Fusion Cauldroning 101

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akerson
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Fusion Cauldroning 101

Postby akerson » Wed Aug 03, 2016 9:50 am

Hi friends! Abqu here* with his first guide for fusion cauldrons and how you can be come the master alchemist you always wanted! So buckle up, because this is going to be a doozy!

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The Basics

By now you've probably dabbled in using the cauldron. You get more combination slots as you level it up (which also lets you put higher item levels in there too), and you can buy more fusion slots (aka more fusions at once) for gems as you increase the pot's level. You're also probably aware of the "basic" fusions, that let you upgrade your items quality 100% of the time. In case you're not, these are them:

    2 Common = Good
    2 Good = Great
    3 Great = Flawless
    5 Flawless = Epic
    5 Epic = Legendary
    5 Legendary = Mythical (63%)

You've also probably dabbled with mixing items to seemingly crazy results. What is that wizardy that chugs out numbers that I generally don't like? What if I told you that you had the ability to harness that power, and become a wizard yourself?? Read on!

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The Less Basics

Fusion Cauldron output is a pretty simple formula once you get rolling. Here's the steps to figure out what items come out, and how likely they are to come out:

Step 1: Figure out what items can be made

1. Take all your cauldron ingredients, and find the max quality between them and add one. We'll call this quality MAXQ just for simplicity. So if your cauldron has a common knife, great knife, and flawless knife in it -- the max quality is flawless, so MAXQ = epic

2. Make a list of possible outputs -- For EACH cauldron ingredients, add every quality 1 higher than it is currently up to MAXQ to the pot -- even if the ingredients are identical. So if we stick with our same example, the common knife will add good,great,flawless, and epic to the pot, the great will add flawless and epic, and the flawless will add a final epic knife making our possible outputs: 1 good, 1 great, 2 flawless, 3 epic.

3. Calculate fusion values for each item. Fusion value is a simple equation -- A*NQL/LVL^B (more on that equation in a sec)

4. Calculate the percent chance -- for each output, it's just fusion value / sum of all fusion values.

"So what do all those variables mean Abqu*???" you might be chanting rhythmically. Well, LVL is just the item level of the output item (for a knife LVL = 1), and A & B are just constants from a table based on the quality of the item, that table looks like this:

Code: Select all

Quality       A     B
Good          4    1.25
Great         3    1.5
Flawless      2    1.75
Epic         1.5    2
Legendary     1    2.5
Mythical     0.25   3


If you're smart, you'll notice that fusion value decreases heavily with quality thanks to a decreasing numerator and an exponentially increasing denominator all things equal, which for the not-math savvy means mythics are REALLY hard to craft. But you already knew that right?

What gets interesting is the NQL, which stands for nearest quality level. For the output item's quality, it looks for the closest quality of ingredient (going downwards only) and uses that ingredient's level. If none can be found, NQL=1. This can be calculated right at the beginning for each quality level based on the ingredients because your ingredients aren't changing -- but the game calculates it on the fly for each output (heh heh #suboptimality). So let's say you have a great club fusing with a legendary knife to try and get that mythic knife you always wanted, here's what NQL would look like:

Code: Select all

Mythical   Knife Lvl
Legendary  Knife Lvl
Epic       Club Lvl
Flawless   Club Lvl


Why is this important? Because if you remember part 1 (if you forgot already, we need to have a chat...) we can actually create a mythical club as well as a mythical knife, so NQL is sort of a field leveler that gives your low level items a bump up in fusion value and your higher level items a bump down to keep your expected output relative to your inputs.

If you were REALLY smart, you'd say, "Hey Abqu * -- if my outputs are always 1 quality higher than my inputs, how would I ever get NQL = 1??" And that's where the magic comes in. Either by design or by bug, NQL DOES NOT CHECK COMMON LEVEL INGREDIENTS. With NQL = 1, fusion value is REALLY low for higher level items. Meaning, if I fused a common wisdom ocarina with a flawless goddess tear -- my odds of getting a good/great wisdom ocarina are REALLY low. If I had used a good ocarina instead, I'd eliminate the good craft but my great craft would be huge.

Step 2: Figure out the likelihood for success
As your quality of ingredients goes up, you'll notice you start to get a lower % chance of success. If you fail, the fusion will not happen and you'll get back your ingredients, minus one that's destroyed. No bueno. The good news is fusion success is really easy to figure out:

1. Figure out total ingredients. Just count them! We'll call this value IngredientCount

2. Calculate the Average quality. AVGQ = (sum of all ingredient numerical qualities + 1)/IngredientCount. The numerical count is just 0-6, 0 being commons and 6 being mythicals.

