[Shaman] Itemizing Enhancement at 70 - Page 33

Disquette · 06/02/07, 4:23 PM

Originally Posted by Pater

Your model is saying that optimal hit is 27.6%? Doesn't that indicate a bug, since hit has no effect above some point (either 24.6% or, more likely, 25.5%)?

I was following the other thread, and I'm pretty convinced that he's right. You do add another 1% miss per mob level difference above you, at least for those 3 levels. People in other forums have done pretty good testing showing that with 8% to hit, you have some misses (single wielding), but at 9%, they disappear.

On the other hand, when they do that, the parry rate observed goes up. So, more hits are getting through the miss barrier, but then that's more for the parry rate to catch. It's kind of hard for me to wrap my mind around the way we should look at it. :-\

Disquette · 06/02/07, 4:25 PM

Originally Posted by Tornhoof

Yah, i updated my code to include the other glancing blow chances:

As for Edit1:

It is a linear scale from 10% procrate for 1.3s weapons up to 20% for 2.8s weapons, which appears to be correct at the time of writing on PTR. Is fairly consisten with your method of 36% max and using the 3s cd.

As for Edit2:

SS,Weapon mastery are later on multiplied in the final dps calculations, this is just for internal testing and the 1.4 should be pulled down to the final dps calculations for a cleaner layout.

As for Edit3:

mhwhitedps := 1 / 100 * (hitwhite * 100 + basecrit - glancing - dodge) * (wdps1 + ap / 14);

The relevant part

1 / 100 * (hitwhite * 100 + basecrit - glancing - dodge)

Hitwhite is actually a value below 1, as in 0.95.

The other values are percent type, so the parenthesis are actually for example: 95+40-25-5.6, this gets divided by 100, to actually get a meaningful factor.

haha, yeah, i caught some of my mistakes while you were writing your response, which is why they're edited out. You really do some neat stuff in here, but the ones I have left unresolved remain in my post.

thanks for the explanation ;-)

Tornhoof · 06/02/07, 4:34 PM

                // calculation below, all values in percent unless noted otherwise
                float glancingreduction = 25; // XX% reduced damage
                float glancingchance = 25; // chance to happen == XX%
                float glancing = glancingreduction * glancingchance / 100; // this value is used in the closed-form of the attacktable below
                float dodge = 5.6f; // 5.6% dodge chance of the boss
                float hitwhite = (float)Math.Min(100 - 5 - 19 - 0.6f + hit, 100); // 100% - 5% base - 19% dw - 0.6% wskilldifference + hit, upto a maximum of 100
                float hityellow = (float)Math.Min(100 - 5 - 0.6f + hit, 100);// 100% - 5% base - 0.6% wskilldifference + hit, upto a maximum of 100
                float avghit = (hityellow + hitwhite) / 200; // average hit value, already normalized to 0<=x<=1
                float noncrit = (1 - crit / 100 ); // the chance not to crit
                // weapon speed incl.flurry
                // 30% * flurry uptime + possible haste effects, calculating the effective speed
                float wsmh = ws1 / (1 + haste / 100 +  0.3f * (1 - (float)Math.Pow(noncrit,3))); 
                float wsoh = ws2 / (1 + haste / 100 + 0.3f * (1 - (float)Math.Pow(noncrit,3)));
                float avgspeed = (wsmh + wsoh) / 2; // average again for some uses
                // windfury, already normalized to 0<=x<=1
                float wfnerf = 0.1f + ((0.2f - 0.1f) / (2.8f - 1.0f)) * (avgspeed - 1.0f);
                float wfproc = 2 * wfnerf;
                // stormstrike, stormstrike is basically a weaponspeed*10 increase of dps
                float ssmh = 1 + hityellow/100 * wsmh / 10;
                float ssoh = 1 + hityellow/100 * wsoh / 10;
                // haste is a factor just as stormstrike
                float hastemh = ws1 / wsmh;
                float hasteoh = ws2 / wsoh;
                // attack power including unleashed rage:
                // noncrit to the power of the swings we do in 10s, including 2 stormstrike and possible WF procs
                float ap = baseap * (1 + 0.1f * (1 - (float)Math.Pow(noncrit, (avghit * (1+2*wfnerf)*(20 / (wsmh + wsoh)) +2))));
                float wfap = (475 + ap);
                // closed form of an attack table, parenthesis are used to calculate the actual dpsfactor
                float mhwhitedps = 1 / 100f * (hitwhite + crit - glancing - dodge) * (wdps1 + ap / 14);
                float mhyellowdps = 1 / 100f * ((hitwhite / 100f * hityellow / 100f) * 100f + crit - dodge) * wfproc * 1.4f * (wdps1 + wfap / 14);
                float mhdps = 1.1f * ssmh * hastemh * (mhwhitedps + mhyellowdps);
                float ohwhitedps = 0.5f * 1 / 100f * (hitwhite + crit - glancing - dodge) * (wdps2 + ap / 14);
                float ohyellowdps = 0.5f * 1 / 100f * ((hitwhite / 100f * hityellow / 100f) * 100f + crit - dodge) * wfproc * 1.4f * (wdps2 + wfap / 14);
                float ohdps = 1.1f * ssoh * hasteoh * (ohwhitedps + ohyellowdps);
                float finaldps = mhdps + ohdps;
                return finaldps;

