Hi all,
I have always wondered about the distribution of merchant values when one identifies weapons and armor, including the minimum and maximum values.
I have several theories that I wanted to test out, and wanted to share some of them to see if you have made similar observations and could perhaps confirm or disprove some of them. In all these calculations I have excluded the inscription Value for Money.
Theory 1 - Range of identified items: If the value of an unidentified item is u, then the merchant value after identification is in the set r * ( u + {1,2,...,u} ), where r denotes the rarity parameter: r = 1 for whites and blues, r = 2 for purples, and r = 4 for golds. For example, if a gold unid has an unidentifed worth of 50g, then the identified value is anywhere between 4 times and 8 times that worth, in steps of 4 gold (excluding exactly 4 times or 200g), i.e., possible values range from 204, 208, 212, ... all the way to 400g. Note that every item from the Hall of Hero chest (maybe also Z-chest) has an unidentified value 50g. I believe Sigils work the same way. I'm not sure if this also applies to old-school items. All of this again without the Value for Money inscription.
Theory 2 - Unidentified Values: I think it's safe to say that the value of items dropped in the end-game is generally higher than that of areas earlier on in the game. In general, I have observed that the unidentified gold value is also lower, and that identification follows the rule of Theory 1. Specifically, each item has a sort of "level" associated with where it's dropped, which may or may not be linked directly to the level of the foe who drops it. This includes the super high gold values of items dropped from the nightfall treasures in the real of torment, which to my knowledge yield the highest possible merchant value of a gold weapon. Some have seen values of over 700g, and I'm very curious what the highest possible value is... I don't have much evidence for this hypothesis, but perhaps the highest unidentified value is 100g, and if Theory 1 holds true, the highest identified value would be 800g. I'm not sure if a more formal theory behind this exists - for example what are these underlying levels or how they depend on the area in which they are dropped...
Theory 3 - Distribution of identified values: I have also noticed that lower values in the range of Theory 1 are much more common than high values, so I decided to make a database with drops from the HA chest. In a sample of over 250 items, I have not seen a single drop that doesn't follow the rule from Theory 1, so all identified items are one of the 50 values between 204 and 400. Putting the values in 5 buckets a 40-gold ranges (204-240, 244-280, 284-320, 324-360, and 364-400) and plotting how many identified values were observed (chart below), we clearly see that higher-valued items are much rarer: Almost half of the values are between 204 and 240 gold, while only 8% are in the highest quintile. Every fifth item is worth 204 gold! This suggests that the distribution of gold values is heavily skewed towards lower-valued items.
Notes: I observed every gold value except 252, 320, and 384, but that is probably due to the sample size. I have tracked also the weapon type, with no noticeable differences. I have made similar observations from other areas, and Sigils seem to follow the same trend, with 1,001g being much more common that those valued 1,900g and more.
I'd be very curious to hear your thoughts, if you have made similar observations, and if we can somewhere find proof of those game mechanics, understanding some trends better. For example, although higher-valued items are rarer, i'd be curious to know the distribution function.
Cheers!
Alugian
https://preview.redd.it/7o6q94eeb2d81.png?width=1485&format=png&auto=webp&s=bbe4cf5bdc68761505b5696aa1da96566d52f597
![Merchant Value Distribution [Game Mechanics]](https://b.thumbs.redditmedia.com/D3TQSNV-oILGamshejOcSXHr44HVnPiJ_Y5IcopUFTI.jpg "Merchant Value Distribution [Game Mechanics]")
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