A simple linear regression analysis on the remaining turtles (everything that isn’t a Fanged Gray Turtle or a Six-Segmented Harold Clone) gives the following formula:
10.56lb base weight if green...
+2.02lb if grayish-green,
+5.47lb if greenish-gray,
+0.359lb/Wrinkle
+0.142lb/Scar
+0.598lb/Segment
+1.000lb/Abnormality
This does a reasonable job of prediction, but has a residual with a fairly-large ~2lb standard deviation. Our standard-deviation math suggests that this means we should give the Tyrant answers overestimating each turtle by 2.4-2.5lb, and should expect to lose on average ~35gp/turtle to error.
That seems like we might be able to improve on it, but I’m not sure how. I haven’t been able to find any useful interactions yet. There does seem to be an obvious explanation of all the traits except Abnormalities being driven by some hidden Age variable: old turtles start getting grayish, are wrinklier, have grown more shell segments and accumulated more scars, and are larger. However, I’m not sure how actionable this is for us.
The one thing it does look like I can do is adjust the amount of overestimation I do: it does seem that our estimate is less accurate as turtles get older and larger, and so rather than overestimating by 2.44lb for every turtle I should overestimate the larger ones by more and the smaller by less. That’s not going to be a very large improvement, though. I feel like there ought to be something else to do, but haven’t found anything yet.
Haven’t found anything particularly good, but I’ve probably gone as far as I’ll go. I’ve done some analysis trying to predict how much variance we expect from each turtle so that I know how much to overestimate, and for the non-special turtles I’m predicting:
Abigail: 23.0lb
Bertrand: 19.0lb
Chartreuse: 26.2lb
Donatello Dontanien: 21.1lb
Espera: 17.3lb
(Flint is already estimated as a gray turtle as 7.3lb)
Gunther: 30.0lb
(Harold is already estimated as a six-segmented clone as 20.4lb)
Irene: 23.7lb
Jacqueline: 20.0lb
I’m rounding these to 0.1lb even though I’m allowed to go more granular, because if the Tyrant weighs to the same precision we do he will also be rounding to 0.1lb, which means we don’t gain anything from more precision (estimating 7.25lb gives a payoff exactly halfway between estimating 7.3 and 7.2).
I’ll put these estimates in the parent comment for ease of GM extraction.
The one interesting thing I’ve turned up is that Abnormalities appear to convey a very large amount of variance: each abnormality adds ~1lb of average weight, but actually slightly over 1lb of stdev-weight. I suspect that abnormalities are adding weight in a highly-random way: my weight estimates for Espera, Irene and Jacqueline (0-abnormality turtles) are relatively low as a result because my confidence was higher, while my estimate for Gunther (6 abnormalities?) has a lot more safety margin built in.
A simple linear regression analysis on the remaining turtles (everything that isn’t a Fanged Gray Turtle or a Six-Segmented Harold Clone) gives the following formula:
10.56lb base weight if green...
+2.02lb if grayish-green,
+5.47lb if greenish-gray,
+0.359lb/Wrinkle
+0.142lb/Scar
+0.598lb/Segment
+1.000lb/Abnormality
This does a reasonable job of prediction, but has a residual with a fairly-large ~2lb standard deviation. Our standard-deviation math suggests that this means we should give the Tyrant answers overestimating each turtle by 2.4-2.5lb, and should expect to lose on average ~35gp/turtle to error.
That seems like we might be able to improve on it, but I’m not sure how. I haven’t been able to find any useful interactions yet. There does seem to be an obvious explanation of all the traits except Abnormalities being driven by some hidden Age variable: old turtles start getting grayish, are wrinklier, have grown more shell segments and accumulated more scars, and are larger. However, I’m not sure how actionable this is for us.
The one thing it does look like I can do is adjust the amount of overestimation I do: it does seem that our estimate is less accurate as turtles get older and larger, and so rather than overestimating by 2.44lb for every turtle I should overestimate the larger ones by more and the smaller by less. That’s not going to be a very large improvement, though. I feel like there ought to be something else to do, but haven’t found anything yet.
Haven’t found anything particularly good, but I’ve probably gone as far as I’ll go. I’ve done some analysis trying to predict how much variance we expect from each turtle so that I know how much to overestimate, and for the non-special turtles I’m predicting:
Abigail: 23.0lb
Bertrand: 19.0lb
Chartreuse: 26.2lb
DonatelloDontanien: 21.1lbEspera: 17.3lb
(Flint is already estimated as a gray turtle as 7.3lb)
Gunther: 30.0lb
(Harold is already estimated as a six-segmented clone as 20.4lb)
Irene: 23.7lb
Jacqueline: 20.0lb
I’m rounding these to 0.1lb even though I’m allowed to go more granular, because if the Tyrant weighs to the same precision we do he will also be rounding to 0.1lb, which means we don’t gain anything from more precision (estimating 7.25lb gives a payoff exactly halfway between estimating 7.3 and 7.2).
I’ll put these estimates in the parent comment for ease of GM extraction.
The one interesting thing I’ve turned up is that Abnormalities appear to convey a very large amount of variance: each abnormality adds ~1lb of average weight, but actually slightly over 1lb of stdev-weight. I suspect that abnormalities are adding weight in a highly-random way: my weight estimates for Espera, Irene and Jacqueline (0-abnormality turtles) are relatively low as a result because my confidence was higher, while my estimate for Gunther (6 abnormalities?) has a lot more safety margin built in.