For commented code, please ask if something is still unclear, I refactored the code to contain percentage type values only, if not noted otherwise:

Now to that attack table formula:

If we consider the table: 10% miss, 5% dodge, 25% glancing (with 25% reduction), 25% crit, 35% normal:
average hit is 100 dmg:

for 100 hits it looks:
10 misses, 5 dodges, 25 hits with 75 dmg, 25 hits with 200 dmg, 35 hits with 100 dmg

summed up this adds up to: 10375 dmg in 100 hits = 103.75 dmg/hit

for my equation:

1 / 100f * (hitwhite + crit - glancing - dodge)

(90 + 25 - (25*0.25) - 5) = 103.75

same value, this is just an example not a proof, proof is a bit lengthy and ugly without proper mathematical notation, given that my attacktable example is correct, the formula is a correct closed-form expression of the table.

Stormstrike, or how I think stormstrike should be looked at, considering one weapon now for simplicity:

Stormstrike allows us one more swing (with yellow hit rating) every 10 seconds. So if we actually do 4 swings per 10s (with a non flurried 2.5s weapon), we now do 5 swings in 10s. This is a net increase of 25%.
We can convert the 25% for this example to a formula 1 + weaponspeed/10.
In other words I see Stormstrike as another haste effect, just like flurry, but not a crit dependent one, but a speed dependent one:
Another example: 2s weapon, 5 swings, 6 swings with stormstrike, increase is 20%.
By using this factor on the same "level" as Weapon mastery I assume that it can proc everything (including flurry, windfury and crits).
This simplifies the whole equation extremely, this is probably not 100% correct, since I don't really factor in the gain from the yellow hit (the correct way would be SSMH/whitehit to compensate for the hit reduction later on).

@Disquette:
Your Edit 4, should be explained by my Stormstrike explanation above:
Your Edit 5, was a bug in my code, this is fixed in the maple output now it correctly scales up to 40%, apparently a misplaced parenthesis caused this.

Additionally in the c# output in this post, I modified glancing to be 25%,25% as suggested by Pater above, I also changed the max hit value to 24.6% as suggested. The difference between your testSham.vbs and my math equation is now less than 1%. So I guess they should be correct more or less.

Disquette · 06/02/07, 4:47 PM

Ok, thanks very much for the commented code. I'd like to restate my final question...

EDIT 5:
I think I'm going to leave it here for now, with one final question. Your optimizing for highest dps, as I understand it. That's why:

weapon speeds end up at their max (2.79999 in your output) , paramaters C2 and C4
+hit ends up at its max (27.6000000) , parameter C6

Yet hit doesn't end up at its max, parameter C8.
Instead, you optimize that the best value of +crit to have is 35%, not the 40% that your code runs to.

So.... Either more crit can be a bad thing, and apparently we *want* crit to be less than 36%, or there's something fishy in the code, or you ran it with parameters other than the ones you listed. While I'd like to guess that you had C8 different for your run than what you listed as the input, it's hard for me to believe that you randomly chose "35.19" as the upper bound in that respect.

I think i understand stormstrike, by the way, since you're simply saying that it has the value of a regular attack, but with the yellow hit table (neat, btw).

Edit for above responses:

thanks!

Tornhoof · 06/02/07, 5:13 PM

Originally Posted by Disquette

Ok, thanks very much for the commented code. I'd like to restate my final question...

Yes there was something fishy in the original code (misplaced paranthesis), it is now fixed and properly reaches the max value of 40%.

