Reddit: "PSA: Companion Locket is Extremely Good"

u/Devilnaht

"Just thought I'd bring some more attention to this trinket which ends up being one of the absolute strongest summoner trinkets in the late game. First, a quick caveat: summons which do not take slots still count against you for the purposes of Companion Locket, so be careful with using them if you go this route.

That said, after some testing, here's a way to understand how its damage increase works:

First, you take the total number of summon slots you have. You start with 100% damage increase, then add 90%, then 80%, etc, until you've done this a number of times equal to your summon slots. So if you have 5 total, it would be: 100%+90%+80%+70%+60% = +400%. Note that if you have more than 10 summons, there's a floor of 0%, so you won't ever add a negative value.

Expressed more mathematically, with n = total summon slots, you find the sum from k=0 to k=n-1 of (100-10k), unless n >= 10, where the sum will always just be 550%.

Then, you subtract from this damage total in a similar manner for the number of slots used. So if we have 5 total slots and use 3 of them, we subtract 100%+90%+80% = 270%. With n = total slots and m = used slots, it's the sum from k=0 to k=m-1 of (100-10k).

Thus, the overall damage increase would be 400%-270% = 130%. There's a way to express this as a unified formula, but it's kind of obnoxious in text form.

I've also included an image which shows its effectiveness for all possible number of summon slots (well, except 1 total slot, but... yeah). The Eff. Sum. column means how many summons you would need to give an equivalent amount of summon damage without using Companion Locket. Note that this is assuming you have no other sources of +summon damage, which would slightly change the numbers, and the best option for each number of total slots is highlighted in green. Companion Locket reaches its maximum utility at 8 summon slots, where it gives the effective damage of +3.2 summons, but it remains viable between about 4 and 11 total slots."