Best in Slot for SMN after 2.1?

[T0rin]

Alright, so at a very basic level, in order to determine which items are indeed BiS, you have to have a method for determining how much each stat "weighs". Stat weight is basically a numerical representation of how much one thing is worth compared to another thing, so you can assign values to every item to determine how good things actually are, in terms of contributing to damage.

One of the major misconceptions about stat weights, is they were static. People bandied around data like "1 WD is worth 6 INT" or "1 INT is worth 6 CRT", etc. In reality, stat weights vary, sometimes greatly, from one person to the next, from one gear set to the next. In order to actually come up with realistic stat weights, you need a working and reliable damage formula.

This is where EasymodeX, those who inspired him and those who contributed data sets to refining the current formula come in. In this thread, you can see the formula being refined as more data sets are introduced, to get it to the point where a formula can be used for any class, any stats, to come up with a reliable damage number.

So, it's all just hokum, right? Nobody really knows, blah blah blah, right? Well, that was my basic stance a month ago. I believed one train of thought on stat weights. I believe differently now, or more accurately, know better. So, we've got this damage formula: (WD*.2714745 + INT*.1006032 + (DTR-202)*.0241327 + WD*INT*.0036167 + WD*(DTR-202)*.0010800 - 1) * (Potency/100)

The first thing we need to determine an actual BiS, is confirmation that this formula can indeed reliably and more important, accurately, determine damage values from stats. I'm going to give a single example, but in the process of my research, I had many many examples. I sat down in front of FFXIV:ARR, and I literally cast a single spell on a Striking Dummy hundreds of times in some cases. I tested Bio, Bio II, Miasma, Miasma II, Ruin, Ruin II, Fester, Blizzard II and Tri-Disaster. I just sat there, cast spells, wrote down the damage values that popped up. I wanted to eliminate potentially inaccurate parsing results from the equation, as well as record individual DoT ticks for validation.

So, here is an example set of data for Bio that I recorded earlier this morning for purposes of explaining this:

109 148 105 153  99 108  99 163 109 109 108 101 102  99 110 110 153 106
109  99  99 101 101 109 100 107 165 105 108 105 105 105 100 159 165 100
153 105 109 163 148 108 110 107 106 109 109 102 107 108 165 101 108 110
165 157 103 162  99 106 107 101 154 108 157 105 157 107 109 103 103 101
 99 105 101 103 160 150 103 107 110 163 108 102 109 103 110 108  99  99
163 150 160 107 101

This was taken with 71 WD, 490 INT, 280 DTR and 563 CRT. So, before I can compare these results to the formula, I first need to come up with the non-crit values of all of these numbers. If a number was great than 120, I divided it by 1.5 to get the non-crit value. I'm left with this:

109  99 105 102  99 108  99 109 109 109 108 101 102  99 110 110 102 106
109  99  99 101 101 109 100 107 110 105 108 105 105 105 100 106 110 100
102 105 109 109  99 108 110 107 106 109 109 102 107 108 110 101 108 110
110 105 103 108  99 106 107 101 103 108 105 105 105 107 109 103 103 101
 99 105 101 103 107 100 103 107 110 109 108 102 109 103 110 108  99  99
109 100 107 107 101

The average of all of these numbers is 105.031578947368. So, now we take the damage formula, plug my stats and potency for Bio (40) in and end up with this: (71*.2714745 + 490*.1006032 + (280-202)*.0241327 + 71*490*.0036167 + 71*(280-202)*.0010800 - 1) * (40/100)

What we get back is an un-modified value of 80.50345644. Now we need to apply the SMN trait "Main and Mend II" acquired at level 40, that "Increases base action damage and HP restoration by 30%." 80.50345644 * 1.3 = 104.6544934, which is within the acceptable range of +- 5% deviation compared to our in-game data collected and averaged to be 105.031578947368.

So, from this we can conclude that the formula, which again, I tested on far more than just Bio with i89 gear, I tested with 10 different skills across 5 different sets of varying ilvl gear, is giving us accurate results. Since we know we can rely on this formula for accurate results, we can now take to the task of finding stat weights.