[1458.21819938620320, [hit = 27.6000000000000014, crit = 40., ws1 = 2.79999999999999982, ws2 = 2.79999999999999982]]

FunkaliciousFrk · 06/02/07, 5:26 PM

Okay, so my little brother is an enhancement shaman in my guild. He is currently wielding Wicked Edge of the Planes and Gladiator's axe. He has ~27 crit, 24.85 hit, and 1440 attack power unbuffed. What weapon enchants would be optimal for raiding?

Malan · 06/02/07, 5:40 PM

Originally Posted by FunkaliciousFrk

Okay, so my little brother is an enhancement shaman in my guild. He is currently wielding Wicked Edge of the Planes and Gladiator's axe. He has ~27 crit, 24.85 hit, and 1440 attack power unbuffed. What weapon enchants would be optimal for raiding?

Really? Because according to your profile you aren't in a guild.

Disquette · 06/02/07, 5:46 PM

Hey Tornhoof, so i used your calculator, and excel-ified it. You can find that here:

http://www.discofiend.com/wow/Shaman...nhance_DPS.xls

Now, here's the thing. When I plugged in values going from 20% hit to 24.6% hit, and 20% crit to 24.6% crit, it also shows how much more valuable crit is than hit. In fact, it matches the simulator results really closely.

ASSUMING I DID THE RIGHT TRANSCRIPTION OF THE CALCULATIONS!

I did the comparison using the 24.6% = max miss rate (even though I agree with you, it's probably 27.6%), and I increased both hit and crit from 20% to 24.6%, and made a matrix of the dps increases (note that i applied an armor factor, for completeness's sake).

Attached is a jpg of the results and a jpg of the formulas in the sheet, if you want to double check them.

EDIT - don't be alarmed by the "30% hit" and "30% crit" in the formulas screenshot. Once I saw the results and how out of whack they were, I realized that's because it's hit-capped at 24.6%, which is why i redid the calculations maxing out at the 24.6% values ;-)

Pater · 06/02/07, 5:47 PM

It seems like there are now three or more simulators/calculators for predicted DPS with various inputs. Can we settle on a standard benchmark input to compare and tune our simulators against each other? (Disquette and I have been doing this in PMs for a couple of weeks now, but it would be great if we could bring in everybody, including Tornhoof and anyone else.)

Here's what I would propose as the baseline case:
Player: AP 2200, total hit 22%, crit 25%, 0 bonus weapon skill, 10.0 SS cooldown
Mob: L73, with 30% armor mitigation, attack from behind (no parry or block)

As far as weapons go, I think Decap/Clad Cleaver are the easiest to obtain of the good combos. But arguments for other could be made. WF/WF weapon buffs.

Thoughts/comments?

Disquette · 06/02/07, 5:56 PM

Well, personally I'd love to use Tornhoof's for the simple fact that it's not a sim. What we really need, however, is a test to see how well these match reality.

Until bliz gives us a real target dummy, it's going to be hard to figure out what's best. I'll be honest, I don't know how a couple of Tornhoof's lines of code work, but when I look at the individual output of the line, and do some testing, the numbers magically pass a gut check.

As I've said before, I really don't like maintaining code, so I'm more than happy to wash my hands of my own. ;-) But the code needs to be *right*, which ever one we settle on. I think I'd be happy with Tornhoof's version once I understand:

ap := baseap * (1 + 0.1 * (1 - noncrit^(avghit * (1+2*wfnerf)*(20 / (wsmh + wsoh)) +2))).
later version of the same line:
float ap = baseap * (1 + 0.1f * (1 - (float)Math.Pow(noncrit, (avghit * (1+2*wfnerf)*(20 / (wsmh + wsoh)) +2))));

Not because it makes a huge difference, the numbers seem about right to me. But because I want to know exactly what's up in that exponent. I can probably figure it out, but it's a little odd looking, and it's going to take a little while to do so.

One thing I'm not sure that his code accounts for at the moment is the split of OH to MH windfuries. That would be critical to add (if it's not already there) so that a person doesn't think that 2.8/1.5 is the same dps as 1.5/2.8!

Pater · 06/02/07, 6:04 PM

I agree it would be nice to have a target dummy. I found one set of blood elves at the top of the BE side of BT in SMV that are all L70 and have reasonably good respawn. I think they're called Demon Hunter Initiates. (There are also some "Demon Hunter Supplicants" nearby that are also L70 but I haven't tested to make sure they all have the exact attributes the Initiates have.) If we model attacking from the front, we could collect data on them all night long--though it would be more for "rates" (results per swing) than net DPS, because they die fast. That's fine for a sim like yours and mine (since we have good visibility on results-per-swing), but not for Tornhoofs, since he just outputs dps, right?

