Growth model

The growth model is the set of rules that specify how a character evolves according to the experience gained.

In order to make more challenging the game I defined three tier of experience gained per levels: 1-20 (A), 21-40 (B), 41-50 (C).
I think at the moment 50 could be a good level cap.

The three tier have to be modelled by three different functions.
This is the way I thought:
growth_graph.gif
This graph is made using gnuplot.

These are the function I used to obtain such result: A, B, C
As you can see there's a great error in tier B. I was very tired when I wrote it so if someone could fix this error I'll be very thankful!
These are the table used to plot the entire growth model:

A (t1.txt)

1    80
2    452
3    1247
4    2560
5    4472
6    7054
7    10371
8    14481
9    19440
10    25298
11    32104
12    39906
13    48747
14    58669
15    69713
16    81920
17    95326
18    109969
19    125885
20    143108

B (t2.txt)

21    2229
22    2527
23    2849
24    3196
25    3569
26    3968
27    4393
28    4847
29    5328
30    5839
31    6380
32    6951
33    7553
34    8187
35    8853
36    9553
37    10287
38    11055
39    11858
40    12697

C (t3.txt)

41    190186
42    204237
43    218968
44    234396
45    250537
46    267407
47    285022
48    303398
49    322552
50    342500

This is the python script I used to generate the tier:

with open('t1.txt', 'w') as t1:
    for i in range(1, 21):
        t1.write("{0}\t{1}\n".format(i, int((0.8*i**2.5)*100)))
with open('t2.txt', 'w') as t2:
    for j in range(21, 41):
        t2.write("{0}\t{1}\n".format(j, int(((0.026*j**2.7))*100)))
with open('t3.txt', 'w') as t3:
    for k in range(41, 51):
        t3.write("{0}\t{1}\n".format(k, int(((0.027*k**3)+k)*100)))

I multiplied each formula per 100 to have greater values.
All the file I used are in the dropbox. Growth model folder.

To fix B tier you could rewrite t2.txt using some correct values and then obtain a formula using some mathematical method. This link could be usefull.

If you look for other growth model you can see that other model is VERY simple!

TIPS:
You can invert the order of the A and B formulas to have a curve with a slight slope in A and a steeper curve in B! Try it!

Salvo diversa indicazione, il contenuto di questa pagina è sotto licenza Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License