Analysis of the relation between eaten candies and HP gain in "Candy box!" (http://candies.aniwey.net/).

candies_hps.py

#!/usr/bin/env python

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import linregress

# Set nice options for plots and use of LaTeX.
from matplotlib import rc
rc('text', usetex=True)
rc('font', family='serif')
rc('font', serif='Tex Gyre Pagella')

# load data
candies, hp_gains = np.loadtxt('candies_hps.txt', unpack=True)

# fit (linear regression on loglog)
log_candies = np.log(candies)
log_hp_gains = np.log(hp_gains)
slope, intercept, _, _, stderr = linregress(log_candies, log_hp_gains)

# define model
a = np.exp(intercept)
b = slope
model = lambda x: a * x ** b

# plot everything
plt.plot(candies, hp_gains, 'ko', label='measurement')
xs = np.linspace(0, np.max(candies), 10000)
plt.plot(
    xs,
    model(xs),
    'r-',
    label='$\\Delta(n) = {:.3f}\\cdot n^{{{:.3f}}}$'.format(a, b)
)
plt.legend(loc='upper left')
plt.xlabel('number of candies eaten $n$', ha='right', x=1)
plt.ylabel('absolute HP gain $\\Delta$', va='top', y=1)
plt.savefig('candies_hps.pdf')

candies_hps.txt

# candies hpGain
100     13
2035    44
2514    48
2727    49
3140    52
3504    54
4068    58
4653    61
5001    63
5737    66
7538    74
8625    78
10871   86
12303   90
15814   100
18996   108
22055   114
24904   120
26144   122
28353   126