Research:Dark Sight
From Discworld MUD Wiki
Duration
Observations
| duration | modifier | area | self | target | |----------+-------------------------+------+------+--------| | 532 | near a proper party | 362 | 283 | 362 | | 532 | near a proper party | 362 | 283 | 362 | | 532 | near a proper party | 362 | 283 | 362 | | 532 | near a proper party | 362 | 283 | 362 | | 532 | near a proper party | 362 | 283 | 362 | | 535 | area considered holy | 362 | 283 | 362 | | 535 | area considered holy | 362 | 283 | 362 | | 528 | far from a proper party | 362 | 283 | 362 | | 528 | far from a proper party | 362 | 283 | 362 | | 528 | (none) | 362 | 283 | 362 | | 528 | (none) | 362 | 283 | 362 | | 528 | (none) | 362 | 283 | 362 | | 528 | (none) | 362 | 283 | 362 | | 517 | (none) | 353 | 277 | 353 | | 517 | (none) | 353 | 277 | 353 | | 517 | (none) | 353 | 277 | 353 | | 535 | (none) | 369 | 289 | 369 | | 535 | (none) | 369 | 289 | 369 | | 540 | (none) | 366 | 292 | 366 | | 535 | (none) | 362 | 289 | 362 | | 528 | (none) | 353 | 283 | 353 | | 540 | (none) | 353 | 292 | 353 | | 550 | (none) | 362 | 299 | 362 | | 570 | (none) | 362 | 312 | 362 | | 562 | (none) | 353 | 305 | 353 | | 570 | (none) | 362 | 312 | 362 | | 225 | (none) | 79 | 118 | 254 | | 225 | (none) | 79 | 118 | 254 | | 232 | (none) | 79 | 121 | 254 | | 232 | (none) | 79 | 121 | 254 | | 232 | (none) | 79 | 123 | 254 | | 247 | (none) | 79 | 127 | 254 | | 250 | (none) | 79 | 129 | 254 | | 249 | (none) | 79 | 129 | 254 | | 258 | (none) | 79 | 132 | 254 | | 262 | (none) | 79 | 134 | 254 | | 265 | (none) | 79 | 137 | 254 | | 577 | (none) | 362 | 318 | 362 | | 588 | (none) | 362 | 324 | 362 | | 595 | (none) | 362 | 330 | 362 | | 603 | (none) | 362 | 337 | 362 | | 273 | (none) | 79 | 139 | 254 | | 277 | (none) | 79 | 142 | 254 | | 292 | (none) | 79 | 148 | 254 | | 295 | (none) | 79 | 150 | 254 | | 300 | (none) | 79 | 153 | 254 | | 303 | (none) | 79 | 155 | 254 | | 310 | (none) | 79 | 158 | 254 | | 315 | (none) | 79 | 159 | 254 | | 315 | (none) | 79 | 160 | 254 | | 318 | (none) | 79 | 161 | 254 | | 319 | (none) | 79 | 163 | 254 | | 322 | (none) | 79 | 164 | 254 | | 325 | (none) | 79 | 165 | 254 | | 325 | (none) | 79 | 166 | 254 | | 330 | (none) | 79 | 167 | 254 | | 330 | (none) | 79 | 168 | 254 | | 333 | (none) | 79 | 169 | 254 | | 615 | (none) | 362 | 343 | 362 | | 615 | (none) | 362 | 343 | 362 | | 480 | (none) | | 251 | | | 622 | (none) | 362 | 349 | 362 | | 630 | (none) | 362 | 355 | 362 | | 637 | (none) | 362 | 362 | 362 |
Analysis
Went with scipy's curve_fit: numpy's polyfit works too, but I guess it's more likely that a square root would be used in the code, rather than a polynomial:
from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt
bonus = [283, 283, 283, 283, 277, 277, 277, 289, 289, 292, 289, 283, 292, 299, 312, 305, 312, 118, 118, 121, 121, 123, 127, 129, 129, 132, 134, 137, 318, 324, 330, 337, 139, 142, 148, 150, 153, 155, 158, 159, 160, 161, 163, 164, 165, 166, 167, 168, 169, 343, 343, 251, 349, 355, 362]
duration = [528, 528, 528, 528, 517, 517, 517, 535, 535, 540, 535, 528, 540, 550, 570, 562, 570, 225, 225, 232, 232, 232, 247, 250, 249, 258, 262, 265, 577, 588, 595, 603, 273, 277, 292, 295, 300, 303, 310, 315, 315, 318, 319, 322, 325, 325, 330, 330, 333, 615, 615, 480, 622, 630, 637]
def func(x, a, b):
return a * np.sqrt(x) + b
popt, pcov = curve_fit(func, bonus, duration)
predict = lambda x: func(x, *popt)
p_bonus = np.arange(100, 500)
p_duration = predict(p_bonus)
plt.scatter(bonus, duration)
plt.plot(p_bonus, p_duration, c = 'r')
plt.show()
Then an approximation is: duration = 50.79484076 * sqrt(bonus) - 327.43039153. Could be off by a couple of seconds (possibly some rounding is causing that).
