Item Creation in D1

[Nystul]

Something else i'd find interesting is how to calculate the occurence of a certain prefix, as has been done in the guide for uniques?
(this should be something like NumberofMonsters*(0.107*(11+0.89*(averageMlvl+1))*0.84*wantedNoaffixes)/DropRangeAverageMonster ?)
(for monsters only that is)
for instance, on dlvl 14, average mlvl is around 26 for normal, what would mean
(185 average monsters as by Jarulf guide) (i want a pre&suffix item)
(185*0.107*(11+0.89*(27))*0.84*0.167)/(26-13)=97.3/13=7.48
7.48% of the monsters will drop a magical item with a pre and suffix of qlvl 13-26?
and as such a Tower Shield (with 2 affixes) drop will be 1/13th of those (qlvl 20 rolled between 13 adn 26) being 0.575 % of the monsters. it being Saintly (24) and Tiger (21) would be another 1/13 and 1/13, becoming 0.0034 % of your monsters on dlvl14 will drop a Saintly Tower Shield of the Tiger on normal?
(as such finding a Saintly Tower Shield of the Tiger would happen 1 in 29361 games, when clearing dlvl14 of monsters on normal difficulty?)

hope anyone can clear this somewhat up for me ;)
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This would be very ambitious to do correctly. I doubt very much that Jarulf calculated the unique item odds by hand... almost certainly he wrote a short computer program to do it. Even then, I'm not sure how rough his estimates are. Your first problem is that you assume every monster on dlvl 14 has an mlvl of 26. Obviously this isn't right... you have to consider each monster type which means that for maximum accuracy you would have to actually consider each combination of monsters and the probability of that combination occuring. You also have to consider the bosses and their probability of showing up on the level: since bosses always drop magic items they are pretty significant. There are also chests, barrels, etc. to consider.

Still, we could ignore all of that and just try to get the case of a single, non-boss, mlvl 26 monster right. So you start with .107 as the odds of the monster dropping an item, which seems to be correct. From there, Jarulf's Guide says we determine the base item. Bows count twice. We can take any base item with qlvl between 1 and 26, which I believe is all of them. By my count, 114 (including bows twice, and not including Hellfire items) with tower shield being one of them. So we now have (.107/114) odds of the monster dropping a tower shield. Then we get your step for determining if the item is magical, but don't forget that this is a percentage: (11+ .89*27)/100. Since a tower shield could be a Stormshield, we'll also have to multiply by .98 to exclude the 2% chance that a magical item could actually be unique. This gives us about one magical, non-unique tower shield for every 3100 regular, mlvl 26 monsters. Now, there is only a 1/6 chance of that tower shield having *both* a prefix and a suffix, so we are up to roughly 18600 monsters.

Now we look at the possible prefixes and suffixes on a shield, between qlvl 13-26. For suffixes, we've got 1)wolf , 2)tiger, 3) ages. That's it, 1/3 chance! So your odds of getting the right suffix with any prefix now have us up to roughly 55800 monsters. For prefixes we have 1+2) glorious (double chance), 3)crimson, 4)ivory, 5)lapis, 6)jade, 7+8)blessed, 9)cobalt, 10)crystal, 11)garnet, 12) obsidian, 13+14) saintly, 15)diamond, 16)ruby, 17) sapphire. So, 2/17 chance.

Then if my calculations are correct, the odds of getting a saintly tower shield of the tiger from a mlvl 26, non-boss, monster (on any difficulty, since the possible base items are the same) is roughly 1 per every 474,300. So if we take your original assumption of 185 mlvl 26 monsters on a level, with no bosses, chests, etc., we would get roughly a 1/2563 chance of finding it on the level.

That said, bosses are very significant because they can't drop things like scrolls or potions, and they always drop a magical item. They aren't as significant in this case as they are in the unique item case, but you would certainly want to take them into consideration.