:51, 9 October 2008 (UTC)

My apologies for the poor choice of words on the original edit - I should have been more clear in my initial comments as to what I meant. I can certainly see how the possibility for confusion was there. As for the scalability of this trinket, I think this was probably poor wording again on my behalf(Which I again apologise for.). To clarify, what I meant was that in general, gearing for Crit, for the majority of classes, with perhaps the exception of Elemental Shamans and perhaps Boomkins(Which I profess I know little about) is a poor choice, as stats like Spell Damage, Spell Hit, and Spell Haste provide far more benefit in the long run.

Spell hit factors out because regardless of using TLC (or not) the optimum choice is always to cap out spell hit. Similarly spell haste factors out too. Because you are casting faster you get a faster chance to gain a TLC charge and discharge it.-BP

I do however see the logic behind your argument, in that while you may not gear or gem for crit, that your crit is bound to increase in high-end(SW:P, BT content gear) "indirectly" - in the sense that your crit will increase naturally from normally gearing. The degree to which your crit increases past early-mid T5 content without specifically gearing for it however is quite arguable.

I believed the same until I tested it. Once into BT, there are a very limited number of gear choices once you exclude the gear that's clearly inferior to other gear. What matters is how fast you cast spells with the capability to crit. For example, TLC quickly gets exceptional for an elemental shaman, but always sucks for an affliction warlock.-BP

All that aside, I think it's a bit of a generalise to label this trinket as one of the "best you can use" for SWP and BT content. I know for Fire Mages in particular, due to Cooldown stacking, that Trinkets such as Hex Shrunken Head, and the Skull of Gul'dan provide a larger bonus overall than that provided by the Lighting Capacitor in most contexts. For classes like Warlocks, I imagine stacking Trinkets with Bloodlust and Drums of Battle also provide more overall benefit than the average gains of TLC.

My testing has shown that for elemental shamans, and mages that spam [Arcane Missiles] that this trinket really is the best by a very large margin. This is due to the high crit rates of both, as well as the large number of crits per minute possible. (3 per chain lighting, 5 per AM) It was also the best for Destro Warlocks, but they had to have truly godly gear. Gear so good there might be only one or two warlocks like that per server. I didn't test other builds because I came to a general conclusion. My general conclusion was that once you get past a certain threshold of crits per unit of game time, TLC rockets to the top of the pack.-BP
Look at it another way, if you are able to proc TLC every 3 seconds for 900 damage, then you need to find another single trinket that can add 300dps. One doesn't exist. But if it takes you 30secs to proc for 900, then finding a trinket that adds 30dps is easy. I recommend throwing in various gear sets into a tool like Maxdps's [1]'s and seeing what it spits out. With full Kara gear, TLC is way down on the list as a downgrade. Make up a char with full BT gear and suddenly TLC is an upgrade. I don't know the math used behind their calculations, but the dps results seem to be comparable to my own.-BP

I just had a quick look at the old revision of this page, and it seems like it may have been a transcription error, however I can't seem to resolve why the previous editor why multiply by time(t) and divide 1 by the by chance to proc.

Ya. I was confused too. I was never able to wrap my head around that one. But he did seem very sure of himself so I didn't remove it. He did come up with the same numbers as you, so I'm just going to guess that he did it right, but explained it wrong.-BP

Regarding the readability of the page, I feel it is at points hard to follow as well, however keeping the information regarding how to calculate the Trinkets average damage would I feel be a large benefit to everyone, as it would give those who care a firmer understanding of how the trinket works, and to consequentially value it correctly for their current set-up.

I agree on keeping that info, just structuring it differently.-BP

As for looking at your Spreadsheet, I had a quick look but I arrived at slightly different numbers. If we take Critical Strike Damage as S, Non-Crit Damage as D, and Critical Strike Chance as C, with a Bonus B(Bonus, not multiplier)

You used the following for average damage per hit:

C * S + D

I believe this to be incorrect. This solution says that: A spell ALWAYS hits for it's average damage, and THEN it has a chance to hit for it's critical strike damage.

I believe the more correct solution should use logic like the following: A spell ALWAYS hits for it's average damage, and THEN it has a chance to hit for an ADDITIONAL Critical Strike BONUS Damage. I.e.