FunkaliciousFrk · 06/02/07, 6:30 PM

Originally Posted by Malan

Really? Because according to your profile you aren't in a guild.

If you look at the date that i registered, you'll see that it was before this 'guild/char' stuff. So hush it. Funky @ mannoroth, guild : illuminati. If you really wanna be a cock about it, that's me.

Malan · 06/02/07, 6:38 PM

Originally Posted by FunkaliciousFrk

If you look at the date that i registered, you'll see that it was before this 'guild/char' stuff. So hush it. Funky @ mannoroth, guild : illuminati. If you really wanna be a cock about it, that's me.

Funny. I registered 2 months prior to you and that was definitely the rule at the time.

Fill out your profile. - If the space under your forum name is blank, you're not ready to post.

Tornhoof · 06/02/07, 6:43 PM

Originally Posted by Disquette

As I've said before, I really don't like maintaining code, so I'm more than happy to wash my hands of my own. ;-) But the code needs to be *right*, which ever one we settle on. I think I'd be happy with Tornhoof's version once I understand:

ap := baseap * (1 + 0.1 * (1 - noncrit^(avghit * (1+2*wfnerf)*(20 / (wsmh + wsoh)) +2))).
later version of the same line:
float ap = baseap * (1 + 0.1f * (1 - (float)Math.Pow(noncrit, (avghit * (1+2*wfnerf)*(20 / (wsmh + wsoh)) +2))));

One thing I'm not sure that his code accounts for at the moment is the split of OH to MH windfuries. That would be critical to add (if it's not already there) so that a person doesn't think that 2.8/1.5 is the same dps as 1.5/2.8!

Well the first line is for Maple, the second is c# and both are wrong :/

correct one is:

float ap = baseap * (1 + 0.1f * (1 - (float)Math.Pow(noncrit, (avghit * (1+2*wfnerf)*(10/wshmh + 10/wsoh) +2))));

The exponent is:

(1+2*wfnerf) is just the theoritcal compensation that we have 1.4 (for a 20% chance) number of swings with Wf, compared to non wf, 1/5th chance to gain 2 extra swings = 1.4*swingswithoutwf. (5*1.4 = 7 = 5 + 0.2*5*2)
(10/wsmh + 10/wsoh) calculates the swings for 10s. for two 2.5s weapons this is 8
At the end i add 2 swings for stormstrike, so technically we have 10 swings which could proc windfury, for the 20% proc chance example, we should get 2 procs out of it, resulting in 4 extra "swings".
This is multiplied with avghit to compensate that actually some miss.
It is not 100% correct, since avghit is just an approximation, but it should be fine.
I also don't know if a windfury proc crit renews unleashed rage.

And yes you're right it does not compensate for oh/wf ratio. I had a previous version which compensated for it, but that bugged out a bit.
I have yet to build a proper closed expression for that.

Disquette · 06/02/07, 6:47 PM

Just a head's up, I might not be around here much longer. While sparing the details, there's a good chance, as of this afternoon, that I might be quitting WoW for good (which, while disappointing in some senses, is very good in others). So.... with quitting the game (possibly, not definite), if you have any residual questions about the sim, now's a good time to ask them. I think Pater's is just as good, if not better than mine, though, so I think there's really not much lost.

For the next few days, if/until it happens "for certain", I'll be around here as normal.

Disquette · 06/02/07, 6:48 PM

Originally Posted by Tornhoof

Well the first line is for Maple, the second is c# and both are wrong :/

correct one is:

float ap = baseap * (1 + 0.1f * (1 - (float)Math.Pow(noncrit, (avghit * (1+2*wfnerf)*(10/wshmh + 10/wsoh) +2))));

Ok, that sits well with me, thanks :-)

I also don't know if a windfury proc crit renews unleashed rage.

pretty sure it does. should be very easy to test - turn 90 degrees away from a mob, your specials can hit, your white hits can't. Stormstrike with one weapon and wait for a stormstrike non-crit and a WF crit. It might be easier to do this single weilding, but it would take longer to get such an occurrence.

FunkaliciousFrk · 06/02/07, 6:49 PM

Originally Posted by Malan

Funny. I registered 2 months prior to you and that was definitely the rule at the time.

Happy? As far as I recall, that wasn't the rule at the time, but oh well. Far be it from me to try to take away from your nitpicking.

