Graduate stats likely come from 2d10 drop anyone under 60 total. No obvious big jumps at particular thresholds, so assume each extra point helps about the same given the stat type.
For completing my Great Quest: +8 WIS, +2 CHA, based on assuming each stat point provides the equivalent of x bits of evidence you’ll complete it, depending on the stat, estimated by looking at prior history in your range of stats of the change in prob given that total stats didn’t change.
For breaking the system: +10 CON. Best chance of surviving while not on a Great Quest, breaks the theoretical limit by the most, not awful for Great Quest.
Life after Questing: +6 CHA, +4 STR. Really quite good for your Great Quest even if not the best, and you no longer have silly weaknesses like talking and jars, so e.g. if there’s another fairy later you don’t run such a big risk of losing out on a free +10 stats by sounding simultaneously entitled and disinterested.
Analysis:
Some basics: Each stats has range 2-20 (and maybe comes from 2d10 somehow?). Sum of stats is in range 60-100. You have 62 and are going to 72. More stats generally gets better results. Baseline 62 gives 40% to quest; baseline 72 gives 69% to quest. Average graduate stat sum is 70.4. Total graduates 7387. Maybe stats come from a roll of 2d10 and you only graduate if your stats are at least 60 in total? P(12d10>=60)=74% so probably generated 10K folks and filtered to >=60, yeah. Stats are probably anti-correlated in our sample?
Let’s try simple logistic regression. Normalize, fit, predict. You’re 38% to succeed, that checks out. Try some simple changes? +10 to any stat, even though that brings you above 20. WIS gets to 73%, CHA/CON to 70%, INT/STR to 65%/61%, and DEX down to 34%. Huh! groupby(‘dex’).mean() ==> yeah, much higher chances with low dex, dunno if that’s because dex is useless and stats anti-correlated, or dex is harmful. Anyway this model’s got CHA/CON/DEX/INT/STR/WIS coeffs at [2.5, 2.5, −0.3, 1.7, 2.0, 2.7]. As I see it so far, there are three main considerations: pump WIS to 20 and CHA to 6 to maximize chance of quest, pump CON to 24⁄20 to maximize survivability past that of any adventure who has ever lived (can we pass 20?? :D), or mostly ignore quest considerations because we have other goals, which probably means maxing some stat or shoring up CHA/STR.
Let’s check a random forest to see if there are major discontinuities. Oh, it’s way different! Here +10 to CHA does very very well, almost 90% quest success. groupby(‘cha’).mean() ==> I see a jump of almost +10pp from 5->6 and 13->4 CHA. Maybe we invest 10 in CHA? Or maybe 2 in CHA and then… nah, not really better. But this is misleading too, because folks with CHA=14 just happened to have better stats on average. Better than CHA=13 for everything but DEX which has negative predictive success.
Okay fine, let’s try to do something like the right thing. I’d like to know the change in success rate when adding one point to one stat, with the sum of the other stats remaining constant. And I might only care about this in the lowish range of stat sums, 60 to 75, say. We’ll just grab the average for a sec. The average what. …evidence of success provided by seeing +1 in a certain stat given that all other stats are equal? Sure, maybe that’s the model used to generate quest prob. Laplace to estimate prob of success with total stats = x, wlog cha = y. Got CHA/CON/DEX/INT/STR/WIS [1.4, 1.1, −0.1, 0.6, 1.4, 1.8] for the whole 60-100 range, or [0.4, 0.3, −1.0, 0.3, 0.4, 0.8] for just 60-75.
Should also check that there’s no obvious reason the model assumption of e.g. 4->5 is in some ways the same as 18->19, but meh, we’re done here.
Graduate stats likely come from 2d10 drop anyone under 60 total
I think you’re right. The character stats data seems consistent with starting with 10000 candidates, each with 6 stats independently chosen by 2d10, and tossing out everything with a total below 60.
One possible concern with this is the top score being the round number of 100, but I tested it and got only one score above 100 (it was 103), so this seems consistent with the 100 top score being coincidence.
Fixed your spoilers for you. You used the markdown syntax but you are not in the markdown editor, so instead you should just start with >! and then proceed as usual.
