How much does the trainer cost to raise your skill?

[ewjax]

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

[aspomwell]

Nerdally done!

Bravo!

[Dogma]

Also an engineer and lord knows I wouldn't do this kind of math for free. Maybe to win an argument but never just unwarranted.

I wonder if NPC faction and PC Charisma factors in...

[jaroh]

I helped collect some data for this experiment. It was very surprising when we realized that the trainer cost was the same regardless of skill being trained. I didn't remember that from way back when on original EQ. How did I not know that?