For the next exercise, I'm going to use the "old"/current BiS set:

Allagan Grimoire of Casting
Summoner's Horn
Summoner's Doublet
Summoner's Ringbands
Allagan Rope Belt of Casting
Allagan Breeches of Casting
Allagan Boots of Casting
Hero's Necklace of Casting
Tremor Earring of Casting
Hero's Bracelet of Casting
Hero's Ring of Casting
Vortex Ring of Casting

This set confers the following attribute bonuses: 71 WD, 224 INT, 60 DTR, 224 CRT and 37 SS. Add that onto our base stats (with Soul of the Summoner) and we get total stats of: 71 WD, 499 INT, 262 DTR, 565 CRT and 378 SS. These stats are going to be our baseline for determining stat weights.

We start with some basic assumptions.. the aforementioned stats, the aforementioned damage formula, potency of 40 for Bio, our base damage and our modified damage values. From this point on, the base (un-modified) damage is fairly irrelevant, as the modified damage is what is representative of what we see in the game. From here, we need to come up with damage modified by critical hits.

The formula I am using, which again, I have verified with large data sets in game to be accurate with my selection of gear sets is: 0.0697 * CRT – 18.437. This formula came from Valk's work and has been independently verified by multiple people.

So I put my value of crit in and get the following formula and result: 0.0697 * 565 - 18.437 = 20.9435% chance to critical. Now we need to turn this number into something we can multiply our base damage value by, to get a crit modified damage average. So we have a 20.9435% chance to crit for +50% damage. So we'll do something like this: 1 + 0.5*(0.0697 * 565 - 18.437)/100 = 1.1047175. Basically, averaged out, we are applying a 10.47175% bonus to damage for our critical hits.

We take our calculated base [modified] damage of 105.3834666 (calculated using the above formula with the BiS set stats), multiply it by 1.1047175 and get back a result of 116.4189598 damage, modified to include the average crit damage contribution.

Just to make sure nobody is lost so far... for our BiS set stats (71 WD, 499 INT, 262 DTR, 565 CRT and 378 SS) we have a crit modified damage value of 116.4189598. This is our baseline damage that our stat weights will be calculated against. To get our stat weights, what we're going to do is perform this same calculation, but each time with a single stat increased by 1. What this is going to do is give us a damage value that we can compare against our baseline damage, to determine how much damage was added by increasing a single stat by 1.

We'll start with WD: (72*.2714745 + 499*.1006032 + (262-202)*.0241327 + 72*499*.0036167 + 72*(262-202)*.0010800 - 1) * (40/100) * 1.3 * (1 + 0.5*(0.0697 * 565 - 18.437)/100) = 117.6488683. So, the difference (delta) between this calculated value with +1 WD over our baseline is 0.946083514. This number is important, as we are going to divide this number by the delta for INT, to come up with the stat weight for WD. But, before we go there, let's calculate the other stat's deltas.

INT: (71*.2714745 + 500*.1006032 + (262-202)*.0241327 + 71*500*.0036167 + 71*(262-202)*.0010800 - 1) * (40/100) * 1.3 * (1 + 0.5*(0.0697 * 565 - 18.437)/100) = 116.6242629, delta of 0.157925509.

DTR: (71*.2714745 + 499*.1006032 + (263-202)*.0241327 + 71*499*.0036167 + 71*(263-202)*.0010800 - 1) * (40/100) * 1.3 * (1 + 0.5*(0.0697 * 565 - 18.437)/100) = 116.4768719, delta of 0.044547822.

CRT: (71*.2714745 + 499*.1006032 + (262-202)*.0241327 + 71*499*.0036167 + 71*(262-202)*.0010800 - 1) * (40/100) * 1.3 * (1 + 0.5*(0.0697 * 566 - 18.437)/100) = 116.4556858, delta of 0.028250875.

Now that we have our deltas, we can figure out the stat weights... since we want everything to be relative to INT, we divide the stat delta in question to the stat delta for INT, which comes up with a number relative to 1 INT.

