[Unofficial] The complete guide to fusing mechanics

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TehHammer wrote:

Fusings are very similar odds except for 6 linking. The odds of 6 linking is more like 1 in 1200 instead of 1 in 306, something like (I just quadrupled all the chances except 6L):

6L capable item
0/1/2/3/4/5 links odds on the first roll (socket)
400:360:320:120:20:1

These aren't 100% accurate, but they're close.

Thanks, tpapp157 and TehHammer. I didn't realize the 4S items just had a truncated probability distribution. I'm a little surprised as the odds of a 4S seem worse than 1:9. Maybe it's just my bad drop luck. LOL!

I haven't seen those really low 6L fusing orb odds in the other threads. Where did they come from? I know Chris confirmed the 100:90:80:30:5:1 socket rolls and that fusings are on a similar mechanic but I haven't seen anything to indicate drastically worse odds on 6L fusing.

There's another thread kicking around where someone did a monte carlo on 6S rolls and the effect of not duplicating is substantial.

When you're just grinding loot out in the wild you need to remember that the rarity of a 4L item is compounded by the rarity of rolling four sockets in the first place. That makes the chance of a 4L dropping much lower than if you simply crafted it with Jewelers and Fusings.

Oh, right. So I'll only see 1 of out 81 pairs of boots with a 4L. No wonder they feel so rare. They are! LOL! I suddenly need fusing orbs.

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MorriganGrey wrote:

I haven't seen those really low 6L fusing orb odds in the other threads. Where did they come from? I know Chris confirmed the 100:90:80:30:5:1 socket rolls and that fusings are on a similar mechanic but I haven't seen anything to indicate drastically worse odds on 6L fusing.

cough, research, cough...

To expound on this, I had a script that would systematically trade in magic/rare items (usually chests/bows) and record the sockets in the results. I crafted several (20+) 5L items, and left dozens more behind (in search of a 6L). In my entire time running this script, I saw 1 6L item. There were several hundred (I'd actually guesstimate around 2000) 6 sockets rolled but just the 1 6L turned up.

This was using the vendor recipe that rewards you with a new item of the same base type when you sell 5 items of the same base type to the vendor. You used to be able to see the sockets/links before you sold the items to the vendor. I'm a large part of the reason you can't see those sockets/links anymore (hence the name change from the devs in the signature - clever devs).

Aside from all of that, I've probably rolled another 1500 fusings in my game time on 6S items. Never once rolling a 6L. In my mind, there's no way a 6L is in the same 1:306 odds of being rolled as the 6S is. I'm conservatively guessing 4 times less likely (1:1200).

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MorriganGrey wrote:

There's another thread kicking around where someone did a monte carlo on 6S rolls and the effect of not duplicating is substantial.

It's tricky with a fusing sim for a couple of reasons.

First the odds are unknown, so it's all a guess.

Second, you can roll the same number of links two times in a row, just not the same links in the same locations. For example, a 4S item could look like:

O-O

O O

And reroll as:

O O

O-O

Same link count, different configuration. My link simluator takes this into account, but I didn't bother with reporting odds, as it wouldn't be accurate. My fusing sim actually goes on the 1:306 odds of rolling a 6L on the first roll, which, as I've mentioned, I believe to be inaccurate.

That "gut feeling" can be shored up with some statistics. ;-) You seem to have reasonable evidence to reject 1 in 306 if your recollection of how many trade-ins you've done and fusings you've rolled is accurate.

Rolling 1500 fusings with no 6L at all is adequate statistical evidence to reject 1/306 with p<0.05, especially since fusings can't reroll the same sockets so the hypothesis you were testing is that it would be slightly better than 1/306. I'm afraid to ask how you got that many fusings!

As for the vendor trade-ins, you have to make the assumption that the sockets on the item you're offered is not related to the items you trade. If you really are at one 6L in 2000 (and not 1800 or fewer), you again can reject the hypothesis that the 6L probability is 1/306 with p<0.05. Alternatively you can reject the hypothesis that sockets are not related to the trade-in items. i.e. there might be a relationship between affixes/sockets/links on the traded items and what is offered in exchange.

You don't have anywhere near enough trials to make any sort of guess as to what the real underlying probability might be. You can only say it's worse than 1 in 306.

I've been playing for 9 months and I was #3 on the ladder in 0.9.7-0.9.8 when it migrated and I peaked at #2 or #3 on the ladder in 0.9.9+. I've seen a lot of fusings, I've definitely used over 1200 on 6S items, although I haven't kept specific track, just knowing how many times I've blown 20 or 30 on a 6S item and how many times I've used 60+ to roll a 5L (the highest I went on one item was around 150), it's pretty clear in my mind I'm well over 1200 fusings rolled. Heck, I'm about a quarter of the way there with just the 2 5L items I wear on a daily basis (my bow and chest, each over 120 fusings).

The script made it easy to keep track as I logged the results when they hit 6S or 5L or 6L and total rolls. I never went back and counted all of the logs (as they are each individual logs rolling anywhere from 8000 to 42,500 items (and with 1:306 odds of giving a 6S that's between 28 and 139 6S on average on a complete run through the stash page), but I'm certain it rolled at least 2000 different 6S items (a very conservative, low end guess), only one of which was 6L.

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TehHammer wrote:

To expound on this, I had a script that would systematically trade in magic/rare items (usually chests/bows) and record the sockets in the results.

How did you not get banned for that?

1200 fusings with no 6L is not enough to reject the hypothesis of 1 in 306, just enough to consider yourself unlucky. LOL! As I said, 1500 fusings is. You might want to start a tally if you're really curious since with enough trials you'll eventually get the real probability.

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TehHammer wrote:

I've been playing for 9 months and I was #3 on the ladder in 0.9.7-0.9.8 when it migrated and I peaked at #2 or #3 on the ladder in 0.9.9+. I've seen a lot of fusings, I've definitely used over 1200 on 6S items, although I haven't kept specific track, just knowing how many times I've blown 20 or 30 on a 6S item and how many times I've used 60+ to roll a 5L (the highest I went on one item was around 150), it's pretty clear in my mind I'm well over 1200 fusings rolled. Heck, I'm about a quarter of the way there with just the 2 5L items I wear on a daily basis (my bow and chest, each over 120 fusings).

The script made it easy to keep track as I logged the results when they hit 6S or 5L or 6L and total rolls. I never went back and counted all of the logs (as they are each individual logs rolling anywhere from 8000 to 42,500 items (and with 1:306 odds of giving a 6S that's between 28 and 139 6S on average on a complete run through the stash page), but I'm certain it rolled at least 2000 different 6S items (a very conservative, low end guess), only one of which was 6L.

It's important to remember that first the mechanics might not be the same. And secondly you have to roll both a 6S and a 6L. Or perhaps more equivalently you saw a 1/2000 of a jewelers rolling a 6L as it's 6S roll.

Pretty much necro but interesting thread though.