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!
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 that's 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!
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.
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!
Credits: Fusion Cauldroning 101 by akerson