In [3]:
ECPlot()
from math import comb as mC
from math import factorial as mF
import matplotlib.pyplot as plt
from matplotlib.ticker import PercentFormatter as PF
import numpy as np
import pandas as pd
import seaborn as sns
#Colors.
C = ['#440154FF',
'#3B528BFF',
'#21908DFF',
'#5EC962FF',
'#FDE725FF']
def swingProb(N):
"""
Probability.
Parameters:
N : Number of game wins to win series.
Returns:
outcomes : (w, l)
W - probability of wins starting with 'W'.
L - probability of losses starting with 'W'
"""
W = 0
L = 0
#Wins starting with W.
#Insert 0 to N-1 Ls into N Ws.
for l in range(N) :
p = mF(N-2 + l) / (mF(N-2) * mF(l) * (2 ** (N+l-1)))
W += p
#Losses starting with W.
for w in range(N-1) :
p = mF(N-1 + w) / (mF(w) * mF(N-1) * (2 ** (w+N+1-1)))
L += p
S = mC(2*(N-1), (N-1)) / 2**(2*N-2)
return(W, L, S)
def ECPlot() :
sns.set()
#Plot.
fig = plt.figure(figsize = (12, 7))
ax = fig.add_subplot(xlim = (2, 200), ylim = (0, 75))
#Title.
ax.set_title("How Much Does Game 1 Matter?", fontsize = 24)
#x-axis.
ax.set_xlabel("Number of Wins Needed", fontsize = 18)
#y-axis.
ax.set_ylabel("Probability", fontsize = 18)
ax.yaxis.set_major_formatter(PF())
ax.tick_params(axis = 'both', labelsize = 16)
#Data
N = range(2, 200)
W = []
L = []
S = []
for n in N :
D = swingProb(n)
W.append(D[0]*100)
L.append(D[1]*100)
S.append(D[2]*100)
ax.plot(N, W, lw = 3, c = C[0], alpha = 0.4, label = "Series Win if Game 1 is a Win")
ax.plot(N, L, lw = 3, c = C[3], alpha = 0.4, label = "Series Win if Game 1 is a Loss")
ax.plot(N, S, lw = 5, c = C[1], label = "Swing Probability")
ax.legend(fontsize = '18', loc = 'upper right', bbox_to_anchor = (1, 0.5))
fig.savefig('2025.10.31EC.png', bbox_inches = "tight");
ECPlot()
a = swingProb(3183)
a[0]-a[1]
0.0100013336403737
a = swingProb(3184)
a[0]-a[1]
0.009999762585764904