ewjax
04-03-2020, 10:18 AM
Before anyone says it - yes, this is extremely nerdy. Sue me. I'm an engineer, this is the sort of thing that I'm good at.
So, I got curious to see just how much would it cost to raise skills using the class trainer vice doing them in the field, and started collecting data. It is useful to note that the trainer seems to charge the same amount regardless of which skill is in question, i.e. it costs the same amount to raise 1HS from 90 to 91 as it does to raise Sense Heading from 90 to 91, as an example.
So I set about collecting data, using a range of characters and levels, and then entered it into an excel spreadsheet, and used the least-squares curve fitting function of excel (which is actually quite powerful) to fit (trainer costs) vs (current skill), using a 3rd order polynomial fit, i.e.
y = c3 * x^3 + c2 * x^2 + c1 * x + c0
where
y = trainer cost
x = current skill
c3, c2, c1, c0 = fitting coefficients
I'll show the raw and fitted data below, but to cut to the chase, here are the results:
Coeffs
c3: 9.99389E-06
c2: -2.97456E-04
c1: 2.68839E-03
c0: 0.00000E+00
*Note it is possible to force the constant or c0 term to 0, which I have done in this case
Stated fully, we have:
y = 9.99389E-06x^3 - 2.97456E-04x^2 + 2.68839E-03x
This is useful to answer a couple of key questions:
Predict how much the trainer will charge to raise any particular skill
Answer questions such as, "what would be the total cost if I just use the trainer to raise my research skills from 0 to 175"
The answer to the first question is given directly by the fitting equation. The answer to the second is given by using kindergarten calculus and simple integration of the polynomial fitting equation, i.e.
(total cost to raise skill from 0 to x) = (1/4)*9.99389E-06x^4 - (1/3)*2.97456E-04x^3 + (1/2)*2.68839E-03x^2
So to answer the question: raising skill from 0 to 175 will cost roughly 1853pp.
Here's the raw and fitted data (in plat), and the difference between the two (in coppers). As can be seen, the fit nails the actuals within just a few coppers. I'll also attach the graph.
Skill Actual Predicted Delta
0 0.000 0.000 0
12 0.000 0.007 7
16 0.002 0.008 6
38 0.219 0.221 2
25 0.033 0.037 4
50 0.640 0.640 0
63 1.488 1.488 0
65 1.663 1.663 0
70 2.160 2.159 -1
77 3.007 3.006 -1
100 7.290 7.288 -2
105 8.573 8.572 -1
110 10.000 9.998 -2
115 11.576 11.575 -1
120 13.310 13.309 -1
125 15.208 15.208 0
130 17.280 17.279 -1
135 19.531 19.531 0
140 21.970 21.969 -1
145 24.603 24.603 0
150 27.440 27.440 0
155 30.486 30.486 0
160 33.750 33.750 0
165 37.238 37.239 1
170 40.960 40.961 1
175 44.921 44.922 1
180 49.130 49.131 1
185 53.593 53.595 2
190 58.320 58.321 1
196 64.348 64.349 1
200 68.590 68.591 1
202 70.778 70.779 1
215 86.151 86.151 0
220 92.610 92.610 0
225 99.383 99.383 0
230 106.480 106.479 -1
235 113.906 113.904 -2
So, I got curious to see just how much would it cost to raise skills using the class trainer vice doing them in the field, and started collecting data. It is useful to note that the trainer seems to charge the same amount regardless of which skill is in question, i.e. it costs the same amount to raise 1HS from 90 to 91 as it does to raise Sense Heading from 90 to 91, as an example.
So I set about collecting data, using a range of characters and levels, and then entered it into an excel spreadsheet, and used the least-squares curve fitting function of excel (which is actually quite powerful) to fit (trainer costs) vs (current skill), using a 3rd order polynomial fit, i.e.
y = c3 * x^3 + c2 * x^2 + c1 * x + c0
where
y = trainer cost
x = current skill
c3, c2, c1, c0 = fitting coefficients
I'll show the raw and fitted data below, but to cut to the chase, here are the results:
Coeffs
c3: 9.99389E-06
c2: -2.97456E-04
c1: 2.68839E-03
c0: 0.00000E+00
*Note it is possible to force the constant or c0 term to 0, which I have done in this case
Stated fully, we have:
y = 9.99389E-06x^3 - 2.97456E-04x^2 + 2.68839E-03x
This is useful to answer a couple of key questions:
Predict how much the trainer will charge to raise any particular skill
Answer questions such as, "what would be the total cost if I just use the trainer to raise my research skills from 0 to 175"
The answer to the first question is given directly by the fitting equation. The answer to the second is given by using kindergarten calculus and simple integration of the polynomial fitting equation, i.e.
(total cost to raise skill from 0 to x) = (1/4)*9.99389E-06x^4 - (1/3)*2.97456E-04x^3 + (1/2)*2.68839E-03x^2
So to answer the question: raising skill from 0 to 175 will cost roughly 1853pp.
Here's the raw and fitted data (in plat), and the difference between the two (in coppers). As can be seen, the fit nails the actuals within just a few coppers. I'll also attach the graph.
Skill Actual Predicted Delta
0 0.000 0.000 0
12 0.000 0.007 7
16 0.002 0.008 6
38 0.219 0.221 2
25 0.033 0.037 4
50 0.640 0.640 0
63 1.488 1.488 0
65 1.663 1.663 0
70 2.160 2.159 -1
77 3.007 3.006 -1
100 7.290 7.288 -2
105 8.573 8.572 -1
110 10.000 9.998 -2
115 11.576 11.575 -1
120 13.310 13.309 -1
125 15.208 15.208 0
130 17.280 17.279 -1
135 19.531 19.531 0
140 21.970 21.969 -1
145 24.603 24.603 0
150 27.440 27.440 0
155 30.486 30.486 0
160 33.750 33.750 0
165 37.238 37.239 1
170 40.960 40.961 1
175 44.921 44.922 1
180 49.130 49.131 1
185 53.593 53.595 2
190 58.320 58.321 1
196 64.348 64.349 1
200 68.590 68.591 1
202 70.778 70.779 1
215 86.151 86.151 0
220 92.610 92.610 0
225 99.383 99.383 0
230 106.480 106.479 -1
235 113.906 113.904 -2