Craft Calculations

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AutXAutY
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I did a bunch of calculation for the probabilities of different kinds of exalts crafting different artifacts  at different essence scores.
 
In general, I used the following assumptions: Everyone has Craft 5, Attribute 5, and a Specialty. Everyone uses a 1-point stunt, a willpower, and a full excellency.
 
Most calculations are done using Anydice, and just throw all 6+ rolls together (using a total difficulty based on goal number + (difficulty-1)*terminus). Which slightly underestimates the chances, since a roll of <4 successes only contributes 0 successes, not negative. The exception is Sovereigns, who I did using a simulation of 1,000,000 rolls per build.
 
Celestial Exalted
Lunars
                                                             AVG Successes     2           3           4          5          na
No Charms                                             51                       99.77%  57.01%  0.19%  0%         0% 
Wonder-Weaving Art                              65                       100%     95.05%  15.13% 0.02%   0%     
E2, WWAx2, Silver Crucible Refinement  87                       100%      99.98%  87.20% 12.90% 0% 
E3, WWAx2, SCR                                     91                      100%      99.99%  93.27%  22.92% 0% 
E4, WWAx3, SCR                                     112                    100%      100%     99.86%  84.39%  0%  
E5, WWAx3, SCR, Unbound                     149                     100%     100%      100%    100% 0.15%
Demiurge's Dream
 
Umbral - assume 5+ Penumbra
                                                             AVG Successes      2           3           4          5         na
They don't have charms.                         51                       99.77%  57.01%  0.19%   0%.      0%
 
Hearteaters - assume a defining intimacy
                                                             AVG Successes      2          3             4         5.        na
They don't have charms.                            51                    99.77%  57.01%  0.19%  0%       0%
 
Terrestrial
Dragonblooded - Assuming Flawless Facet Realization always has enough failures to reroll

                                                             AVG Successes        2           3             4         5        na
No Charms                                                  39                    90.97%  7.36%     0%         0%       0%
E2, Strike the Dragon-Anvil,                        58                   99.95%    81.57%  3.91%    0%       0%
Flawless Facet Realization
E3, StDA, FFR, Eternal Omphalos Forge        71                   100%       98.8%    37.30%  0.29%   0%
E4, StDA, FFR, EOF                                       76                   100%       99.59%  53.87%  1.04%   0%
E5, StDAx2, FFR, EOF                                   80                    100%      100%      97.24% 39.90% 0%
 
Sovereigns - Assume always at max anima, assume you always spend extra time for Prismatic Design Realization. Treat excellency as (Higher of Essence or 3)+Anima
                                                             AVG Successes        2           3             4         5        na
No Charms                                                  39                    90.97%  7.36%     0%         0%        0%
E1, Prismatic Design Realization,                 68                    100%     95.50%  25.60%   0.53%   0%
Flawless Diamond Talent
E3, PDR, FDT, Every Work a Glory                 90                    100%.    99.96%  87.44%   23.59%  0%
E4, PDR, FDT, EWaG                                     95                    100%     99.99%  93.95%   36.92%  0%
E5, PDR, FDT, EWaG                                   101                    100%     100%     97.35%   51.78%  0%
 
Architects - Assume always in a city
                                                             AVG Successes        2           3             4         5        na
No Charms                                                  39                    90.97%  7.36%     0%         0%        0%
E1, Seasoned Tinker Ingenuity,                    51                   100%     90.66%    02.15%  0%       0%
Towering Achievement Motivation
E2, STI, TAM                                                61                    100%    99.57%.    23.39%  0.01%   0%
E3, STI, TAM, City-Uplifting Masterworks     84                    100%    100%       98.54%   29.4%.  0%
E4, STI, TAM, CUM                                       94                    100%    100%       99.95%   71.63%  0%
E5, STI, TAM, CUM                                      104                   100%      100%     100%     95.11%   0%
 
Dream-Souled - Assume always upholding your Ideal
                                                             AVG Successes        2           3             4         5        na
No Charms                                                  39                    90.97%  7.36%     0%         0%       0%
E1, Dreamstuff-Sculpting Reverie                45                    98.68%  28.16%   0.01%    0%       0%
E2, DSR                                                       49                    99.58%  45.08%   0.04%    0%       0%
E3, DSR                                                       52                    99.88%  62.31%   0.22%    0%       0%
E4, DSR                                                       55                    99.97%  76.90%   0.86%    0%       0%
E5, DSR                                                       59                    99.99%  87.35%   2.64%    0%       0%

I haven't included Solars because they're a pain to calculate, and haven't included other Exigent types because that's a lot of things to write down, I might add both of those later. I haven't run through all the DB signature possibilities because there's a lot of them. 
 
