I experimented with Nemesis Infusion at the Blacksmith. I share my findings and based on them calculate the odds of crafting the best possible items in the game.

## Guide to Nemesis Infusion

### The Basics

According to the glossary on monsters: Level 50+ Monsters have a 0,5% base chance to spawn as Nemesis increasing their stats and rewards and granting access to Nemesis Items.

Nemesis Items are the items marked with a light blue outline, they spawn with at least one attribute that is locked and whose rank is above the maximum rank available for that item. For the example, this amulet rolled with 5 additional ranks of Melee Resistance and 6 additional ranks of Ranged Resistance.

Upgrading the Watchtower and the Castle has the following the benefits:

- Watchtower Rank 3: Nemesis Items can now roll with up to 3 Nemesis Attributes.
- Watchtower Rank 5: Nemesis Attributes can now roll up to Rank 8.
- Castle Rank 1: Nemesis Items now have a minimum of 2 Nemesis Attributes.
- Castle Rank 2: Nemesis Attributes now have a minimum Rank of 4.
- Castle Rank 3: Unlocks the ability to perform a Nemesis Infusion at hte Blacksmith which converts an item into a Nemesis item.

Here are a few additional facts:

- Unlocking a Nemesis Attribute on an item and rerolling attributes replaces it with a regular attribute whose max rank is equal to the item’s max rank.
- If you remove all Nemesis Attributes from a Nemesis item this way, it still retains the light blue outline and it is still considered a Nemesis Item.
- If you increase the max attribute rank on a Nemesis Item by adding Paragon levels to it, then the rank of the Nemesis attribute increases as well, see the picture below.

Based on all these facts the best in slot (BiS) items in the game should be of Mythical rarity with 6 desirable attributes, Paragon level 10 so that their max attribute rank is 20, and finally the 3 most desirable of those attributes should be Nemesis Attributes with 8 additional ranks each.

The most difficult step in crating these BiS items is landing the Nemesis Attributes. I wanted to know just how difficult it is so I made some experiments and built up a model to calculate the odds.

### Empirical Data

The building upgrades that determine the maximum and minimum number and rank of Nemesis Attributes apply to the Nemesis Infusion at the Blacksmith, so I knew each of my items will get 2 to 3 Nemesis Attributes with additional ranks of 4 to 8. I wanted to know the odds so I went ahead using Nemesis Infusion on a lots of items and recoded my results.

**Experiment #1: 500 Mythical items**

I used nemesis infusion on 500 items, and recorded the additional ranks gained. From this data I could deduce the proportion of 2 and 3 Nemesis attributes, as well as the distribution of additional ranks. In total 244 and 256 items got 2 and 3 Nemesis Attributes respectively, so I expect the actual probabilities here to be fifty-fifty.

I also got a total of 1256 Nemesis Attributes, the counts of ranks 4 to 8 were: 258, 267, 255, 248, 228. I was too lazy to apply a Chi-squared test to the results but this again looks to me like a uniform distribution.

I forgot to record which of the 6 attributes became Nemesis, but I didn’t notice anything out of the ordinary.

**Experiment #2: 100 Epic items**

Since utility attributes are fairly unappealing at the moment, I thought that in some cases it would be beneficial to forego those attributes and try to craft a lower rarity item. In theory this would make it easier to land the Nemesis Infusion on the desired attributes, but only if you are not penalised for having less attributes on the items. This time I only recorded the number of Nemesis Attributes, there was a 51 to 49 split between 2 and 3 Nemesis Attributes respectively, so the fifty-fifty assumptions seems correct on lower rarity items as well.

### The Math

After my experiments I had the probabilities at my disposal. I also made two further assumptions:

- Which attribute turns into a Nemesis Attribute is uniformly selected.
- The additional ranks gained are independent of each other, so that for example, landing a +8 on Attack Speed, doesn’t influence the chance of doing the same with Critical Chance.

If you have an item with 6 attributes, then you have 6 choose 3 = 20 ways that you can select 3 of them. The chance of hitting the best item requires getting 3 Nemesis Attributes (1/2) landing on the 3 most desirable ones (1/20) and each gaining 8 additional ranks (1/5^3), multiplying these odds together we get 1/5000 chance of hitting a BiS item on Nemesis Infusion.

Trying to do the same for an epic rarity item with only 4 attributes you have 4 choose 3 = 4 ways to select 3 attributes, so the chance of hitting the perfect infusion is still a whooping 1/1000.

Good luck with your infusions!

Great job, I’m on my way to paragon 10 as I write this message, the calculations are accurate and amazing.

Its seems that atm BiS is truly someone of one in thousands to land.