Deconstruction Rates

Some conclusions and data just in time for it to get mucked up in update 9.1:

Lesser Essences from Level 1 Decon
1 - 18
2 - 17
3 - 16

Conclusion: 1d3.

Lessers from Level 2
2 - 7
3 - 12
4 - 25
5 - 19
6 - 9

Conclusion: 2d3.

Lessers from Level 3
5 - 2
6 - 4
7 - 4
8 - 16
9 - 9
10 - 3
11 - 1

3d3 + 2 fits this, but 2d4 + 3 fits the current data almost exactly as well (least squared error). It is also possible there are other values not yet observed.

Lessers from Level 4
11 - 1
12 - 1
13 - 1
14 - 4
15 - 10
16 - 11
17 - 12
18 - 4
19 - 3
20 - 1

The only dice that fit this range are 1d10 + 10, 3d4 + 8, 9d2 + 2, of which only 3d4 + 8 comes anywhere close to matching the distribution. As with level 3, it is possible that there are other values not yet observed.

Lessers from Level 5
23 - 1
24 - 0
25 - 0
26 - 0
27 - 3
28 - 3
29 - 7
30 - 6
31 - 13
32 - 6
33 - 13
34 - 10
35 - 8
36 - 3
37 - 4
38 - 3
39 - 2
40 - 2
41 - 1

There are 6 possible dice that fit this, but there are almost certainly values that have not been observed yet at the edges of the range, so it's unlikely any are accurate.

.

Taking the average result of each distribution, we have:
1 - 1.96
2 - 4.15
3 - 8.00
4 - 16.06
5 - 32.75

This screams to the recognizer of patterns for 2, 4, 8, 16, 32, but the recognizer of patterns is easily deceived. If we trust it for now, this suggests that the ranges for Levels 1, 2, and 3 are accurate, while an as-yet unobserved result for level 4 could be 21 (which allows 5d3 + 6). Level 5 has the appropriate shape distribution, but if we may be permitted a flight of fancy we could propose possible results of 22 and 42, which allows 10d3 + 12. Thus, in sum:

1 - 1d3
2 - 2d3
3 - 3d3 + 2
4 - 5d3 + 6
5 - 10d3 + 12

Looks pretty nice to me.

.

Greater Essences from Level 1 Decon
1 - 18
Total Decons - 51

Greaters from Level 2
1 - 12
2 - 22
T - 72

Greaters from Level 3
1 - 8
2 - 5
3 - 3
T - 39

Greaters from Level 4
1 - 2
2 - 2
3 - 5
4 - 6
T - 48

Greaters from Level 5
1 - 6
2 - 6
3 - 4
4 - 7
5 - 5
T - 85

It certainly looks to me like that on getting a greater essence threat, the system rolls 1dLevel. For the greater threat itself, I have graphed the results with 95% confidence intervals:

http://img.photobucket.com/albums/v4...aterthreat.jpg

Where the red line signifies 1 in 3. The current overall average is .376 +/- .116, my justification for picking 1 in 3 is everything else in this system is d3, so this probably is too. This also has the tidy result that the average level 5 decon will produce one (1) greater essence. I do not see any justification for thinking that greater threat is level dependent in any systematic way.

You can pull a few more data points from my own experiences

Thanks, that data is a big help.

- Confirmation of a 21 from level 4, reinforcing the 5d3 + 6 hypothesis.
- For level 3, occurrences of 12s. To retain an xd3 form, we have to suppose the possibility of either a 13 (4d3 + 1) or a 4 (4d3). 4d3 fits the current data better, plus it has an average of 8 instead of 9, so my guess is that eventually we would see a 4 result. With our 139 observations, there is only an (80/81) ^ 139 = 17% chance of not seeing one so far, so it's unlikely but not ridiculous.
- The level 5 hypothesis is still more extrapolation than fitting, but with your data added in here's what the graph looks like:

http://img.photobucket.com/albums/v4...ol/L5Decon.jpg

The very edges (22 and 42) are 1 in 59409 chances, so it's prohibitively unlikely that we'll see them before update 9.1.

So to sum up:

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

Got a 22 from a level 4 today, suggesting that level 4 is actually 6d3 + 4 and that it's also possible to get a 10.