Deconstruction Rates - Update 9.1

[Kinerd]

During Update 9, I found the following (with assistance from Lithic's data):

Level 	 Lessers
1	 1d3
2	 2d3
3	 4d3
4	 6d3 + 4
5	 10d3 + 12

And for greaters, a 1 in 3 chance of generating any number up to and including the level of deconstruction. Hence, the average return for each level of deconstruction were:

Level 	Lessers	Greaters
1	2	1/3
2	4	1/2
3	8	2/3
4	16	5/6
5	32	1

Two changes with Update 9.1 stated:
"Deconstructing low tier effects on high-end loot will now return more reward essences."
"It is now possible to deconstruct crafting Shards using the Deconstruction Eldritch Device."

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First, let us investigate what it means to be "high-end" and "loot". I have observed several divergences from the patterns found above. The format I will be using is "item's minimum level - deconstruction level : lesser essences, greater essences". Thus, "8 - 1: 4, 1" refers to a minimum level 8 item, level 1 deconstruction, which returned 4 lesser essences and 1 greater essence. (An "r" following the item's minimum level denotes that it was race-restricted.)

8 - 1: 4, 1
6 - 2: 12, 2
10 - 2: 7, 0
10 - 2: 7, 0
12 - 2: 3, 3
12 - 2: 4, 3
12 - 2: 4, 3
10r - 2: 6, 3
10 - 3: 35, 1
10 - 3: 38, 0
13 - 3: 14, 2
14 - 3: 13, 0
14 - 3: 13, 2
10 - 4: 24, 5
12 - 4: 24, 0
14 - 4: 37, 0
15 - 4: 21, 5
16 - 4: 23, 1
16 - 4: 24, 4
11 - 5: 36, 6
12 - 5: 40, 6
12 - 5: 46, 0
12 - 5: 48, 1
15 - 5: 43, 0
16 - 5: 33, 6
13r - 5: 33, 6

All told, 15 instances of more lessers than expected, 9 instances of more greaters than expected, and 2 instances of both more lessers and more greaters. The overall rate of aberration was 7.5% +/- 10.8%. As the level of error indicates, comparing rate of aberration on a decon level basis (or even worse, a minimum level basis) is useless at this point.

In any event, we can notice immediately that all levels of deconstruction have a chance of producing unusually high rewards. We can also notice that what it means to be "high-end" is very oddly defined - a mere minimum level 6 item produced unusually high rewards. It is also interesting that the aberrant greaters are never more than +1 from the original distribution.

It is worth noting the possibility that the underlying distributions were also changed, that perhaps a level 1 deconstruction is now a 1d4 rather than a 1d3. This is unlikely: over 41 level 1 deconstructions, I have 11 1s, 18 2s, 11 3s, and exactly 1 4, which came on one of two minimum level 8 item level 1 deconstructions.

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Next, I will treat Shards vs. Items. Both the language of the release notes and my findings suggest that Shards do not receive the "more reward essences", which is to say they are not considered "loot", although it's conceivable that this is only because the shards I have deconstructed so far aren't "high-end" enough yet. How the equivalent of item minimum level is determined on a shard is anyone's guess, but for now I have lots of data on +1 and +2 shards and have seen nothing out of the ordinary. For a +2 shard level 2 deconstruction, I have:

Lessers	Count
2	12
3	40
4	55
5	37
6	21

This fits a 2d3 distribution nicely. By comparison, my non-shard level 2 deconstructions have:

Lessers	Count
2	8
3	14
4	32
5	27
6	12
7	2
8	0
9	0
10	0
11	0
12	1

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Now, there is also the question of the chance of generating greaters at all. Before update 9.1, I hypothesized that this was simply d3 across all deconstruction levels, and the data was consistent with that hypothesis. As mentioned earlier, I do not have enough data yet to make a worthwhile comparison between minimum levels, or between deconstruction levels, but I do have enough to look at between Shards and Items. Currently, the rates I have are 34.5% +/- 13.0% vs. 36.7% +/- 10.8%, respectively. My guess is these will converge on 33%, and therefore that "more reward essences" refers specifically to the number generated rather than the chance of generation (in the case of greaters). In any event, there is no evidence currently to suggest that Shards have less of a chance of generating greater essences than Items.

