NCB (#13 Penn State @ Purdue): Which will OCCUR FIRST?

6:32 PM
Penn State:: Scores 5+ Points
Purdue: Makes a 3-Pointer

Inputs To Solve

#### User / Market Estimates ####

# over / under
expected_total_pts = 135.5

# point spread (Purdue favored)
spread = 5
pn_expected_pts = (expected_total_pts - spread)/2

print("The expected points scored by Penn State is %s" % round(pur_expected_pts,3))

# 3 Pointers Made
Purdue_3PM = 187/24
print("Purdue's 3PM per game is %s" % round(Purdue_3PM,3))

The expected points scored by Penn State is 65.25
Purdue’s 3PM per game is 7.792

## Inputs Defined in the Problem

Purdue_3PT = 1
Penn_ST_pt = 5

Method to Solve

[1] Estimate lambda_pn - expected arrival rate of a point by Penn State
[2] Estimate lambda_pur - expected arrival rate of a 3PM by Purdue
[3] Use the Poisson Distribution assumptions and the ‘first to’ equation to compute the probability Penn State scores 5+ points before Purdue makes 1 3-Pointer. (p_pn5).

## [1]

lambda_pn = pn_expected_pts

## [2]

lambda_pur = Purdue_3PM

## [3]

import math

n = Penn_ST_pt
m = Purdue_3PT

p_pn5 = 0
for k in range(n,n+m):
    ans = math.factorial(n+m-1)/(math.factorial((n+m-1)-k)*math.factorial(k))
    ans1 = (lambda_pn/(lambda_pn+lambda_pur))**k
    ans2 = (lambda_pur/(lambda_pn+lambda_pur))**(n+m-1-k)
    p_pn5 += (ans*ans1*ans2)

Solution

print("The probability of Penn State scoring 5+ points before Purdue makes 1 3-Pointer is ~%s" % round(p_pn5,3))

The probability of Penn State scoring 5+ points before Purdue makes 1 3-Pointer is ~0.569

Info

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Posted on 2/11/2020