Ister, Ziqual and Fizz seem to have some pretty deterministic structure connecting them.
Ister always predicts an integer between 51 and 60 inclusive.
Ziqual’s prediction is equal to (Ister − 50) * (Integer from 1 to 10) - (one of 0, 1). Multipliers in the 5 to 7 range are most common.
Fizz’s prediction is less than or equal to (Ister’s prediction + 10). Fizz’s prediction is greater than or equal to 44.
Separately, a scatterplot of Liboulen and Colleen’s predictions has a lot of structure: [Scatterplot removed since it seems to show up through the spoiler. Message me if you want to see it.]
Note that each of the 3 “axies” of this “prism” has 10 separate blobs of points. This makes me suspect that Liboulen and Colleen are each a weighted sum of 3 underlying integer variables that each range from 1 to 10. (There would also need to be a small noise term or other factor, since the points do not perfectly fit this pattern.) The noise term seems to only apply to Coleen’s estimates, as Liboulen’s estimates have way less distinct values.
Bella seems to have some interactions with these two. Linestra is an almost perfect clone of Colleen, but her estimates are either 1.7 or (occasionally) 1.9 lower.
It feels like it should be easy enough to find the coefficients corresponding to the 3 visible slopes formed by the edges of this figure. Based on some data slicing and eyeballing the graph above, I think the coefficients for L are 5, 1, 1, and the coefficients for C are approximately 3.6, −1.25, and 2.47
I am sure that there is a linear algebra regression to find the exact values, but I haven’t figured it out yet.
A summary of some interesting results. I am leaving how I found some of this out for now, for brevity’s sake.
I have manage to extract 6 integer variables that range from 1-10.
3 of them are from the components of (Coleen, Linestra, Liboulen, Bella), the other 3 are from (Fizz, Ister, Ziqual).
Each of them has a very similar histogram, sort of like a truncated normal distribution. A linear regression of them with Holly gives approximately 1 as their coefficient, except for 1 variable (which I am calling X2 for now) which has a coefficient of roughly −1.
All of these underlying variables have a magnitude of correlation with the candidate succeeding, between 0.11 and 0.17 , with X2 being the only negative correlation.
When looking at the Fae council, I noticed:
When Linestra is gone, Colleen predicts exactly 50 each and every time. This suggests that she is plagiarizing Linestra. She only ever gives 50 rating when Colleen is missing or predicting 48.3.
When Colleen is gone, the correlation between Linestra’s rating and the candidate being chosen is almost halved. This is consistent with the council using a voting process.
At this point I am throwing everything that I found in a linear regression, because I ran out of time. My pick is:
Candidate 11, with an estimated 0.91 chance of success.
Candidates 19 and 7 would be my next choices, with 0.87 and 0.85 estimated chances of success respectively.
If I had had more time to work on this, I would have like to look at:
Why do 3 of the “stats” have diminishing returns, while the other 3 have increasing returns?
Are there any temporal trends?
Can I find anything else out from the sick days?
Why does adding the Bella/L/L stats together result in a spike for very low stats? (aphyer seems to have figured this one out.)
How does the voting system of the faye council work?
What is up with Amy’s ratings?
What is up with Ziqual’s off-by-one ratings?
Is the “noise” in Linestra’s ratings actually related to the other stats?
If I was designing the puzzle, I would try to have one of the possible choices be someone the council would be unlikely to select, but who actually the best. Looking at aphyer’s comments, the reversal on the “physical” stats might be setup for the optimal answer.
A few miscellaneous observations:
Ister, Ziqual and Fizz seem to have some pretty deterministic structure connecting them.
Ister always predicts an integer between 51 and 60 inclusive.
Ziqual’s prediction is equal to (Ister − 50) * (Integer from 1 to 10) - (one of 0, 1). Multipliers in the 5 to 7 range are most common.
Fizz’s prediction is less than or equal to (Ister’s prediction + 10). Fizz’s prediction is greater than or equal to 44.
Separately, a scatterplot of Liboulen and Colleen’s predictions has a lot of structure: [Scatterplot removed since it seems to show up through the spoiler. Message me if you want to see it.]
Note that each of the 3 “axies” of this “prism” has 10 separate blobs of points. This makes me suspect that Liboulen and Colleen are each a weighted sum of 3 underlying integer variables that each range from 1 to 10. (There would also need to be a small noise term or other factor, since the points do not perfectly fit this pattern.) The noise term seems to only apply to Coleen’s estimates, as Liboulen’s estimates have way less distinct values.
Bella seems to have some interactions with these two. Linestra is an almost perfect clone of Colleen, but her estimates are either 1.7 or (occasionally) 1.9 lower.
It feels like it should be easy enough to find the coefficients corresponding to the 3 visible slopes formed by the edges of this figure. Based on some data slicing and eyeballing the graph above, I think the coefficients for L are 5, 1, 1, and the coefficients for C are approximately 3.6, −1.25, and 2.47
I am sure that there is a linear algebra regression to find the exact values, but I haven’t figured it out yet.
A summary of some interesting results. I am leaving how I found some of this out for now, for brevity’s sake.
I have manage to extract 6 integer variables that range from 1-10.
3 of them are from the components of (Coleen, Linestra, Liboulen, Bella), the other 3 are from (Fizz, Ister, Ziqual).
Each of them has a very similar histogram, sort of like a truncated normal distribution. A linear regression of them with Holly gives approximately 1 as their coefficient, except for 1 variable (which I am calling X2 for now) which has a coefficient of roughly −1.
All of these underlying variables have a magnitude of correlation with the candidate succeeding, between 0.11 and 0.17 , with X2 being the only negative correlation.
When looking at the Fae council, I noticed:
When Linestra is gone, Colleen predicts exactly 50 each and every time. This suggests that she is plagiarizing Linestra. She only ever gives 50 rating when Colleen is missing or predicting 48.3.
When Colleen is gone, the correlation between Linestra’s rating and the candidate being chosen is almost halved. This is consistent with the council using a voting process.
At this point I am throwing everything that I found in a linear regression, because I ran out of time. My pick is:
Candidate 11, with an estimated 0.91 chance of success.
Candidates 19 and 7 would be my next choices, with 0.87 and 0.85 estimated chances of success respectively.
If I had had more time to work on this, I would have like to look at:
Why do 3 of the “stats” have diminishing returns, while the other 3 have increasing returns?
Are there any temporal trends?
Can I find anything else out from the sick days?
Why does adding the Bella/L/L stats together result in a spike for very low stats? (aphyer seems to have figured this one out.)
How does the voting system of the faye council work?
What is up with Amy’s ratings?
What is up with Ziqual’s off-by-one ratings?
Is the “noise” in Linestra’s ratings actually related to the other stats?
If I was designing the puzzle, I would try to have one of the possible choices be someone the council would be unlikely to select, but who actually the best. Looking at aphyer’s comments, the reversal on the “physical” stats might be setup for the optimal answer.