gistfile1.py

import random

BASELINE_CONVERSION_RATE = 0.05
NUM_EMAILS = 4
NUM_PEOPLE_PER_EMAIL = 125

def did_convert():
    return random.random() < BASELINE_CONVERSION_RATE

def avg(vals):
    return sum(vals) / float(len(vals))

max_by_min_conversion_increases = []
max_conversions = []
min_conversions = []

for i in range(10000):
    vals = []
    for j in range(NUM_EMAILS):
        vals.append(avg([did_convert() for _ in range(NUM_PEOPLE_PER_EMAIL)]))

    max_conversions.append(max(vals))
    min_conversions.append(min(vals))

    if min(vals):
        # If the min is 0 we would have an infinite increase, so while removing
        # these slightly skews the data, we have no choice!
        max_by_min_conversion_increases.append(max(vals) / min(vals))

print 'Avg increase from min --> max:', avg(max_by_min_conversion_increases)
print 'Avg max conversion: ', avg(max_conversions)
print 'Avg min conversion: ', avg(min_conversions)