C * (SB) + D

Which may or may not appear intuitively incorrect, however I can assure you it is quite correct, since you only strike for an additional bonus on crits. Using your logic, negating the need to include Critical Strike Bonus Damage, one would expect the formula to appear like the following:

(1 - C)D + C * S

Which, as you no doubt probably know says: A spell hits for it's average damage only when it doesn't crit, otherwise it crits for its critical strike damage. In terms of your Spreadsheet, you'd need to change Cell 44 from "=(B42*B9)+B40", to something like "=(B40*B9*0.5)+B40"

I thought I included critical strike bonus damage, as well as modifiers to that bonus damage. I'll play with the spreadsheet a bit later to see what you mean.-BP

I also arrived at dissimilar numbers for time to proc the trinket. I believe(As noted in your Spreadsheet I think), that your method of calculating the average number of casts required to proc the trinket is flawed. Your calculation for calculating the probability to proc the trinket on the first cast is indeed correct I believe, however the probability to proc it at least once in two casts, is quite different to the method your using, which is what I believe was mentioned earlier, with the probability of an event being 1 - N. I think however, in terms of average number of casts, it is sufficient and simpler to calculate the number of casts required to proc as:

T / (C)

With T = Cast Time, and C = Crit Chance. That being said, the method I used for calculating the average DPS resulted in slightly higher DPS(Using numbers from my old edit of this page, I arrived at numbers around 5 DPS higher, even after correcting the faulty average damage listed in your spreadsheet).

Yup. I know my formula is incorrect on that part. I wasn't too worried because I also did not include the 2.5 sec CD after a discharge. I figured underestimating the dps slightly in one spot and overestimating slightly in another (by ignoring the 2.5) that it would tend to wash out. However the amounts are just an educated guess. (BTW I have no intention of attempting to model the 2.5sec CD. It would be far to big of a pain with little benefit. Plus even if successfully modeled it will confusing as hell to explain on the wiki.)

Please keep me updated as to what you think we should do regarding the calculations on this page, as I'm quite confident that the previous calculations of the user before me were incorrect, and I'm even more confident that my calculations were correct, albeit poorly worded. Perhaps a rephrasing of my accompany comments, coupled with a removal of what could probably be misconstrued as biased comments (Such as my comment reg. poor scalability)and the re-insertion of my calculations would be a suitable edit for this page? Please forgive any poor grammatical errors in this message.

My suggestion is to pull the majority of the info off the main page and onto a second (perhaps trancluded) page. The math that remains on the main page should be simple enough for someone who hasn't finished high school to understand. That means a simple statement of "Average damage of this trinket when it procs is <Blah>. Here is the formula: <Foo>" How that translates into dps is what's shunted to another page, or a hidden box with a <show> to click on. I would also like to see a nice easy to read graph on the main page.
Formating everywhere should use formula boxes, and where the math gets funky I would prefer to use a typeset like latex. I think the first step is to sort out the wall of math before worrying about the rest of the write up at all.
I also think the entire section where a dps number is calculated into an equivalently spell damage number is both confusing and stupid. Nobody takes a dps number and calculates it into spelldamage... that's backwards. If anyone's wants that comparison they will take a spelldamage number and turn it into a dps number. (As to your grammar errors? Pfft. Me no care.)
My gut feeling is that there is a magic number where the curves intersect for everyone. Anything below that magic number means TLC sucks, anything above means TLC is the best choice. Some builds will be incapable of reaching that magic number. I haven't attempted to calculate this out, but my guess is magic number is the ratio of crits per minute to spell damage.-BP

Edit: To try and reconcile the differences in the average DPS of both our calculations, I plan on writing a quick program some time tomorrow to simulate 1,000,000,000 or so casts around 1,000,000 times using input I gave in my previous edit of the page. I'll post the results up here, along with the accompanying results when I have time. Look forward to your reply. Thanks. --WMA (talk) 14:33, 9 October 2008 (UTC)

