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Ancient Crafting Calculations - When to use each Recipe

So you've reached a point in S6 where you're looking to upgrade all your Legendary items into Ancient ones? zork-tdmog shared on Reddit some calculations he worked on to figure out what's more efficient: crafting Legendaries from rare items, or rerolling current owned ones.

He says the "magic number" is around 63. You can check his reasoning below, but long story short an item with crafting odds below of 1 out of 50 via the rare-to-legendary recipe should be farmed with that, and those with odds above 1 out of 70 should be crafted via the reroll-legendary.

Keep in mind his calculations take into account a specific material-per-hour farming ratio - one that some players might consider unattainable.

Should I Use the Rare-to-Legendary recipe or the Reroll-Legendary recipe?

 

In my spreadsheet I compare the odds when crafting an ancient legendary via the reforge-legendary-recipe against odds to craft the same item via the rare-to-legendary recipe.

It turned out the magic number is: 63.8957.

Constants:

• 400 Death Breath in 60 minutes
• 200 white crafting materials in 5 minutes
• 4 Forgotten Souls in 2 minutes
• 10 Bounty materials in 10 minutes
• Odd to craft an ancient item via the reroll-legendary recipe is fixed: 1 out of 10. 50 tries are needed for a chance of 99.48% to get the ancient item.

Material	Amount	Minutes	Amount/Minute	Recipe Amount	Minutes per Recipe
Death Breath	400.00	60.00	6.67	25.00	3.75
Crafting mat	200.00	5.00	40.00	150.00	3.75
Forgotten Soul	4.00	2.00	2.00	50.00	25.00
Bounty mat	10.00	10.00	1.00	25.00	25.00

Calculation

The odds to craft an ancient item via the rare-to-legendary recipe depends on the pool the item is selected from.

I used this document as my source: Legendary Drop Rates 2.4.1

I then checked how many tries are needed to get the same chance (99.48%) to roll the same ancient item via the rare-to-legendary recipe.

Result

Weapon	Odds 1 out of N	N tries needed for 99.48%
Anc. Lidl. Wall	20	102
Anc. Standoff	35	181
Anc. 2H Mighty	60	313
Anc. 1H Mighty	80	418
Anc. Hack	110	575
Anc. Furnace	190	995
Anc. Shard of Hate	460	2415

When multiplied with the amount of time that is needed to get the materials the following data is given:

Weapon	Number of tries for 99%	leg-reroll FS in hours	leg-reroll BM in hours	Number of tries for 99%	rare-to-legendary DB in hours	rare-to-legendary CM in hours
Anc. Lidl. Wall	50.00	20.83	20.83	102.00	6.38	6.38
Anc. Standoff	50.00	20.83	20.83	181.00	11.31	11.31
Anc. 2H Mighty	50.00	20.83	20.83	313.00	19.56	19.56
Anc. 1H Mighty	50.00	20.83	20.83	418.00	26.13	26.13
Anc. Hack	50.00	20.83	20.83	575.00	35.94	35.94
Anc. Furnace	50.00	20.83	20.83	995.00	62.19	62.19
Anc. Shard of Hate	50.00	20.83	20.83	2,415.00	150.94	150.94

The materials needed per crafting odds is nearly constant for the rare-to-legendary recipe.

Thus the even point where both recipes take nearly the same amount of time to get to the desired result is 1 out of 63.8957.

Conclusion

• Any item with crafting odds below of 1 out of 50 via the rare-to-legendary recipe should be crafted with the rare-to-legendary recipe.
• Any item with crafting odds between 1 out of 50 and 1 out of 70 should be crafted with both recipes.
• Any item with crafting odds above 1 out of 70 should be crafted with the reroll-legendary recipe.

Of course the above data is only true for the constants given. Different material farm parameters will net you different results.

BM = bounty material
CM = crafting material
DB = death breath
FS = forgotten soul

To help players use this information jmdbcool replied with a link to the Drop Rates spreadsheet and associated the recipe choice to those ratios!

This is some great research! To expand on this in a way any class can use, here's all the drop rates (go to Drop Rates tab):
https://docs.google.com/spreadsheets/u/1/d/1cM-s4e66ql2zsrkfkfKXmvVJ4zmngzxdzVLk9gvLvT8/htmlview?sle=true

These are given as percentages (instead of 1 out of x) but the math is the same if you do some conversions.

• Your magic number (again, based on your farming rates): 1/63.8957
• As a percentage: 1.565%
• That's for ancients, so when talking about any item (like the rates on the google doc) it's times 10 = 15.65%.

So 15.65% is your cutoff point. Odds better than that, it's better to upgrade rares; odds worse than that, it's better to reroll. In other words:

Amended conclusion:

• Any item with drop rate above 20% should be crafted with the rare-to-legendary recipe.
  • Barbarian Examples: Lidless Wall (50%), Standoff (28.57%)
• Any item with drop rate between 20% and 14.29% should be crafted with both recipes.
  • Barbarian Example: Any 2H Mighty Weapon (16.67%)
• Any item with drop rate below 14.29% should be crafted with the reroll-legendary recipe.
  • Barbarian Examples: Any 1H Mighty Weapon (12.5%), Hack (9.09%), Furnace (5.26%), Shard of Hate (2.17%)