2. If AVGQ<=3, subtract 1 from AVGQ

3. Chance = 0.75*IngredientCount/AVQ

4. If IngredientCount = 5 and AVGQ < 6, Success = 100%, otherwise Success = Chance (capped at 100%)

Obviously, as your quality of inputs goes up, AVQ goes up, and thus success goes down. Three really good fusions to point out at 100% -- CF (common + flawless, get with the lingo!) is the highest "common" fuse (see step 1 why commons are important!) that gets the AVQ bump down to keep it at 100%. Fantastic fuse to do because it takes the NQL shennigan and combines it with the AVGQ shennigan for a double entendre. FFFE is considered one of the "go-to's" by the Shop Heroes pros to reduce ingredients on a epic buff. However, 2xCommon + Epic has some serious merit with higher level equipment (they need to be higher level because of the NQL trick to reduce "bad" crafts). For a level 50 item, CCE has a 5.67% chance of legendary with a ~40% chance of getting an epic back. There's even some merit in CFE to get shorter craft times at the expense of a lower epic/legendary yield. Gamblers beware!

Step 3: Calculate Fuse Time

The bane of everyone's existance! The formula is actually really easy --

1. Figure out how many UNIQUE ingredients you have. Quality matters -- a good knife does not equal a great knife for this number.
2. Figure out the highest numeric quality ingredient -- again 0 = common, 6 = mythic
3. Figure out the highest level of ingredient
4. Use the item level to look up the fuse time (i'm not going to list all the levels, but I'll say after 40 fuse times get REALLY long really fast in a curve that can only be explained as the CC devs were cackling menacingly as they coded it in). We'll call this D.
5. Fuse time (in seconds) = D*(Quality+1)^1.25/Unique

The only important things to note is item level and quality make your times ridiculously long as they go up, and your inputs matter -- by just fusing two different grade items (or two same grade items but different item levels) you cut your time in half. When you're doing high level crafting, 5 different inputs is critical -- 5x of the same Lv50 Legendary will take 9 days 9hrs to craft!

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TL;DR

So what's this mean for you? Well, here's my short list of current tips that I'll eventually update as I, Abqu *, come up with more good tips:

#1 Stay away from goods and greats for fusions unless you're trying to fuse a great or flawless!!! With how NQL is calculated, there's absolutely no reason to use more than commons as "ingredient fodder"

#2 CF crafts are the biggest bang for your buck. You'll easily make epics, the ingredients are easy, 100% success, and your output is super efficient

#3 Use higher level higher quality inputs that are easy to craft to make legendaries out of lower level harder to craft items. Goddess Tears and Wisdom Ocarinas are great for this. For example, an epic goddess tear and 2 common adamantium helms give a 37% chance of epic helm, 4^ chance of legendary helm, and 2% chance of legendary tear for a whopping 43% of good outputs. Four flawless helms and a goddess tear only up your chances for that ada helm to 9% for significantly more inputs.

#4 If you're going to do FFFE (or any full craft small bump), consider making the epic the lower level and the flawless your target items. You'll have a higher chance of getting a legendary out of it.

#5 ???

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A Gift

So now that I've probably filled your head with so much math you'll explode, I want to say I've done all the hard work and made a google sheet to share with everyone. You'll have to download/copy it to play around with it, but I think that's a small price to pay. Just edit anything in bright yellow and have fun!

http://www.bit.ly/shfusecalc

Hope you guys enjoyed, that's it for now! Let me know if you have any questions, or if you find any particularly fun/useful fuses! Thanks for reading all the way through, you're a champ :D

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* Not actually Abqu, just posing as him so that way people like my guide
Last edited by akerson on Fri Mar 03, 2017 2:33 am, edited 1 time in total.
"I believe the forum ban was deserved, as he has been out of line, and warned.

I believe a permanent game ban was out of line."

-Abqu

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Richard
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Re: Fusion Cauldroning 101

Postby Richard » Wed Aug 03, 2016 9:57 am

Wow Abqu*, amazing guide! :D

Lettuce inspected. Hamster approved.
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Abqu
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Re: Fusion Cauldroning 101

Postby Abqu » Wed Aug 03, 2016 10:07 am

Richard wrote:Wow Abqu*, amazing guide! :D

Lettuce inspected. Hamster approved.


Thanks! I* worked very hard at this. I just hope all the time and effort I* put in will help people.

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Shiroe
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Re: Fusion Cauldroning 101

Postby Shiroe » Wed Aug 03, 2016 11:22 am

Thanks, Abqurson. ;)

Now, if only google would stop being rude and let me save it as an open document spreadsheet... (for some odd reason excel does succeed...)
as of 2016-09-11: Player level: 44, City: Eolythes, Blueprints: 517, Mastered: 419, Crafted: 78.61K
(except for tier 1 and some tier 2 artifacts mostly running my shop/gearing self sufficient)

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Mr. Door
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Re: Fusion Cauldroning 101

Postby Mr. Door » Wed Aug 03, 2016 12:11 pm

Thank you akerson! To me, this was the Last Great Unwritten Guide. I'd just reached the point in the game where the cauldron is more than just a place to make precrafts, and was itching for some guidance.

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Re: Fusion Cauldroning 101

Postby Haze » Wed Aug 03, 2016 1:44 pm

Great guide, I can tell you put a lot of work into both your post and the spreadsheet.

