The Math of Fusings

honestly i don't understand why people think it can't simply be math'd based on the known mechanics.

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sage2050 wrote:

what? no you don't. if you know how the roll works (we do) you can write an algorithm for it. it's just a series of random selection.

Have you actually read the thread? A Fusing rolls a number that corresponds with certain grouping. You can't tell a program to do that without knowing what each of the numbers for each grouping is. That isn't a known thing, just guesses. You can't simply tell a program to guess it.

To requote myself:

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Fusing rolls are done similarly, there are odds for socket grouping. Assume they weighted the fusing odds something like 300:270:240:60:10:1 or 200:180:160:60:10:1, one of those is probably close to the fusing odds, although I doubt a dev will confirm or give us actual numbers. Based on how common it is to see 6L take over 1000 fusing orbs and even over 2000 fusing orbs, I'd guess that my first batch of odds is more accurate (1:881 odds of 6Ling an item).

So basically you roll (based on 1st set of guessed odds) a number between 1 and 881, if you roll a 300 or lower, the first socket is grouped in a 1 socket group (aka, no links). If you roll a 301 to 570, you get a 2 socket group (aka 1 link between 1st and 2nd sockets). If you roll a 571 to 810, you get a 3 socket group (aka 2 links between 1st, 2nd and 3rd sockets). If you roll a 811 to 870, you get a 4 socket group (aka 3 links between 1st, 2nd, 3rd and 4th sockets). If you roll a 871 to 880, you get a 5 socket group (aka, links between 1st, 2nd, 3rd, 4th and 5th sockets). If you roll a 881, you get a 6L item.

Those numbers (300:270:240:60:10:1) are how a program would roll, it's going to tell you odds directly how you feed it odds.

I always assumed it was 1/3rd chance of a link appearing and if it rolls the same links as it had it simply rolls again.

this seems to follow my experience with them and follows the general trend fairly well.

6s 6l would be around 1/240 which would change slightly depending on the initial starting point.


I suppose an easy way to test that if any one has the currency would be to simply get a bunch of 3 socket no linked gear and if each link is 1/3rd chance you should end up with a 3l on a no linked gear 1/5th of the time after fusing it.


better yet if you assume gear is rolled in the same way when it is created you could simply collect 3 socket gear and you should notice approximately 4/9ths have no links 4/9ths are 2 linked and 1/9th is 3 linked.



This is all just a theory though.

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Saffell wrote:

An orb of fusing will never yield the current configuration.

Wrong.
Happened to me several times, lost some orbs, didnt change a thing.
I dont think this is a bug, so this assumption is wrong, therefore your whole calculation.

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KalHirol wrote:

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Saffell wrote:

An orb of fusing will never yield the current configuration.

Wrong.
Happened to me several times, lost some orbs, didnt change a thing.
I dont think this is a bug, so this assumption is wrong, therefore your whole calculation.

No, he's right. You can have a 4 socket item that has a link in the first slot and not other links, then hit it with a fusing and have only one link somewhere else, but it absolutely will not roll an identical link pattern as was previously there, much like every other orb in the game.

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Grizdale wrote:

I always assumed it was 1/3rd chance of a link appearing and if it rolls the same links as it had it simply rolls again.

If you test this theory with a 3 socket or less item it will be somewhat consistent with reality. But if you test this theory with 4S+ items, you'll find very, VERY quickly that it is not how the fusing mechanics work. The Mechanics are known, it's the odds that are in question. And the odds of rolling a 6L are far worse than 1 in 240.

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TehHammer wrote:

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Grizdale wrote:

I always assumed it was 1/3rd chance of a link appearing and if it rolls the same links as it had it simply rolls again.

If you test this theory with a 3 socket or less item it will be somewhat consistent with reality. But if you test this theory with 4S+ items, you'll find very, VERY quickly that it is not how the fusing mechanics work. The Mechanics are known, it's the odds that are in question. And the odds of rolling a 6L are far worse than 1 in 240.

I don't see how my assumption is missing any mechanics.

All we know about fusings is as follow (at least as far as I am aware)

---fusings cannot result in the same configuration it started with
---6l gear has a low chance of rolling but we don't even have a half decent estimation on the chances as no one has done the statistics on it. so to assume 1/240 is wrong simply based on belief would be a bad assumption. people do often take a lot more to get a 6l but thats how random number generators work.


unless I am missing something I do not see how my assumption is missing mechanics.

I'm going to work off of the assumption that getting a 6L using Fusings on a 6-socket item has the same chance of success as using Jeweler's Orbs on an item in an attempt to get 6 sockets: roughly 1/306, or 1/305 after considering that the orb will never give return the exact same configuration.

If that is the case, then I've calculated the data for how many Fusings it would take to forge a 6L, going up to 50,000 Fusings (requiring more than 6522 is a one-in-a-billion chance, but Excel has a bunch of rows and I felt like using them). Statistically, it looks like this:
* Mean: 305. Makes sense, given the 1/305 chance.
* Median: 211. This means you have a 50% chance of requiring 211 Fusings or less; this is much less that what people would think.
* Lower and upper quartiles: 88 and 422.
* 10th percentile: 32. That means 10% of 6L forgings require 32 Fusings or less.
* 90th percentile: 701. That means 10% of 6L forgings require 701 Fusings or more.
* Average absolute deviation: 224.04, 73.5% of the mean. Very swingy results, more swingy that what most people are comfortable accepting mentally.

For comparison, here's some statistical figures on rolling a six-sided die:
* Mean: 3.5
* Median: 3.5
* Average absolute deviation: 1.5, 42.9% of the mean. In other words, if you think a six-sided die gives swingy results, the whole Fusing thing is almost twice as swingy proportionally, with 305 being the average roll.

Given these statistics, it's completely reasonable to believe that, despite the nightmare stories of items needing hundreds of Fusings to achieve 6L, that the 1/305 chance is currently in effect. With a field that is nearly double the deviation (proportionally) of a six-sided die, and has a median positioned much lower than the mean, it's very difficult to get your head around through experimentation; the unlucky outliers take not arithmetically, not even geometrically, but exponentially larger than the median values, which is why the mean is so far from the median, and the deviation so large. One in ten of these fusing affairs goes to 700 Fusings, and it only takes one of those to really sour a player and make all sorts of false psychological signals come into play -- for example, thinking that that a 200-some Fusing was "lucky" while the 500+ was actually more statistically close to the average, because no one likes believing that they just lost 300 Fusings to bad luck, while gaining 300 to good luck is a lot easier to swallow.

Or, it could be a totally different chance and I'm way off base. If the devs won't release the information, compiling large amounts of data -- and I do mean large -- and properly applying this kind of model to it could reveal the true chance. However, I do believe that the current chance, if not 1/305, is still very close, or we'd be hearing nightmare stories about Fusing a 6L that make the current stories sound like rainbows and lollipops.

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ScrotieMcB wrote:

I'm going to work off of the assumption that getting a 6L using Fusings on a 6-socket item has the same chance of success as using Jeweler's Orbs on an item in an attempt to get 6 sockets: roughly 1/306, or 1/305 after considering that the orb will never give return the exact same configuration.

i really really really hope this part is wrong i spend 102 jewlerys so far to het my vaal regalia to 6s

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ventiman wrote:

i really really really hope this part is wrong i spend 102 jewlerys so far to het my vaal regalia to 6s

You can find Chris himself saying it was accurate in version 0.9.13f (iirc), with the caveat that these things are subject to change in future patches. Since that version is late in closed beta, it's probably right, sorry.

Random is Random is Random. If the odds are truly low, and they are... then chances are you wont have much luck getting a 6 socket item to link entirely.