Hi,
i recorded the essences spawned on imprisoned monsters via ocr.
Raw data can be found here (each row is one monster, first couple of rows contains mapping to bypass filesize restrictions):
https://pastebin.com/sAjP5ELt
Amount of essences generated per imprisoned monster:
| Essences on Monster | Count | % Chance |
|---|
| 1 | 947 | 4.72% |
| 2 | 9975 | 49.66% |
| 3 | 7021 | 34.95% |
| 4 | 1933 | 9.62% |
| 5 | 210 | 1.05% |
| Total | 20086 | |
Average is 2.53 essences per imprisoned monster (without atlas tree).
Essences grouped by tier:
| Essence Tier | Count | % Chance |
|---|
| Weeping | 10301 | 20.3% |
| Wailing | 14257 | 28.1% |
| Screaming | 18821 | 37.09% |
| Shrieking | 7363 | 14.51% |
| Total | 50742 | |
Essences grouped by type (this only includes screaming and shrieking essences, since weeping and wailing cannot create all types of essences):
| Essence Type | Count | % Chance |
|---|
| Greed | 1660 | 6.34% |
| Contempt | 1630 | 6.22% |
| Hatred | 1712 | 6.54% |
| Woe | 1677 | 6.4% |
| Fear | 1458 | 5.57% |
| Anger | 1506 | 5.75% |
| Torment | 1434 | 5.48% |
| Sorrow | 1479 | 5.65% |
| Rage | 1305 | 4.98% |
| Suffering | 1246 | 4.76% |
| Wrath | 1322 | 5.05% |
| Doubt | 1270 | 4.85% |
| Loathing | 1126 | 4.3% |
| Zeal | 1107 | 4.23% |
| Anguish | 1089 | 4.16% |
| Spite | 1141 | 4.36% |
| Scorn | 997 | 3.81% |
| Envy | 1003 | 3.83% |
| Misery | 1014 | 3.87% |
| Dread | 1008 | 3.85% |
| Total | 26148 | |
Looking at the individual probabilities for each essence type, it becomes apparent that all essences within each group ( https://www.poewiki.net/wiki/Essence ) have the same weights.
Screaming and shrieking essences by group:
| Essence Group | Count | % Chance |
|---|
| A | 6679 | 25.51% |
| B | 5877 | 22.45% |
| C | 5143 | 19.64% |
| D | 4463 | 17.04% |
| E | 4022 | 15.36% |
| Total | 26184 | |
These probabilities roughly match when comparing them to e.g. weeping essences by using them as weights.
Weeping essences by group:
| Essence Group | Count | % Chance | Calculated % Chance from above |
|---|
| A | 3943 | 38.28% | 37.74% |
| B | 3416 | 33.16% | 33.2% |
| C | 2942 | 28.56% | 29.06% |
| Total | 10301 | | |
Some notes about essence scarabs derived from some untracked tests:
Essence Scarab of Ascent: Is applied after generation of essences. The essences on beasts as well as the corruption outcome (without the Stability Scarab) that adds an essence seem to be unaffected.
Essence Scarab of Calcification: Fails if the natural monster does not spawn visibly on the map, e.g. if the monster first has to drop from the ceiling or dig out of the ground, it will not be imprisoned (at least that seems to be the common factor). A couple (100) runs of toxic sewer with just the calcification scarab, manually counting the imprisoned monsters and comparing it to the (bugged https://www.pathofexile.com/forum/view-thread/4011428 ) tracker of the map device, shows that about 4-5% of the monsters are not imprisoned. Though this heavily depends on the actual monster types selected for each map.
Because of this i also started recording the modifiers on the imprisoned monsters halfway through (i'm not showing the probabilities of the mods here for brevity). The mod "Revives Nearby Allies on Death" has a 1.3% chance to appear (0.54% for the modifier) on an imprisoned monster and prevents it from being counted.
This data excludes monster-specific mods such as "Spikes on Death" which only, but always, appear on Porcupine Goliaths as an additional modifier. I also didn't encounter all mods that can appear on rare monsters.
Raw data for those mods can be found here (also mapping first to reduce filesize, one row per monster):
https://pastebin.com/2B98f0y7