I never realized the fusion cauldron was quite so complicated, looks like I've been fusing things the wrong (or long) way. I mostly work on getting legendary pieces for my heroes who are part of a team or max level.

Some of the math went over my head a bit and it will take me time to understand some of your guide. One thing that would help me (and maybe others) would be to give some clear, concise examples of what you would put in the cauldron to make (for example) mythic noble plate or legendary bloodlust gauntlet, or whatever. You touched on this with the knife example, I'd just like to see a specific list of the quality and item types you would use to make one or two specific items is all.

Thanks again for putting in the work we can all benefit from.

-Haze

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akerson
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Re: Fusion Cauldroning 101

Postby akerson » Wed Aug 03, 2016 2:26 pm

Haze wrote:Great guide, I can tell you put a lot of work into both your post and the spreadsheet.

I never realized the fusion cauldron was quite so complicated, looks like I've been fusing things the wrong (or long) way. I mostly work on getting legendary pieces for my heroes who are part of a team or max level.

Some of the math went over my head a bit and it will take me time to understand some of your guide. One thing that would help me (and maybe others) would be to give some clear, concise examples of what you would put in the cauldron to make (for example) mythic noble plate or legendary bloodlust gauntlet, or whatever. You touched on this with the knife example, I'd just like to see a specific list of the quality and item types you would use to make one or two specific items is all.

Thanks again for putting in the work we can all benefit from.

-Haze


Legendary bloodlust gauntlet I'd recommend either CCE of the same item, or one common as a different one. Im not at home to try, but it youre going to mix I recommend a higher lvl item than the gauntlet that you wouldn't mind an epic of to cut down the time a bit more (I think -- use the calculator and mess around!!)

Mythics I don't have any advice right now other than mix your favorite 5 legendaries close in level and hope for the best.

I'd love to give specific tips on like hey you should do this for best outcomes, but unfortunately there's a bit of artistry with whatever blueprints youve got. But I want to stay on top of my tips section as I (or anyone !) Figure out some more tricks (:
"I believe the forum ban was deserved, as he has been out of line, and warned.

I believe a permanent game ban was out of line."

-Abqu

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Mr. Door
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Re: Fusion Cauldroning 101

Postby Mr. Door » Wed Aug 03, 2016 2:39 pm

Examples and sample formulas will hopefully start showing up in the responses to the guide, but I think Haze's point comes not from specifically wanting a Bloodlust Gauntlet/ Noble Plate recipe, but from the fact that the examples you do use (Ocarina and Goddess Tear) are so rarefied. It makes the guide feel like it's only for one-percenters, when it doesn't need to be. If your examples were a little lower level, and not from premium packs and rare blueprints, more people would grasp the concepts more quickly.

I had something similar written in my first comment, but deleted that part because your work was so excellent I just wanted to be positive about it.

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akerson
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Re: Fusion Cauldroning 101

Postby akerson » Wed Aug 03, 2016 3:03 pm

Mr. Door wrote:Examples and sample formulas will hopefully start showing up in the responses to the guide, but I think Haze's point comes not from specifically wanting a Bloodlust Gauntlet/ Noble Plate recipe, but from the fact that the examples you do use (Ocarina and Goddess Tear) are so rarefied. It makes the guide feel like it's only for one-percenters, when it doesn't need to be. If your examples were a little lower level, and not from premium packs and rare blueprints, more people would grasp the concepts more quickly.

I had something similar written in my first comment, but deleted that part because your work was so excellent I just wanted to be positive about it.


Thanks! I can definitely update to different stuff, just give me examples of what people care about. This is important for basically everyone to speed their progress up, so I definitely want to make it more accessible. Any suggestions totally welcome I'm not offended. I actually wanted to get this (and the calculator) out before I left for the weekend so I definitely plan on going through with a second pass and tightening it up -- especially to make it more cohesive in a topic thats super math heavy. Anything that doesn't make sense or doesn't apply let me know so I can fix later :D

Thx for the praise everyone <3 expect more from me in the future!
"I believe the forum ban was deserved, as he has been out of line, and warned.

I believe a permanent game ban was out of line."

-Abqu

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Fenix
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Re: Fusion Cauldroning 101

Postby Fenix » Wed Aug 03, 2016 3:07 pm

Interesting guide Abqu, I would say great but that math was like... way more complicated than anything I was expecting or wanting. I've been looking for a guide for fusion for awhile and this... might work if I can understand any of that math.

I mean everybody has known about Common+Flawless = Epic for like forever now but as for a solution for quicker Legendaries I haven't seen much. I saw 2 things that might work I guess just looking at them.

What I'll take away from this is to try Common+Common+Epic for a Legendary and probably more reliably try Flawless+Flawless+Flawless+Epic.

I'd do that CCE or FFFE thing others do but I read that and my brain doesn't understand it lol. I guess I'm getting old and prefer things worded the long way.
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