Divine orb behaviour.

As for my previous calculatons;
Using the chances of each individual mod:

1/5
1/18
1/10
1/6
1/3

The chance for all mods to remain the same is
(1/5)*(1/18)*(1/10)*(1/6)*(1/3) = 6.1728e-005 ~= 0.01%

The chance for no mod to remain the same is
(4/5)*(17/18)*(9/10)*(5/6)*(2/3) ~= 0.3778

The chance for 1 mod to remain the same is
(1/5)*(17/18)*(9/10)*(5/6)*(2/3)+
(4/5)*( 1/18)*(9/10)*(5/6)*(2/3)+
(4/5)*(17/18)*(1/10)*(5/6)*(2/3)+
(4/5)*(17/18)*(9/10)*(1/6)*(2/3)+
(4/5)*(17/18)*(9/10)*(5/6)*(1/3) ~= 0.4231

The other ones can be calculated much in the same fashion. I'm sure there are more elegant ways to approach this, but my probability theory is a bit rusty. I figured that some quick calculations in Matlab was faster than reading up on any methods I have probably forgotten about.

As for the statistical properties, the expected value is
SUM(N*Pn)
Where N is the amount of properties changing and Pn is the probability of occurrence.
Using the most common set of probabilities for the above armor, the expected value is 0.856 amount of changed properties after using an orb

The variance is calculated as SUM( Pn*(N-E)^2 ), where E is the expected value.
Plugging in the numbers, the variance can be calculated to amount to 1.664.

Likewise, the expected value of the third use of the orb should be equal to 0.837, while the variance is 1.647.

Adding all 4 cases:
Expected value: 3*0.856 + 1*0.837 = 3.405 unchanged mods
Variance: 3*1.664 + 1*1.647 = 6.639
Resulting standard deviation: sqrt(6.639) = 2.577

TJJ has seen a total of 6 unchanged mods.
The result obtained by TJJ can be calculated to be (6-3.405)/2.577 = 1.007 standard deviations away from the mean.
It should be remembered though, that the probability is not normally distributed, so the guideline that 68.2% of the results should be within 1 standard deviation doesn't apply here.

If you consider though, that for a single use of an orb the standard variation is sqrt(1.664) ~= 1.290, then the values of up to 1.290+0.856 = 2.146 (unchanged mods) lie within 1 standard deviation.
It is known that values up to 2 on the probability curve amount to 96.8% of the possibilities, so everything within a single standard deviation should amount to slightly more.

If I didn't make any mistakes in my reasoning (someone please check :P), I think that it is likely that the chances of having 6 or more unchanged mods in 4 attempts on the above armor given it's shown states is about 1/30 to 1/40.
Interestingly, the odds are different from what I had expected, but it is reasonable enough not to consider it a bug.

I do have to withdraw my comment about seeing the 130%+ armor mod being more rare though, as the 1/27 chance of that happening is more likely after all :P


Also, for anyone reading this, the results of this analysis only apply to the above armor with the mods exactly as shown. I wouldn't want to be quoted that "6 unchanged mods in 4 attempts" is a rare occurence." ;)

it rerolled ALL the mods, that is for sure.
It just gave the same value on some mods, thats all.
I played with plenty divines in legacies, more than 20 i guess, and i can attest they are working as intended, meaning the (re)rolling its done on ALL mods.

Very interesting. at 1/30 or 40 it seems much more likely than I'd ever have guessed.

You lost me ages ago, but I supremely enjoyed this thread. Exactly the sort of thread you wouldn't see on you-know-whose forums! Bring on Path of Matlab!

Petrov.

The last divine shows that it doesn't necessarily reroll all of the mods, if it did, the lightning resistance would have changed. Allowing repeating values completely breaks the description of the orb. Definitely needs fixed.

For example, I have a 1 socket item, if I use a jeweler's orb, it WILL change. Let's say I have a 2 socket item, with no link between the two, if I use a fusing I WILL get a link between the two. Divines should work this way as well, rerolling and landing where they started should be ignored and rerolled again. I imagine if you divined a single mod item, it would change, it would never remain the same, just as my previous examples.

I, of course, am using a very rudimentary view of these orbs, at more complicated stages, they act quite similarly to the divine. Specifically fusings and chromatics.

With chromatics, you may have a red-red-blue and after a using a chromatic you can end up with a blue-red-red, essentially the same. The item changes, but it may not change in any usable manner (depending on how the item is linked), but it is an allowable change. I imagine a Divine will not allow all mods to be unchanged, if by some ridiculously low probability it did, it would just reroll.

I suppose it is working as intended, but if I spend a divine on an item wanting to change a specific value and all the other values change, but that one remains the same, I will be severely disappointed, as I think most of us would be. In my opinion, the values should always change, unless there is no variance in the mod's values.

"

TehHammer wrote:

Chromatics are the same, as well, if I only have 1 socket and I use a chromatic, it will not remain the same color, it will change.

...and if you use a chromatic orb on an item with two sockets, it's perfectly normal for one of the sockets to remain the same color. Same with fusing orbs and links, and I believe with alteration/chaos orbs and affixes.

Maybe divines don't reroll in the event of an exact-same result and should, but I don't think it's necessary for it to change all the mod values every time it's used.

Blessed orbs always change the value of the implicit mod, they never randomize it to be the same as it's current value.

Though I suppose a more comparable test would be to use Blessed on an item with an implicit mod that has 2 or more variable attributes? (though I don't think such an item exists)

"

Skivverus wrote:

"

TehHammer wrote:

Chromatics are the same, as well, if I only have 1 socket and I use a chromatic, it will not remain the same color, it will change.

...and if you use a chromatic orb on an item with two sockets, it's perfectly normal for one of the sockets to remain the same color. Same with fusing orbs and links, and I believe with alteration/chaos orbs and affixes.

Maybe divines don't reroll in the event of an exact-same result and should, but I don't think it's necessary for it to change all the mod values every time it's used.

Yes, my edited post reflects that. Same thing with fusings, a 6 socket item may have a [o-o o o o o] config, after using a fusing it may have a [o o o o-o-o] config. The 2nd and 3rd link slots didn't change.

Fusings, Jeweler's and Chromatics (I am assuming Divines as well) have protection against the item staying identical, which is great, but it still can be horribly annoying if there is one specific mod whose value you want to change, yet doesn't because it isn't forced. That's a horribly valuable orb to waste one because the mechanics of it are kind of trash.