[Natean]

I have some data that you might want Crafting: Essence Deconstuction rates
It contains a large quantity of data, however not the way you have described. I did not wish to record 1000s of data as MinimumLevel:LevelDeconstructed:Lesser:Greater

It is important to record lots of data for it to be solid enough to provide a good estimation, a few hundred data recordings is a good start.

[articwarrior]

by the way, I think the docon rate for greaters at a level 5 rate is 1/2 because sometimes I wont get a greater essence

[Kinerd]

by the way, I think the docon rate for greaters at a level 5 rate is 1/2 because sometimes I wont get a greater essence

To clarify: the table lists your expected return. If you have a 1/3 chance of getting any greaters at all, and on getting a greater you have an equal chance of getting 1, 2, 3, 4, or 5, then your expected return is:

(1/3) * (20% * 1 + 20% * 2 + 20% * 3 + 20% * 4 + 20% * 5) = 1

[articwarrior]

To clarify: the table lists your expected return. If you have a 1/3 chance of getting any greaters at all, and on getting a greater you have an equal chance of getting 1, 2, 3, 4, or 5, then your expected return is:

(1/3) * (20% * 1 + 20% * 2 + 20% * 3 + 20% * 4 + 20% * 5) = 1

ah I understand, so the view on it is broad not specified to "per disjunction"

[Kinerd]

Update!

After playing with the data for awhile, I think that the "more reward essences" means that high-end items have a 50% chance of using a juiced distribution instead of the normal one. For example, the distribution for lessers from a level 2 deconstruction is 2d3. The juiced distribution is 2d4. Hence, if you were to observe a 2, 3, 4, 5, or 6, there's no way to tell which distribution it came from, but if you were to sum the distributions (2d3 * 50% + 2d4 * 50%), you would see:

	2d3	2d4	2d3 + 2d4
2	11.11%	6.25%	8.68%
3	22.22%	12.50%	17.36%
4	33.33%	18.75%	26.04%
5	22.22%	25.00%	23.61%
6	11.11%	18.75%	14.93%
7		12.50%	6.25%
8		6.25%	3.13%

And here is the graph I have charting observations versus the predictions of this model:


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Now, this double distribution is also going to change the average value we'd expect. 2d3 has an average of 4, but 2d3 * 50% + 2d4 * 50% has an average of 2 + 2.5 = 4.5. I currently have the following measurements for average lessers from items with minimum levels at least 8:

Level	n	Act.	Pred.
2	60	4.47	4.50
3	82	9.16	9.00
4	103	18.55	17.50
5	129	34.83	34.50

(I only have 7 measurements of level 1 decons on those items, so I left it off.)

We can also look at Natean's data. He doesn't separate out by minimum level, but because we follow the same principle (of always pursuing the highest level deconstruction), we can guess that the relative populations are roughly the same as mine, and see how the overall numbers shake out:

Level	%>ML8	Act.	Pred.
2	38.46%	4.31	4.19
3	69.49%	9.32	8.69
4	88.79%	18.16	17.33
5	100.00%	35.41	34.50

Without error bars, can't say much, but I will say "not bad!" We can also look at his lesser ranges:
1: 1-5
2: 2-8
3: 4-16
4: 10-26
5: 24-49

Aside from the 5 in level 1, these all fit very neatly into the ranges described by the d4/d3 switch. I would expect to eventually see 27s and 28s from 4, and very eventually see down to 22 and up to 52 on 5s. The shapes of the distribution also resemble the overlapping distributions I described, especially when taking into account that lower level deconstructions see a smaller effect, due to his data (probably) having more low level information there.

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I'm not sure what, if anything, this means for greaters (yet).

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The most updated numbers for chance of producing greaters on a deconstruction are:
Item: 34.3% +/- 4.2% (792 of 2311)
Shard: 35.0% +/- 6.9% (295 of 843)