This is a followup to the D&D.Sci post I made a week ago; if you haven’t already read it, you should do so now before spoiling yourself.
Here is the web interactive I built to let you test your solution; below is a complete explanation of the rules used to generate the dataset. You’ll probably want to test your answer before reading any further.
(Unless you’d prefer to enter your answer, then read through the rules with a slowly growing sense of vindication and/or concern before clicking “Begin Quest!”; or unless you’d like to completely ignore the spirit of the exercise and use the rules to improve your solution. I’m not the boss of you.)
Generation and Selection
An applicant for Adventurer College gets their stats by rolling two ten-sided dice for each stat and then adding them.
Not everyone who applies gets in. Only those with >60 total points are allowed entry; you, with your 62 points, barely made the cut. Of course, you only get the records for those who were accepted; this produces small but non-negligible selection effects.
Advantage and Disadvantage
On graduation, an Adventurer will inevitably find themselves in a party of 3-6 loyal friends who help each other with their Great Quests. Your chances of success are determined by how well you can contribute to a team like that (your Advantage), and how much you get in their way (your Disadvantage). These quantities are calculated as follows:
- Everyone starts with 1 Advantage and 1 Disadvantage.
- You can ignore the Dexterity score; in this world, it’s useless for everything Adventurers do except qualifying for Adventurer College.
- Having unusually high stats allows you to help take skill checks for your team. For every non-Dexterity skill you have above 12 points, add 2 Advantage for every point it exceeds 12 by. (For example, if you had 15 Charisma, that would give you (15-12)*2=6 extra Advantage.)
- Having unusually low stats means you cause trouble for your team. For every non-Dexterity skill you have below 8 points, add 3 Disadvantage for every point under 8. (For example, if you had 5 Charisma, that would give you (8-5)*3=9 extra Disadvantage.)
- If your Strength is greater than your Constitution, you’ll end up committed to physical tasks you don’t have the stamina to see through: that’s +2 Disadvantage.
- For similar reasons, if your Intelligence is greater than your Wisdom, that’s also +2 Disadvantage.
- Being able to out-talk the local Vizier (who has Charisma 16) is very useful. Adventurers with >16 Charisma get an additional +5 Advantage.
Success and Failure
Your odds of success are the ratio between your Advantage and your Disadvantage. That is:
P(Success) = Advantage / (Advantage + Disadvantage)
As Advantage and Disadvantage are both always >0, there is always a chance of success or failure.
With the above in mind, the optimal strategy given your starting position is as follows:
- Get STR and CHA to 8.
- Get WIS above INT.
- Put your remaining skill points into WIS and/or CON and/or INT, while keeping WIS above INT.
You may have several objections to this scenario. Relevant selection effects were only vaguely alluded to, and the dataset contains phenomena – the discontinuity at CHA>16, and the STR-CON interaction – irrelevant to your situation. To this, I can only plead realism: most datasets in the real world are much messier, have much more dubious relevance to your goals, and contain distortions about which the GM provides no hints at all.
You may also object to the use of random elements in scoring. Even with perfect allocation, you can’t get above a 93.75% chance of success: it is not only possible, but plausible, to do everything right and still lose. Meanwhile, refusing the fairy’s offer leaves you a 25% chance of success, deliberately allocating points badly leaves you about one chance in three, and most random allocations still give better-than-even odds. I plead realism here too, but I can see why it might bother some people; as a compromise, I provide probability-of-success alongside success/failure, in case you’d prefer to keep score that way.
Finally, you may object to the ways that the challenge was unfair in your favour. If you didn’t account for selection effects, you may have correctly avoided boosting DEX because you thought it was actively harmful instead of merely useless. If you didn’t look for interactions, you may have dodged the WIS<INT penalty just because WIS seemed like a better place to put points than INT. And I’m pretty sure even the three people who submitted optimal answers on the last post (good job simon, seed, and Ericf) didn’t find them by using the right link function, just because the linkage I set up between predictors and response was so arbitrary and idiosyncratic.
Here, I not only excuse but congratulate myself. The main benefit of exercises like this over Kaggle analyses – aside from Fate’s unwillingness to show up the following week and explain the algorithm it used to choose who would survive the sinking of the Titanic – is that making real-fake-world decisions based on real-fake-world data trains the ability to make mistakes that don't hurt you.
(If you have any other objections, please let me know. I very much want feedback so I can make the next challenge better.)