Choice and reasoning:
Graduate stats likely come from 2d10 drop anyone under 60 total. No obvious big jumps at particular thresholds, so assume each extra point helps about the same given the stat type.
For completing my Great Quest: +8 WIS, +2 CHA, based on assuming each stat point provides the equivalent of x bits of evidence you’ll complete it, depending on the stat, estimated by looking at prior history in your range of stats of the change in prob given that total stats didn’t change.
For breaking the system: +10 CON. Best chance of surviving while not on a Great Quest, breaks the theoretical limit by the most, not awful for Great Quest.
Life after Questing: +6 CHA, +4 STR. Really quite good for your Great Quest even if not the best, and you no longer have silly weaknesses like talking and jars, so e.g. if there’s another fairy later you don’t run such a big risk of losing out on a free +10 stats by sounding simultaneously entitled and disinterested.
Analysis:
Some basics: Each stats has range 2-20 (and maybe comes from 2d10 somehow?). Sum of stats is in range 60-100. You have 62 and are going to 72. More stats generally gets better results. Baseline 62 gives 40% to quest; baseline 72 gives 69% to quest. Average graduate stat sum is 70.4. Total graduates 7387. Maybe stats come from a roll of 2d10 and you only graduate if your stats are at least 60 in total? P(12d10>=60)=74% so probably generated 10K folks and filtered to >=60, yeah. Stats are probably anti-correlated in our sample?
Let’s try simple logistic regression. Normalize, fit, predict. You’re 38% to succeed, that checks out. Try some simple changes? +10 to any stat, even though that brings you above 20. WIS gets to 73%, CHA/CON to 70%, INT/STR to 65%/61%, and DEX down to 34%. Huh! groupby(‘dex’).mean() ==> yeah, much higher chances with low dex, dunno if that’s because dex is useless and stats anti-correlated, or dex is harmful. Anyway this model’s got CHA/CON/DEX/INT/STR/WIS coeffs at [2.5, 2.5, −0.3, 1.7, 2.0, 2.7]. As I see it so far, there are three main considerations: pump WIS to 20 and CHA to 6 to maximize chance of quest, pump CON to 24⁄20 to maximize survivability past that of any adventure who has ever lived (can we pass 20?? :D), or mostly ignore quest considerations because we have other goals, which probably means maxing some stat or shoring up CHA/STR.
Let’s check a random forest to see if there are major discontinuities. Oh, it’s way different! Here +10 to CHA does very very well, almost 90% quest success. groupby(‘cha’).mean() ==> I see a jump of almost +10pp from 5->6 and 13->4 CHA. Maybe we invest 10 in CHA? Or maybe 2 in CHA and then… nah, not really better. But this is misleading too, because folks with CHA=14 just happened to have better stats on average. Better than CHA=13 for everything but DEX which has negative predictive success.
Okay fine, let’s try to do something like the right thing. I’d like to know the change in success rate when adding one point to one stat, with the sum of the other stats remaining constant. And I might only care about this in the lowish range of stat sums, 60 to 75, say. We’ll just grab the average for a sec. The average what. …evidence of success provided by seeing +1 in a certain stat given that all other stats are equal? Sure, maybe that’s the model used to generate quest prob. Laplace to estimate prob of success with total stats = x, wlog cha = y. Got CHA/CON/DEX/INT/STR/WIS [1.4, 1.1, −0.1, 0.6, 1.4, 1.8] for the whole 60-100 range, or [0.4, 0.3, −1.0, 0.3, 0.4, 0.8] for just 60-75.
Should also check that there’s no obvious reason the model assumption of e.g. 4->5 is in some ways the same as 18->19, but meh, we’re done here.
I only just realized that 6 * 20 != 100.
I don’t think this comment needs a spoilerbox.
>! in reply to:
Graduate stats likely come from 2d10 drop anyone under 60 total
I think you’re right. The character stats data seems consistent with starting with 10000 candidates, each with 6 stats independently chosen by 2d10, and tossing out everything with a total below 60.
One possible concern with this is the top score being the round number of 100, but I tested it and got only one score above 100 (it was 103), so this seems consistent with the 100 top score being coincidence.
Fixed your spoilers for you. You used the markdown syntax but you are not in the markdown editor, so instead you should just start with >! and then proceed as usual.