Badge recipes  Results from crafting 127 badges
So I crafted most of my remaining fragments  127 pieces  and noted the results, which can be seen below. Now, as there are 15 groups it means there will be a lot of random variation in the single groups. Still, as I've exhausted my stockpile of components the amount will not increase quickly so I decided to post this anyway now.
So here is the table:
As you can see, only 5 recipes have provided Damage Resistance badges at all. Especially recipes 4 and 9 seem interesting, with high percentages and at least 10 tries.
So if you are interested in crafting damage resistance badges, try the following combinations (in priority order):
2 metals and any 2 other (but each different) components
or 3 metals and any other component or 4 metals
or 3 chemicals and any other component
or 2 edibles and any 2 other (but each different) components
or 2 cloth + 2 chemicals
Based on this a simple rule of thumb is to use at least 2 metals and 1 each of other components.
So you may wonder, what are the recipes? Based on @Grady 's suggestion, I have grouped the possibilities into 15 groups. This is based on some assumptions;
 there is no difference in exakt ordering of components, i.e. AABB = BBAA = ABAB = BABA
 This results in 35 different combinations
 Additionally, it is assumed that at least 3 components of the same kind means only that component is considered. I.e. AAAA = AAAB = AAAC = AAAD
 On the same logic, it is assumed that at least 2 components of the same kind together with 2 different other components means that the main component is considered. I.e. AABC = AABD = AACD
 This ends up with 15 different recipes
Comments


I hesitate to share all my findings since it involved a lot of work with guildmates, but it's always great to see others are working on it too.
Note that my notations are different, I use the order on the crafting page.
A = Metal
B = Edibles
C = Chemicals
D = Cloth
Here are my groupings:
Four of a kind:
1. AAAA
2. BBBB
3. CCCC
4. DDDD
5. Pair A
AABC, AABD, AACD
6. Pair B
ABBC, ABBD, BBCD
7. Pair C
ABCC, ACCD, BCCD
8. Pair D
ABDD, ACDD, BCDD
9. Others:
AAAB, AABB, AACC, AADD, ABBB, ABCD, ACCC, ADDD, BBBC, BBBD, BBCC, BBDD, BDDD, CCCD, CCDD
Specials:
10. AAAC
11. AAAD
12. BCCC
13. CDDD
Some more rules:
 Order does not matter for a given recipe (AABB = BBAA = ABAB = BABA)
 All recipes in the same group are interchangable (meaning they yield the same distribution and results). So from Group 9, (AAAB = ACCC = BBCC)
 Recipes from the different groups can and often yield the same result as another group. Some groups are closer to each other than others. For example, Group 7 and 8 share very close distributions. While Groups 1, 9, 10 are the furthest apart from each other. 
There is also a lot to be learnt if you graph the crafting percentages shown on the screen.
Before August 2018 update:
Before August 2018 update with Crafting Event:
After update:

Thanks for chiming in @Grady . Can you elaborate a little on how you arrived at those recipes? They honestly seem a bit arbitrary, for example why is AAAC a special recipe but not AAAB? How large is your data set? And are your conclusions about best recipes for damage reduction similar to my results?Ingame username: Jubjab

5digit data sets. We did not guess or decide on those recipes, it all worked backwards based on actual testing. The groups fall into place very structured if you graph them and we are 100% certain of the grouping. In fact we were also able to figure out there are exactly 6 distribution patterns A~F. In the worst distribution pattern F for example, recipe group 1~9 will all yield the same result X, while group 10~13 will yield something else.
While there are set structures and patterns, it gets really complicated really fast. And most of this knowledge will not help an average player with normal play style get better badges.
We have no recommendations for which recipe give the most DR badges. It's not yet the focus of our study. 
I've crafted 1000's of badges. There is no recipe. It is random and what you are finding is simply data mining. No fault to you, as it is human nature to try and find patterns in data. We are biologically wired that way. But, rest assured, badges are random. Sorry.

