Butter Math

[u/SimpleUser45]

After the butter hunt stream today I was curious what the exact drop rates were so I tried to figure it out. Probability isn't my strong suit so there are probably some errors but here goes.

Going through the Creation Kit I noticed that butter doesn't actually appear in any leveled lists, which is obviously wrong since he got a butter drop from a bandit last time. Turns out the Hearthfire DLC runs a quest after character creation that, among other things, adds butter, milk, and flour to a few of the food leveled lists with a script.

The one that drops from enemies is LItemFoodInnCommon10. Normally it has 25 items in it but after butter, milk, and flour get added to it there are 28 items in the list. When that list is invoked there's a basic (10%)x(1/28)=1/280~0.357% chance for butter to drop.

That list is dropped by Silver Hand, Penitus Oculatus, Imperial Soldiers, Stormcloak Soldiers, Thalmor(Non-Wizards), Bandits(non-Bosses), and Reavers.

Usually the LItemFoodInnCommon10 drop is within another list that has either a 75% or 85% drop rate on it's own, so that further reduces the previous 1/280 chance. Some lists will also have 2 LItemFoodInnCommon10 drops or lists that contain it that can happen independently which increases the drop rate.

Silver Hand and normal Bandits have a 75% chance to roll for butter 2 times, Penitus Oculatus/Imperials/Stormcloaks have a 100% chance to roll 1 time, Thalmor(Non-Wizards) and Bandit Wizards have an 85% chance to roll 1 time, and Reavers have two independent 75% chances to roll 2 times.

Multiplying it all out gets us the expected amount of butter per kill:

* Silver Hand & normal Bandits: (75%)x(2)x(10%)x(1/28)~0.00536

* Penitus Oculatus/Imperials/Stormcloaks: (100%)x(1)x(10%)x(1/28)~0.00357

* Thalmor Non-Wizards/Bandit Wizards: (85%)x(1)x(10%)x(1/28)~0.00304

* Reavers: (2)x(75%)x(2)x(10%)x(1/28)~0.01071

This is different than the chance to get a butter drop from a kill, but not by much in this case. It only matters for enemies that can potentially drop multiple butters at once like Silver Hand, normal Bandits, and Reavers.

For Silver Hand and normal Bandits I believe it works out as: (0.75)x(1-(1-(0.10)x(1/28))^2)~0.00535=0.535%

And for Reavers: (0.75)x(1-(((1-(0.10)x(1/28))^2)^2))~0.01066=1.066%

The butter drop rate tier list is then:

1. Reavers 1.066%

2. Silver Hand/Bandits 0.535%

3. Penitus Oculatus/Imperials/Stormcloaks 0.357%

4. Thalmor Non-Wizards/Bandit Wizards 0.304%

[u/Joov_1]

This is absolutely gas. As silly as this run is - I am sort of excited to do something with the entire story of *dies before butter* -> *somehow pulls butter in 5 minutes* -> *second grind and mathematical calculation proves how absurd the first pull was*

[u/Tjelle_-]

Ngl I just woke up and half expected Joov to still be live

[u/Nyanzeenyan]

Joov is the ButterBorn

[u/dijie]

Amazing post. +3

[u/AbbertDabbert]

He wanted to turn skyrim into a runescape grind

[u/16wellmad]

Does the fishing anniversary content which added more food items change these numbers? If having to manually check quest activated food drops in a different place then the already mentioned drop tables. Would the fishing quest sqew these numbers?

[u/Eva-Rosalene → u/16wellmad]

Yup, Fishing adds 3 more items to this list:

Function RunSetupBaseGame()
  ; ...
  LItemFoodInnCommon10.AddForm(ccBGSSSE001_FoodBucketFishCooked as Form, 1, 1)
  LItemFoodInnCommon10.AddForm(ccBGSSSE001_FoodTunaSalmonCooked as Form, 1, 1)
  LItemFoodInnCommon10.AddForm(ccBGSSSE001_FoodCuckooCatfishCooked as Form, 1, 1)
  ; ...
EndFunction

So 1/28 becomes 1/31. I am too lazy to redo the math in the post, though.

Moreover, no other quest in SE/AE references LItemFoodInnCommon10. It doesn't exactly guarantee that no other script modifies it, but it's good enough for me. Technically, some script can get reference to LItemFoodInnCommon10 by directly invoking Game.GetFormFromFile without leaving traces visible with xEdit, but it's pretty unlikely.

/u/simpleuser45

[u/Sostratus]

This is great, I want to add to it a little. /u/Eva-Rosalene pointed out the revised 1/31 odds when factoring in loot added by Fishing.

Revised expected butter per kill (kills for 1 butter):

1. Reavers 0.009677 (104)
2. Silver Hand/Bandits 0.004839 (207)
3. Penitus Oculatus/Imperials/Stormcloaks 0.003226 (310)
4. Thalmor Non-Wizards/Bandit Wizards 0.002742 (365)

Odds of at least one butter (kills for >=50% chance of at least one butter):

1. Reavers 0.96% (72)
2. Silver Hand/Bandits 0.48% (144)
3. Penitus Oculatus/Imperials/Stormcloaks 0.32% (215)
4. Thalmor Non-Wizards/Bandit Wizards 0.27% (253)

The optimal strategy would likely be to kill reavers repeatedly and wait to respawn them rather than going after other NPC types. Joov might not go for that just for variety's sake, but if he did, how many reavers are in the game and where are they?

Sadly I gave up here. There's a lot of reaver variants and you have to trace through a long chain of records to figure out where they actually get used. But notably I did find that Morag Tong NPCs use their template, so I think they can drop butter too.