Rob · 06/02/07, 7:01 PM

This him? He needs a slower offhand to go with the rest of that great gear! Anyway, I haven't seen a definitive answer yet on what's the "best" enchant for a shaman. The realistic choices are obviously Mongoose, Crusader, and +20 STR; I believe I've seen something convincing illustrating that Crusader is superior to +20 STR, and I believe I saw an AP equivalency calc on the last two pages saying Mongoose was worth something like 81 AP? So I'm guessing Mongoose.

FunkaliciousFrk · 06/02/07, 7:21 PM

Originally Posted by Rob

This him? He needs a slower offhand to go with the rest of that great gear! Anyway, I haven't seen a definitive answer yet on what's the "best" enchant for a shaman. The realistic choices are obviously Mongoose, Crusader, and +20 STR; I believe I've seen something convincing illustrating that Crusader is superior to +20 STR, and I believe I saw an AP equivalency calc on the last two pages saying Mongoose was worth something like 81 AP? So I'm guessing Mongoose.

He was about to buy the gladiator cleaver a couple weeks back, because of rumors of new glad gear. Since he doesn't pvp much as enh is weak in arena, he's waiting on next season offhand. His dps should increase SUBSTANTIALLY on acquiring it.

Malan · 06/02/07, 7:27 PM

Originally Posted by FunkaliciousFrk

Happy? As far as I recall, that wasn't the rule at the time, but oh well. Far be it from me to try to take away from your nitpicking.

I'll respond just this once more and then that's it from me for this minor derail - the community helps enforce the rules of this forum, and you should be well aware of that since you've seemingly been around just as long as I and many others have. Its how the riff-raff is kept out and I'd hope you could appreciate that.

Tornhoof · 06/02/07, 7:30 PM

Crusader is 60str on Lvl 70, given one proc per minute, results in an uptime of 15s per minute, e.g. 15str., so dual wielding potency is better than dual wielding crusader on 70.

Disquette · 06/02/07, 7:47 PM

Torn, that assumes no instants and no flurry.

I'd look at it as:

60 str
x 25% base ppm
x 1.15 (flurry up half the time, and flurry increases ppm rates)
x 1.20 (guestimate of extra attacks compared to white hits due to Stormstrike and Windfury)

that's 60 x .25 * 1.15 * 1.20 = 20.7 average strength for crusader, which is indeed slightly better than potency.

I think I'm also lowballing both of the two multiples I used... maybe I'll math those up in a bit.

EDIT: more math.

the 1.15 is good for flurry with 20% crit. More than that and you're ever better with crusader.

according to Tornhoof's sheet, Stormstrike alone is worth 24% extra attacks with 2.8 speed weapons (makes sense), though it's not quite right to multiply them with flurry in this case because a single stormstrike every 10 seconds doesn't scale with flurry.

However, we haven't even looked at the fact that you're probably going to have 3 attacks or so from windfury in the same 10 second window. So, I'd say, with slow-ish weapons, and a decent crit rate (20%+), crusader is *significantly* better than potency.

Pater · 06/02/07, 7:56 PM

Anybody have a good handle on statistics? I know just enough to know I'm in over my head.

I have a DPS time-step simulator. My question is: how long should I make combat length to be comfortable that the output number is "good enough" to run it only one time?

I just ran the simulator 10 times at five different combat lengths, and here are the results:

(I see I don't have the right to post attachments, so forced to use imagehosting or something.)

Intuitively, I like the look of the 100-hour run (second-to-last column). That takes only about 5 seconds on my machine, and the standard deviation of the 10 samples I took was only 1 dps.

• Relwin · 06/02/07, 7:59 PM

Originally Posted by Tornhoof

Crusader is 60str on Lvl 70, given one proc per minute, results in an uptime of 15s per minute, e.g. 15str., so dual wielding potency is better than dual wielding crusader on 70.

Assuming you do zero yellow attacks in that minute you'll see that 1PPM on it. As soon as you get that second proc of crusader, assuming zero overlap, Crusader is better.

The two enchants you'll want to look at are Mongoose and Crusader as far as mainhands go at least. Potency on the offhand is acceptable as you don't want your offhand to be sucking up your yellow attacks (Windfuries) nearly as much as your mainhand.

Kaubel · 06/02/07, 8:19 PM

Originally Posted by Malan

I'll respond just this once more and then that's it from me for this minor derail - the community helps enforce the rules of this forum, and you should be well aware of that since you've seemingly been around just as long as I and many others have. Its how the riff-raff is kept out and I'd hope you could appreciate that.

And you should know better than to get in a pissing match. Report it and move on.