WD: 0.946083514 / 0.157925509 = 5.990694731
INT: 0.157925509 / 0.157925509 = 1
DTR: 0.044547822 / 0.157925509 = 0.282081229
CRT: 0.028250875 / 0.157925509 = 0.178887348

For SS, I will fully admit that I have not redone these calculations, because they rely on establishing a specific rotation, applying SS modifiers to each spell, and figuring out and comparing to base (2.5sec) potency totals for a rotation performed within a static time frame. Rather than perform this work for this exercise, since most people will be able to agree that SS has a fairly minor impact on SMN damage overall, I'll simply use the SS weight derived by Eein at chocobro.com of 0.084943755, which about half that of CRT.

We now have stat weights for this particular BiS set of gear. Now coming up with a total stat weight for the set is a simple matter of multiplication... we take our set stat contributions (71 WD, 224 INT, 60 DTR, 224 CRT and 37 SS) and multiply each value by the stat weight, sum it all up and we get: (71*5.990694731)+(224*1)+(60*0.282081229)+(224*0.178887348)+(37*0.084943755) = 709.4778845 weighted INT.

What we see here is that each gear set has its own stat weights, and thus its own calculations to determine how 'good' it is. Previously, we were applying the same weights to every single set to come up with that determination (har!), but that was wrong. So, now that we've got a method, I did some expertimentation with gear sets to find other ~448 accuracy sets that could potentially offer a higher value of weighted INT. What I came up with was 2 sets, identical except for 2 specific slots, that had identical stat contributions and thus identical stat weights. These two sets are:

Allagan Grimoire of Casting
Allagan Circlet of Casting
Summoner's Doublet
Allagan Gloves of Casting
Allagan Rope Belt of Casting
Summoner's Trousers
Allagan Boots of Casting
Hero's Necklace of Casting
Tremor Earring of Casting
Hero's Bracelet of Casting
Allagan Ring of Casting
Vortex Ring of Casting

...and...

Allagan Grimoire of Casting
Allagan Circlet of Casting
Summoner's Doublet
Allagan Gloves of Casting
Hero's Belt of Casting
Summoner's Trousers
Allagan Boots of Casting
Hero's Necklace of Casting
Tremor Earring of Casting
Hero's Bracelet of Casting
Hero's Ring of Casting
Vortex Ring of Casting

You'll notice, the only difference is the belt and non-Vortex ring. You can use either Allagan belt and Allagan ring, or Hero's belt and Hero's ring, and you get the exact same bonuses. Both sets sport 448 ACC, just like the previous BiS set. The calculated stat weights for these two sets are as follows:

WD = 6.120637211, INT = 1, DTR = 0.282081229, CRT = 0.186899974, SS = 0.084943755

If you take the set stat bonuses of 71 WD, 224 INT, 103 DTR, 153 CRT and 48 SS, we get a weighted INT value of 720.2926048, which is 10.8147203 higher than our previous set.

And that's why the new sets are BiS.

[Kevee]

Rather than perform this work for this exercise, since most people will be able to agree that SS has a fairly minor impact on SMN damage overall

I wouldn't be so quick to say this, because this is what we said about DET.

Also, I can't find that weight you mention on chocobro forums.

[T0rin]

I wouldn't be so quick to say this, because this is what we said about DET.

Also, I can't find that weight you mention on chocobro forums.

It was taken from his sim, which is down at the moment. I'm completely open this this value being wrong, and will be working soon to create a SS modifiable timeline to determine how much of a potency multiplier we should apply for 1 SS, but I figured, for the time being, it was 'good enough' to explain what I'd done so far. Both sets have very similar SS values, the 'new BiS' has slightly more. If for some reason SS turned out to be the 'miracle stat', we could potentially need to come up with an SS focused set, but given the dynamics of DoTs benefiting from SS in such a minor way and Ruin being such a minor contribution to overall damage, I wouldn't reasonably expect an SS build to have the potential to be better.

But, like I said, I could be wrong. Hopefully I'll have the time in the next week to do that work, but for now, I do have some faith in Eein's sim's rotation, at least for this purpose.