https://forums.nextgames.com/walkingdead/discussion/comment/297856#Comment_297856rchap said:I've crafted 1000's of badges. There is no recipe. It is random and what you are finding is simply data mining. No fault to you, as it is human nature to try and find patterns in data. We are biologically wired that way. But, rest assured, badges are random. Sorry.
Shteevie said:
In the case of component recipes, we specifically wanted to build a feature that encouraged theorycrafting, pattern recognition, sharing recipes and results, and other forms of discussion. So sharing this down to the percentage is counter to that goal, and would have precluded all of the conversation about this that has come before. Yes, the combinations have an effect; yes, you can get any result with any recipe; and no, we won't say more than that. 
I'm surprised to hear this, as I would assume this is pretty much the only reason for doing this work. Everything else as it seems is random or have specified percentages shown already ingame.Grady said:
We have no recommendations for which recipe give the most DR badges. It's not yet the focus of our study.Ingame username: Jubjab 
DR badges are great but hardly the only goal. Those specified percentages also reveal additional information if you delve deeper.Burmeliinis said:
I'm surprised to hear this, as I would assume this is pretty much the only reason for doing this work. Everything else as it seems is random or have specified percentages shown already ingame.Grady said:
We have no recommendations for which recipe give the most DR badges. It's not yet the focus of our study.
There are many reasons we gather stats and theorycraft. #1 is actually for the Maths, haha. It's always fun to figure out the game mechanics.
If that part is not fun for you, then there is no point spending 100+ hours doing spreadsheets instead of just playing the game itself.
There are also a bunch of other reasons I could think of: such as doing less grind by making the best use of limited resources; reduce wasting valuable resources (time / components) through gaining better understanding of what works and what does not.
https://www.youtube.com/watch?v=aw73qH6RiRQ 
@Grady
@Burmeliinis
I stand corrected then, based on what Shteevie said. I wonder though, if it was intended to be as he stated but was never actually programmed. As I mentioned, I've crafted thousand of badges, looking for a recipe, pattern or something identifiable. And never found it. 
I've always had bad luck crafting DR badges, and I need to give credit to @avelardez
Once I started to consistently use his Metal, Edible, Edible, Cloth recipe, I've gone from my very scientific designations of getting them "hardly ever" to "semiregularly".

An (fictional) example could be that they programmed AAAA to give a DR badge 1% of the time, but using CDDD gives a DR badge 3% of the time. It is statistically significant in this example (300% as much!), but can hardly be felt by the average player. Now even if someone possess this knowledge, he would still have 21.8% chance of getting 0 DR badges crafting 50 sets of all Legendary components. He most likely wouldn't even be able to do 50 crafts since the Cloth component will run out very quickly.rchap said:@Grady
@Burmeliinis
I stand corrected then, based on what Shteevie said. I wonder though, if it was intended to be as he stated but was never actually programmed. As I mentioned, I've crafted thousand of badges, looking for a recipe, pattern or something identifiable. And never found it. 
rchap said:
@Grady
@Burmeliinis
I stand corrected then, based on what Shteevie said. I wonder though, if it was intended to be as he stated but was never actually programmed. As I mentioned, I've crafted thousand of badges, looking for a recipe, pattern or something identifiable. And never found it.
I crafted a badge today with my one of my top recipes for getting damage reduction, and got this one:
Ingame username: Jubjab 
@Grady that is a very impressive proportion of legendary badges from epic components. I get nowhere near that.

I can assure you there are recipes that will increase your chances of getting different badge types.
But sorry, I share them with my guild family only. Although I ask players to keep them within the family it seems that is not what everyone does. I guess I'll have to narrow down who I share with.TJS  Member of WSNation Wars 🇦🇺 Australian Team Captain 
List is wrong. Maybe sample size was too small. For one, ABCD does in fact give crit chance. I got 3 out of 20 attempts.
Secondly, BBCC, can result in all 5 badge types, not just crit damage, damage, or health. 
@DIYer These are just crafting results. They're not "wrong". The sample size is indeed small and there's a lot more to crafting than this.If you want to get better at this game, join Discord and learn badge crafting and much more: https://discord.gg/cDhgv3AJ89

Thanks for digging up this old thread :facepalm: I should probably edit my OP to say that the results shown there mean nothing, with the new information we have about crafting now.
As the crafting results are not random (as I assumed in the OP) the outcomes depend on where in the crafting cycle I was and indeed, which cycle I even was in.
It's fair to say that we have come a long way since only one year back.Ingame username: Jubjab 
Do we have a link where the crafting cycle is documented?

For example JayZ's strategy compendium: https://forums.nextgames.com/walkingdead/discussion/comment/395981/#Comment_395981Ingame username: Jubjab

There's a lot more known since the crafting guide in JayZ's compendium was released. JayZ's compendium makes it a lot more comprehensible, but people who wants to know more should join Magic's Discord https://discord.gg/PvWYqaQIf you want to get better at this game, join Discord and learn badge crafting and much more: https://discord.gg/cDhgv3AJ89

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