Divine orb behaviour.

I got bored this evening and decided to exalt some armour I'm wearing.

In hind sight it was a bad decision, but hey it's only money orbs.

This is what I started out with:



This armour has the following mods:

"

of the Bear (lvl 22, suffix) +18 to +22 Strength

Thickened (lvl 60, prefix) +83% to +100% Armour

Armadillo's (lvl 29, prefix) +24% to +32% Armour, +10% to +11% block/stun recovery

Athlete's (lvl 54, prefix) +80 to +89 Life

The first exalted added:

"

of Iron Skin (lvl 28, suffix) +17% to +19% block/stun recovery

The second exalted added:

"

of the Cloud (lvl 1, suffix) +6% to +11% Lightning resist

Possibly the two worst mods I could have rolled.... but no matter, what's done is done.

So, on with the science! (and the point of this thread.)

I then used a few divines:



So the first has (in all likelyhood) only rerolled 3 of the mods on the item. ("of the Bear", "Athlete's" and "of Iron Skin").



This second Divine has (in all likelyhood) only rerolled 2 of the mods on the item ("of the Bear", and "Armadillo's").



3rd Divine is more effective. It has (in all likelyhood) rerolled 4 mods ("of the Bear", "Thickened", "Athlete's" and "of the Cloud").



The 4th and final(for now!) Divine (in all likelyhood) rerolled 3 mods. ("of the Bear", "Armadillo's" and "Athlete's").

It is possible that each Divine rerolled all of the item's mods, however for so many rolls to result in no change is incredibly unlikely.

It's far more plausible that Divines do not do what their textual description would imply.

"

Randomises the numeric values of the random properties on an item

I would suggest that a Divine orb:
Randomizes the numeric values of a random number of the random properties on an item.

If this is the case, I think that:

a) the textual description needs revising; it's misleading.
b) The trade value of Divines be re-evaluated (downwards) in light of this behaviour.

It is supposed to reroll all the mods values not just some. It may seem like it doesn't just because the numbers on those mods don't vary that much. Each mod doesn't include a ridiculously large gap in stats.

With 2 mods affecting 1 stat it can seem like the orb is doing nothing when the value doesn't change because the individual mod may have changed but the sum of the 2 has not.

The probability of rolling 6 mods and getting the same value again on most of them is pretty small.

bear 5 ****
iron skin 3 *
clouds 6*
thickened 18*
armadillo 9 and 2 **
athlete 10 ***

numbers represent options to choose from on a reroll
stars represent suspected rolls out of 4 possible

the probability of only seeing 1 in 4 rerolls on thickened, given 18 possible values is quite small.

however if you combine that with the other failures...

There is a very very small probability of seeing these results, unless my understanding of the probabilities involved is wrong, or the fact that two of the mods overlap is skewing the probabilities THAT much.

It's still within the realm of possible, but not by much. It's late and my brain is failing me atm... someone can do the combinatorics on it...

"

zeto wrote:

The probability of rolling 6 mods and getting the same value again on most of them is pretty small.

bear 5 ****
iron skin 3 *
clouds 6*
thickened 18*
armadillo 9 and 2 **
athlete 10 ***

numbers represent options to choose from on a reroll
stars represent suspected rolls out of 4 possible

the probability of only seeing 1 in 4 rerolls on thickened, given 18 possible values is quite small.

however if you combine that with the other failures...

There is a very very small probability of seeing these results, unless my understanding of the probabilities involved is wrong, or the fact that two of the mods overlap is skewing the probabilities THAT much.

It's still within the realm of possible, but not by much. It's late and my brain is failing me atm... someone can do the combinatorics on it...

That's true, though the probability is small it is a "possible" explanation.

There may be 6 mods on the item, but for calculating the probability you need to treat them as 5, because there are only 5 visible properties that you can confirm.

To take the block and stun recovery as an example. One mod has 3 possibilities, another one has 2. The total amount of combinations is 6. However, if you can only determine the sum of the two mods, not their individual values, the amount of combinations the observer can distinguish drops to 4.
In this case, the values the mod can take are 27, 28, 29 and 30.
the value 27 occurs only when you roll 10 and 17 on the respective mods, while the value 30 occurs only when you roll 11 and 19 on the respective mods.

Instead of treating the stun/block recovery as two mods, for the purpose of determining the chances of seeing the same value after rolling all the mods, it can be treated as a single mod, with probabilities as follows:
If it originally has the values 27 OR 30, then the probability of rolling the same total is 1/6
Otherwise, the chances of rolling the same number is 1/3.

Incidentally, on each of your attempts, you had values of 28 or 29%, meaning on each of your attempts you had a chance of 1/3 to see the same mod.

The same should be done for armor. If you follow the same reasoning, your first, second and fourth attempt each have a chance of 1/18 to see the same values after rerolling stats. The third attempt had a chance of 1/27.

To summarize your chances of seeing the same value appear on your armor:
Strength: 1/5
Armor: 1/18 (1/27)
Life: 1/10
L.Res: 1/6
recovery: 1/3

It can be calculated that for your attempts other than your third, you had a chance of seeing the following amount of values unchanged:

0:37.81%
1:42.31%
2:16.73%
3: 2.94%
4: 0.23%
5: 0.01%

On your third attempt, chances where as follows:

0:38.52%
1:42.35%
2:16.23%
3: 2.70%
4: 0.19%
5: 0.00%

Values are rounded of course ;)

The amount of values that were unchanged for you were as follows:

first attempt: 2
second attempt: 2
third attempt: 1
fourth attempt: 1

If you compare those values to the probabilities in the tables above, you'll see that the results of your attempts were very common. In fact, rolling the 130% armor mod was far more unlikely, as a 130%+ mod occurs only once every 27 attempts. You should consider yourself lucky ;)

Excellent evaluation renatobaal, I thank you for your effort.

And interesting analysis, although something tells me that it's incomplete. I'm curious how you calculated the total chance to see something unchanged. Additionally, I don't believe this analysis can be complete without ANOVA or something else that takes into consideration the 4 round results in relation to one another.