Summary is that Celestial Exalts are better at making Artifacts than Terrestrial Exalts, exception that Hearteaters and Umbrals don't get charms for crafting so aren't actually very good. And Essence 3 Architects are slightly better than Essence 3 Lunars. Architects are the best among terrestrial, with Sovereigns second best, except at Essence 1 when those reverse. Dragonblooded are third, then Dreamsouled
Last edited by AutXAutY on Tue Sep 20, 2022 1:40 am, edited 2 times in total.
CritianCaceorte
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Huh, that's kind of interesting that Architects end up the winner among the Terrestrials. I just assumed that an Exigent with Craft as one of their 5 Abilities would end up dominating over an Attribute-based Exalt.
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andrix
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I'm actually surprised at just how many terrestrials are able to hit pretty high % for 5 dots, with the massive drop off to N/A. It suggests the math underpinning some of this was actually pretty robust and a lot of the system is working as was probably intended. Whether the complexity and overworked nature of 3e RAW justifies that robustness is another matter.

It's also pretty fitting that Architects are so competent.
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Plutonium
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I've always thought the Craft math and charms and rules at the higher end (artifact crafting and up) made logical sense from a pure simulationist perspective in terms of modeling the level of skill and practice required to craft an actual artifact, but where they break down is when it comes to following the rules in any sort of actual game because the sheer volume of crafting role-playing required to generate the requisite gold points is so monumental and tedious as to border on insanity.
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AutXAutY
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CritianCaceorte wrote: Mon Sep 19, 2022 1:23 am Huh, that's kind of interesting that Architects end up the winner among the Terrestrials. I just assumed that an Exigent with Craft as one of their 5 Abilities would end up dominating over an Attribute-based Exalt.

I think that if Architects where ability-based, they'd have Craft as one of their 5 - it's only that being Attribute-based obscures which abilities they focus on.
Architects also have a lot of conditional charms I'm assuming they get full advantage of - outside a city they lose Essence successes per roll, and rerolling 5s, and their double 9s charm is only once per story.
Architects are also interesting because they have a huge degree of reliability - rerolling 5s and 6s is best on rolls where you roll poorly, because 5s and 6s are normally bad, while adding Extra successes is always the same amount. So Architects do really well on rolls which they where likely to succeed, and poorly on rolls they were likely to fail, compared to their average. You can see this by comparing an Essence 3 Architect making Artifact 3 to an Essence 3 Lunar making Artifact 3 - the Architect actually has a hairbreadth advantage, though both are nearly guaranteed.

andrix wrote: Mon Sep 19, 2022 2:42 pm I'm actually surprised at just how many terrestrials are able to hit pretty high % for 5 dots, with the massive drop off to N/A. It suggests the math underpinning some of this was actually pretty robust and a lot of the system is working as was probably intended. Whether the complexity and overworked nature of 3e RAW justifies that robustness is another matter.

It's also pretty fitting that Architects are so competent.

I'm not sure I'd say it's that high - Dragonblooded only get a 39% chance, and then only at essence 5, and there aren't many essence 5 DBs. Sovereigns have a non-trivial chance at essence 3, but even by essence 5 they're barely above 50/50, and they're spending 4 years of work for a 52% chance of getting anything (plus 18wp, 144m, and a bunch of craft XP). It's only Architects who really have a decent chance of success, and I don't know if there are any Essence 4/5 Architects in Creation.

Plutonium wrote: Tue Sep 20, 2022 12:13 am I've always thought the Craft math and charms and rules at the higher end (artifact crafting and up) made logical sense from a pure simulationist perspective in terms of modeling the level of skill and practice required to craft an actual artifact, but where they break down is when it comes to following the rules in any sort of actual game because the sheer volume of crafting role-playing required to generate the requisite gold points is so monumental and tedious as to border on insanity.

I think there's a degree to which those are different factors - the dice roll mainly determines whether you can succeed, because the line between <1% chance of success and >99% chance of success is pretty small, while the gold points are more about how rapidly you can make the artifacts where you have a good chance of success. I guess the fact that succeeding in fewer rolls reduces costs, and increases the # of gold points awarded to you. I didn't do the math for average number of rolls taken - I don't think I could do it in Anydice, so I'd need to write a bunch of different simulations to account for all the charms.
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