Regression to find formulas from dataset (from an RPG game - Warspear Online)

Question

I'm looking for a formulas from an RPG game, to simplify the designation of the elements I used full names instead conventional letters.

How the system in game was designed? Are there any dependencies here?

Here is the code that you can paste into the sheet in Excel:

$\begin{matrix} \textrm{Level}& \textrm{Staff} & \textrm{Two-Handed Sword} & \textrm{One-Handed Sword}& \textrm{Bow}\\\hline 1 & 29 & ? & 41 & 57\\ 2 & 33 & 74 & 46 & 64\\ 3 & 37 & 83 & 52& 72\\ 4 & 41 & 92 & 57& 80\\ 5 & 46 & 101 & 63& 88\\ 6 & 50 & 111 & 69& 97\\ 7 & 55 & 121 & 76& 106\\ 8 & 60 & 132 & 82& 115\\ 9 & 65 & 143 & 89& 125\\ 10 & 70 & 154 & 96& 135\\ 11 & 75 & 166 & 104& 145\\ 12 & 81 & 178 & 111& 155\\ 13 & 86 & 190 & 119& 166\\ 14 & 92 & 203 & 127& 177\\ 15 & 98 & 216 & 135& 189\\ 16 & 104& 229 & 143& 201\\ 17 & 111& 243 & 152& 213\\ 18 & 117& 257& 161& 225\\ 19 & 124& 272 & 170& 238\\ 20 & 131& 287 & 179& 251\\ 21 & 137& 302 & 189& 264\\ 22 & 145& 318 & 199& 278\\ 23 & 152& 334 & 209& 292\\ 24 & 159& & & \\ 25 & 167& & & \\ 26 & 175& & & \\ 27 & 183& & & \\ 28 & 191& & & \\ 29 & 199& & & \end{matrix}$

What is the value for Two-handed Sword on the 1 (first) level? Because I do not know this value.

And why if I divide e.g Staff/Two-handed Sword (I always get the result 0.4, rounded) or Staff/One-haned Sword (the result 0.7) or One-haned Sword/Two-handed Sword (the result 0.6)?

Whether are the numbers accidental or here is any formula?

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here is values in excel with the result of division

I will expand the question if necessary or missing the information you need.

Main questions:

1. What is the value for Two-handed Sword on the 1 (first) level?

2. Formulas for: Staff, Two-handed Sword, One-handed sword (so that higher levels can be calculated e.g 30,31,32 level etc)

3. Other mathematical formulas

Answer 1

Using the same method as I did in the answer to your other question, I ran a regression on these data in Excel. As it happens, each of these were quadratic this time, too. Here's what I found.

1. In particular, the value for Two-Handed Swords at level $n=1$ is $66$.

2. • The formula for Staff based on Level ($n$) is: $0.0814n^2 + 3.6298n + 25.44$.

   • The formula for Two-Handed Swords based on Level ($n$) is: $ 0.1829 n^2 + 7.7971 n + 57.7872$.

   • The formula for One-Handed Swords based on Level ($n$) is: $0.1148n^2 + 4.8796n + 35.901 $.

   As with last time, the output of these functions must be rounded to the nearest integer.

3. The numbers you get by dividing the two are largely accidental; well, they're basically exactly what you'd expect when you divide two quadratics. But there's nothing particularly special about them.

Good luck with the game!

Answer 2

It's clear from the nicely labeled calculations you made that the three columns for staff and one and two handed swords are proportional. So whenever you know any one of the three values at a level you can find the other two by multiplying or dividing by the right constants.

The colored coincidences are just coincidences.