def true_skill_v(mean_delta, draw_margin, c):
team_performance_difference = mean_delta / c
draw_margin = draw_margin / c
denominator = gaussian.cdf(team_performance_difference - draw_margin)
if denominator < 1e-161:
return -team_performance_difference + draw_margin
return gaussian.at(team_performance_difference - draw_margin) / denominator
def true_skill_v(mean_delta, draw_margin, c):
team_performance_difference = mean_delta / c
draw_margin = draw_margin / c
denominator = gaussian.cdf(team_performance_difference - draw_margin)
if denominator < 1e-161:
return -team_performance_difference + draw_margin
return gaussian.at(team_performance_difference - draw_margin) / denominator
def true_skill_w(mean_delta, draw_margin, c):
team_performance_difference = mean_delta / c
draw_margin = draw_margin / c
denominator = gaussian.cdf(team_performance_difference - draw_margin)
if denominator < 1e-161:
if team_performance_difference < 0.0:
return 1
return 0
v_win = true_skill_v(mean_delta*c, draw_margin*c, c)
return v_win * (v_win + team_performance_difference - draw_margin)
def true_skill_w(mean_delta, draw_margin, c):
team_performance_difference = mean_delta / c
draw_margin = draw_margin / c
denominator = gaussian.cdf(team_performance_difference - draw_margin)
if denominator < 1e-161:
if team_performance_difference < 0.0:
return 1
return 0
v_win = true_skill_v(mean_delta * c, draw_margin * c, c)
return v_win * (v_win + team_performance_difference - draw_margin)
import stdio
import gaussian
#-----------------------------------------------------------------------
# Accept a mean and standard deviation as command-line arguments.
# Write to standard output a table of the percentage of students
# scoring below certain scores on the SAT, assuming the test scores
# obey a Gaussian distribution with the given mean and standard
# deviation.
mu = float(sys.argv[1])
sigma = float(sys.argv[2])
for score in range(400, 1600+1, 100):
percent = gaussian.cdf(score, mu, sigma)
stdio.writef('%4d %.4f\n', score, percent)
#-----------------------------------------------------------------------
# python gaussiantable.py 1019 209
# 400 0.0015
# 500 0.0065
# 600 0.0225
# 700 0.0635
# 800 0.1474
# 900 0.2845
# 1000 0.4638
# 1100 0.6508
# 1200 0.8068
# 1300 0.9106