Instead of including that math and results on this page, I suggest starting up a subpage off of "The Lightning Capacitor" lest this page gets as hard to look at as the main page.--Brunpal (talk) 01:26, 10 October 2008 (UTC)
Having a look at the spreadsheet I don't follow what you say above. You don't include any "="s in your formulas so I'm having to guess at what you mean. In all the formula's above does your formula equal the same thing? If so, is it "total average damage from proc including crit and non crit" or "average damage that is a crit" or something else? I especially don't get this statement:
you'd need to change Cell 44 from "=(B42*B9)+B40", to something like "=(B40*B9*0.5)+B40"
What's the 0.5 from? Is the 0.5 bonus damage from a crit? If so, .5 is incorrect. Crit damage isn't necessarily going to do 50% more than an average hit. That 50% has to be variable because it is affected by talents and items that increase crit damage. For example a +3% bonus to crits (from the meta) means that when you crit you do both the crit portion of the damage, and +3% more to the non crit portion of the damage too.
To clarify what I meant: The formula you initially used in Cell 44 is supposed to show the average damage per hit, including crits. Your initial formula, as I originally said, seems to say: If the spell hits, it does its normal damage, and also has a chance to do it's critical strike damage.
In order to correctly calculate the average damage on a hit, including crits, you'd have to: multiply the chance to crit by the bonus damage granted by a crit - which is the average crit damage minus the average non-crit damage. I.e.
E = (C - D) * B + D
E = Expected Average Damage
C = Average Critical Strike Damage(Cell B42)
D = Average Non-Critical Strike Damage(Cell B40)
B = Critical Strike Chance(Cell B9)
Which is saying: When you hit, your damage is on average your normal damage and X% of your critical strike damage.
So to remove the constant of 0.5(Which you say could be variable from talents etc), you could rewrite Cell B44 as:
=(B42 - B40) * B9 + B40
I hope this clarifies what I meant - if you're still unsure, let me know what explicitly doesn't make sense, and I'll try and expand upon my statement.

So in other words I was double counting normal damage every time there was a crit. I think. Regardless it's fixed now on my version. (I also think.) Cell B44 is "=(B42*B9)+(B40*(1-B9))". I wish I could upload a new version of the spreadsheet with that correction. For some reason the wiki is blocking me with an error that says "The file is corrupt or has an incorrect extension. Please check the file and upload again."

Another way of thinking about it is to consider a char with godly amounts of resilience. Using [Divine Favor] + [Holy Shock] you can guarantee a crit which would be otherwise impossible. If the target has 16.7% resilience or above you will do LESS damage with a crit than you will with a normal hit. For example:
1000dmg Holy Shock. Crits to be 1500dmg.
Resilience reduces damage by 2% per % of resilience 16.7 x2 = 33.4%.
1500dmg x (-.334) = -501 reduction
1500dmg - 501 = 999dmg with crit. Which is less than the 1000 dmg non crit.
I don't expect reductions like this to come up. I just used it as example. However bonuses to TLC discharges will occur (like with the meta.)
I agree that "total damage including crits and non crits" = (1 - C)D + (C * S). I wouldn't have written exactly that way, but I do agree with it. I made changes to my spreadsheet data and I did not get the results I should have. So I certainly agree that there was a problem with Cell 44. I made that change.
Also making that change in Cell 44 drastically reduces the sample number by 100 damage and that flows out to a reduction of ~4 dps of the sample data. I know that my purposeful flaw in calculating cumulative probability will OVERSTATE damage and dps. Yet with a correction of 2 overstatements to mine still you had a larger dps. That shouldn't be the case. Either it should be equal or it should be less.
If nothing else, we should be able to agree on how much damage The Lightning Capacitor does when it discharges. That's the first and easiest step. And it seems we have not agreed on that. I've now come up with 826.88 average dmg on a proc including expected crits from TLC. With a 3% meta that becomes 831.49. Do you concur?
Would not the expected damage, including crits, be dependant on the crit-chance for your Nature School? What Crit-Chance did you use to arrive at these numbers?

20.50% crit rating.

Note that I'm not saying above that I'm right and you are wrong. I'm saying that I couldn't quite follow what you said.--Brunpal (talk) 04:22, 10 October 2008 (UTC)

That crit rating is from the sample starting data in the spreadsheet file. It's based on a warlock in a combination of Kara, S2 PvP and badge gear spamming Shadow Bolts with a little bit of spellhaste. I figured you had that data. It should make a good comparison to check our formulas. Even if we have different mathematical approaches, we should come to the same final numbers. It will be a good check of both our work if we use different approaches but still come to the same results.

The sample data block:

99.00%	Your % to spell hit with spell cast
99.00%	Your base % to spell hit
20.50%	Your base % crit rating from char sheet
5.00%	Your bonus % to crit rating only for spell being cast
2.48	Casting time (seconds)
1	# of chances of a crit per cast*
3.00%	Crit damage bonus to all abilities**
0.00%	Special bonus damage given to trinket***

--Brunpal (talk) 00:44, 11 October 2008 (UTC)