[Maelwys]

So, we've got this damage formula: (WD*.2714745 + INT*.1006032 + (DTR-202)*.0241327 + WD*INT*.0036167 + WD*(DTR-202)*.0010800 - 1) * (Potency/100)

Yup, that's the same one I've been using and it certainly seems accurate.

The formula I am using, which again, I have verified with large data sets in game to be accurate with my selection of gear sets is: 0.0693 x CRT – 18.486. This formula came from Valk's work and has been independently verified by multiple people.

I'm aware of Valk's original formula for Crit chance (indeed, it's still listed on his methodology pages) but it's actually been tweaked slightly since then:

Critical Hit Rate Formula Updates

• Updated formula is 0.0697xCRT – 18.437 (old formula was 0.0693xCRT – 18.486).

It's not vastly different, but might be enough to skew stacked stats in favour of one BIS item or another.

What I came up with was 2 sets, identical except for 2 specific slots, that had identical stat contributions and thus identical stat weights. These two sets are:

(Item lists snipped)

And that's why the new sets are BiS.

Did you consider a Melded Astral Ring? I make it better than the Hero or Allagan one using the above formulas, especially since you can meld Vit and Acc onto it.

The ideal melds on such a HQ Astral would probably be Mk4 Vit, Mk3 Crit, Mk3 Crit and Mk2 Acc... plus either a Mk4 Piety or Mk4 SS for the final slot if you're megarich.
(The stats would end up at 9 Mnd, 7 Vit, 9 Int, 12 Acc, 12 Crit, 8 Det... plus either 6 PIE or 9 SS)

Indeed, I'm aiming at the following gear for my (very eventual) BIS SMN:
+ Hero's Neck
+ Tremor Earring
+ Hero's Wrist
+ Vortex Ring
+ Melded HQ Astral Ring
+ Allagan Weapon
+ Allagan Head
+ Myth Body
+ Allagan Hands
+ Allagan Sash
+ Summoner Legs
+ Allagan Feet
+ HQ Buttons in a Blanket

With the above, I make it a total of 449 Acc, plus an additional +222 Int, 165 Crit, 111 Det and either 32 or 41 SS from gear (depending on whether the 5th Meld on the Astral Ring is Piety or SS)... with HQ Buttons in a Blanket and in-party, my Seawolf would end up with 505 Int, 516 Crit, 328 Det and be sitting at a hair under 4900HP.

Technically maximum DPS could be achieved by picking the Heros Earring over the Tremor one... but we'd need a little more accuracy in order to cap out the pets (433 Acc with Heros compared to 449 Acc with Tremor). A compromise would be to take the Heros Earring but swap the Allagan belt for the Heros Belt (444 Acc and a slightly lower reduction in DPS) if you think that's enough to cap your accuracy.

[T0rin]

I'm aware of Valk's original formula for Crit chance (indeed, it's still listed on his methodology pages) but it's actually been tweaked slightly since then:

Critical Hit Rate Formula Updates

• Updated formula is 0.0697xCRT – 18.437 (old formula was 0.0693xCRT – 18.486).

It's not vastly different, but might be enough to skew stacked stats in favour of one BIS item or another.

Great to know, thank you. I updated my 'math post' to include this formula, and re-did all the math I had done that comes after applying the crit damage multiplier. All sets went up in weighted int, slightly, the "old" BiS more than the new ones. But, in the end, nothing changed in terms of BiS, and the new sets are only 0.04 weighted int less better than they were. So, they're still almost 11 int better than the "old" BiS.

Did you consider a Melded Astral Ring? I make it better than the Hero or Allagan one using the above formulas, especially since you can meld Vit and Acc onto it.

The ideal melds on such a HQ Astral would probably be Mk4 Vit, Mk3 Crit, Mk3 Crit and Mk2 Acc... plus either a Mk4 Piety or Mk4 SS for the final slot if you're megarich.
(The stats would end up at 9 Mnd, 7 Vit, 9 Int, 12 Acc, 12 Crit, 8 Det... plus either 6 PIE or 9 SS)

I did. For the new BiS sets, using these weights (WD = 6.120637211, INT = 1, DTR = 0.282081229, CRT = 0.186899974, SS = 0.084943755) I value the Allagan Ring at 14.35910008 weighted INT.

