def w_within_margin(team_performance_difference, draw_margin):
team_performance_difference_abs = abs(team_performance_difference)
denominator = (Gaussian.cumulative_to(draw_margin - team_performance_difference_abs) -
Gaussian.cumulative_to(-draw_margin - team_performance_difference_abs))
if denominator < 2.222758749e-162:
return 1.0
vt = v_within_margin(team_performance_difference_abs, draw_margin)
return (vt ** 2 +
(
(draw_margin - team_performance_difference_abs) *
Gaussian.at(draw_margin - team_performance_difference_abs) -
(-draw_margin - team_performance_difference_abs) *
Gaussian.at(-draw_margin - team_performance_difference_abs)) / denominator)
def testAt(self):
expected = 0.352065326764300
answer = Gaussian.at(0.5)
self.assertAlmostEqual(
expected, answer, None,
"testAt expected %.15f, got %.15f" % (expected, answer),
GaussianDistributionTest.ERROR_TOLERANCE)
def v_within_margin(team_performance_difference, draw_margin):
team_performance_difference_abs = abs(team_performance_difference)
denominator = (
Gaussian.cumulative_to(draw_margin - team_performance_difference_abs) -
Gaussian.cumulative_to(-draw_margin - team_performance_difference_abs))
if denominator < 2.222758749e-162:
if team_performance_difference < 0.0:
return -team_performance_difference - draw_margin
return -team_performance_difference + draw_margin
numerator = (Gaussian.at(-draw_margin - team_performance_difference_abs) -
Gaussian.at(draw_margin - team_performance_difference_abs))
if team_performance_difference < 0.0:
return -numerator / denominator
return numerator / denominator
def w_within_margin(team_performance_difference, draw_margin):
team_performance_difference_abs = abs(team_performance_difference)
denominator = (
Gaussian.cumulative_to(draw_margin - team_performance_difference_abs) -
Gaussian.cumulative_to(-draw_margin - team_performance_difference_abs))
if denominator < 2.222758749e-162:
return 1.0
vt = v_within_margin(team_performance_difference_abs, draw_margin)
return (vt**2 +
((draw_margin - team_performance_difference_abs) *
Gaussian.at(draw_margin - team_performance_difference_abs) -
(-draw_margin - team_performance_difference_abs) *
Gaussian.at(-draw_margin - team_performance_difference_abs)) /
denominator)
def v_within_margin(team_performance_difference, draw_margin):
team_performance_difference_abs = abs(team_performance_difference)
denominator = (
Gaussian.cumulative_to(draw_margin - team_performance_difference_abs) -
Gaussian.cumulative_to(-draw_margin - team_performance_difference_abs))
if denominator < 2.222758749e-162:
if team_performance_difference < 0.0:
return -team_performance_difference - draw_margin
return -team_performance_difference + draw_margin
numerator = (Gaussian.at(-draw_margin - team_performance_difference_abs) -
Gaussian.at(draw_margin - team_performance_difference_abs))
if team_performance_difference < 0.0:
return -numerator / denominator
return numerator / denominator
def v_exceeds_margin(team_performance_difference, draw_margin):
denominator = Gaussian.cumulative_to(team_performance_difference - draw_margin)
if (denominator < 2.22275874e-162):
return -team_performance_difference + draw_margin
return Gaussian.at(team_performance_difference - draw_margin) / denominator
def testAt(self):
expected = 0.352065326764300
answer = Gaussian.at(0.5)
self.assertAlmostEqual(expected, answer, None,
"testAt expected %.15f, got %.15f" % (expected, answer),
GaussianDistributionTest.ERROR_TOLERANCE)
def v_exceeds_margin(team_performance_difference, draw_margin):
denominator = Gaussian.cumulative_to(team_performance_difference -
draw_margin)
if (denominator < 2.22275874e-162):
return -team_performance_difference + draw_margin
return Gaussian.at(team_performance_difference - draw_margin) / denominator