If I used an Astral Ring melded with SS, using these weights (refactored to use Astral stats, WD = 6.104333403, INT = 1, DTR = 0.282081229, CRT = 0.185618633, SS = 0.084943755) I value the Astral Ring w/ SS at 14.24856722 weighted INT.

If I meld an Astral Ring with 6 PIE instead, I get a value of 13.48407343 weighted INT, obviously even less than the Allagan Ring.

But one thing this does bring up is that for someone going for the Allagan Belt/Ring set, you could temporarily use a melded Astral Ring in lieu of the Allagan Ring, since it is _almost_ as good. I still have never seen the Allagan Ring drop, but I do have the belt, and I do have a melded Astral Ring, so I could start using this newer set sooner.

Technically maximum DPS could be achieved by picking the Heros Earring over the Tremor one...

I show, using the new BiS weights (refactored to include these items instead) that the Hero's Earring is worth 16.61574991 weighted INT and the Allagan Earring is worth 16.91996375 weighted INT. So for Max DPS (which is a valid thing if doing Ex Primals that have significantly lower ACC caps) you'd want the Allagan Earring instead.

...but we'd need a little more accuracy in order to cap out the pets (433 Acc with Heros compared to 449 Acc with Tremor). A compromise would be to take the Heros Earring but swap the Allagan belt for the Heros Belt (444 Acc and a slightly lower reduction in DPS) if you think that's enough to cap your accuracy.

443 wouldn't be enough to cap, but theoretically you can go less than 12 acc (~6?) under 450 and if you got significantly enough secondary stats out of it, it could be worth it. But this set would have 443 ACC (Allagan Ring instead of Astral Ring, since it is better) and a total weighted INT of 719.6903469, so even with less accuracy, it is worse damage.

[Maelwys]

If I used an Astral Ring melded with SS, using these weights (refactored to use Astral stats, WD = 6.104333403, INT = 1, DTR = 0.282081229, CRT = 0.185618633, SS = 0.084943755) I value the Astral Ring w/ SS at 14.24856722 weighted INT.

If I meld an Astral Ring with 6 PIE instead, I get a value of 13.48407343 weighted INT, obviously even less than the Allagan Ring.

But one thing this does bring up is that for someone going for the Allagan Belt/Ring set, you could temporarily use a melded Astral Ring in lieu of the Allagan Ring, since it is _almost_ as good. I still have never seen the Allagan Ring drop, but I do have the belt, and I do have a melded Astral Ring, so I could start using this newer set sooner.

I think I can see where I'm getting slightly different numbers than yours - my Spreadsheet is using the Base stats for my character, along with +30 INT from allocated points, then adds in equipment stat buffs, and finally applies food and party buffs (party buffs being applied last, after food) and THEN factors the sum of all those into the stat formulas.

Base stats for my character are 241+30 INT, 341 Crit, 202 Det.
Food buffs (after equipment) are 10 Crit and 15 Det with HQ Buttons in a Blanket.
In-Party buffs are percentage based and vary slightly depending on gear, but the only one applicable to our purposes here is 3% extra INT which for this setup is 14.

For the equipment combination I posted above (Astral Ring), I'm getting a grand total of 505 INT, 516 Crit, 328 Det.
If I swap the Astral Ring for a Heros Ring (ignoring the accuracy loss for the moment) I get 509 INT, 520 Crit and 320 Det.

Plugging those values into the formulas...

First, for the Astral Ring setup:
Raw Damage = 71*0.2714745 + (505)*0.10060032 + (328-202)*0.241327 + 71*(505)*0.0036167 + 71*(328-202)*0.00108 - 1 = 238.8235116
Crit chance is (0.0697*516 -18.437) = 17.5282%
Crit adjusted Damage = 238.8235116*(1-0.175282) + 238.8235116*1.5*0.175282 = 259.754242980136

Second, for the Hero's Ring setup:
Raw Damage = 71*0.2714745 + (509)*0.10060032 + (320-202)*0.241327 + 71*(509)*0.0036167 + 71*(320-202)*0.00108 - 1 = 237.70899968
Crit chance is (0.0697*520 -18.437) = 17.807%
Crit adjusted Damage = 237.70899968*(1-0.17807) + 237.70899968*1.5*0.17807 = 258.873420466509

Result: an (utterly tiny!) increase in DPS for the Astral ring setup.
(It's certainly possible I've made a maths derp here, or at least a typo copying all the formulas from the spreadsheets... but just wanted to check!)

[T0rin]

For the equipment combination I posted above (Astral Ring), I'm getting a grand total of 505 INT, 516 Crit, 328 Det.

First, for the Astral Ring setup:
Raw Damage = 71*0.2714745 + (505)*0.10060032 + (328-202)*0.241327 + 71*(505)*0.0036167 + 71*(328-202)*0.00108 - 1 = 238.8235116
Crit chance is (0.0697*516 -18.437) = 17.5282%
Crit adjusted Damage = 238.8235116*(1-0.175282) + 238.8235116*1.5*0.175282 = 259.754242980136

Raw Damage = 71*0.2714745 + 505*0.1006032 + (328-202)*0.0241327 + 71*505*0.0036167 + 71*(328-202)*0.00108 - 1 = 211.4584842
Crit chance is (0.0697*516 -18.437) = 17.5282%
Crit adjusted Damage = 211.4584842*(1-0.175282) + 211.4584842*1.5*0.175282 = 229.9909172

If I swap the Astral Ring for a Heros Ring (ignoring the accuracy loss for the moment) I get 509 INT, 520 Crit and 320 Det.

Second, for the Hero's Ring setup:
Raw Damage = 71*0.2714745 + (509)*0.10060032 + (320-202)*0.241327 + 71*(509)*0.0036167 + 71*(320-202)*0.00108 - 1 = 237.70899968
Crit chance is (0.0697*520 -18.437) = 17.807%
Crit adjusted Damage = 237.70899968*(1-0.17807) + 237.70899968*1.5*0.17807 = 258.873420466509

Raw Damage = 71*0.2714745 + 509*0.1006032 + (320-202)*0.0241327 + 71*509*0.0036167 + 71*(320-202)*0.00108 - 1 = 212.0815382
Crit chance is (0.0697*520 -18.437) = 17.807%
Crit adjusted Damage = 212.0815382*(1-0.17807) + 212.0815382*1.5*0.17807 = 230.964218

(It's certainly possible I've made a maths derp here, or at least a typo copying all the formulas from the spreadsheets... but just wanted to check!)

You did. See the above bolded numbers in my damage formulas and how they affect the outcome. Those 2 numbers were not input correctly into the formulas you used when making the comparison. Hero's Ring does more damage on a per cast basis, and one thing you neglected to consider is that it also has 11 spell speed, which is 2 or 11 more than the Astral Ring, depending on how you meld it.

But this does bring up a good point... I need to add some variables to my spreadsheet.. party buffs, race base int variations and food.

[Maelwys]

You did.

Aha! Powers of 10, my sworn enemy, we meet again...


That makes the Heros slightly better than the Astral which is slightly better than the Allagan.
Possibly still a better option if accuracy is lacking, but not "better DPS".

That explains it. Cheers!

(I realise I ignored Spell Speed and Accuracy, I was trying to make the comparison as simple as possible. Obviously not simple enough!!)

[T0rin]

That makes the Heros slightly better than the Astral which is slightly better than the Allagan.

(I realise I ignored Spell Speed and Accuracy, I was trying to make the comparison as simple as possible. Obviously not simple enough!!)

If you factor in spell speed (you should), the Allagan Ring has a weighted INT of 14.35910008 and the Astral Ring has a weighted INT of 14.29614945.

So, from a DPS perspective... Hero > Allagan > Astral.

It is nice, that if you need accuracy on that ring slot, that Astral is almost as good as Allagan, but it is not BiS in any set.. the 4 INT is just worth too much.