NCB (#7 Duke @ Boston College): Which TEAM will be the FIRST to SCORE 15+ POINTS?

7:02 PM
Duke: First to 15+ Points
Boston College: First to 15+ Points

Inputs To Solve

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

# over / under
expected_total_pts = 145

# point spread (Duke favored)
spread = 14.5

bc_expected_pts = (expected_total_pts - spread)/2
du_expected_pts = expected_total_pts - stj_expected_pts

print("The expected points scored by BC is %s" % round(bc_expected_pts,3))
print("The expected points scored by Duke is %s" % round(du_expected_pts,3))

The expected points scored by BC is 65.25
The expected points scored by Duke is 79.75

## Inputs Defined in the Problem

first_to_bc = 15
first_to_du = 15

Method to Solve

[1] Estimate lambda_bc - expected arrival rate of a point by BC
[2] Estimate lambda_du - expected arrival rate of a point by Duke
[3] Use the Poisson Distribution assumptions and the ‘first to’ equation to compute the probability Duke scores 15+ points before BC scores 15+. (p_duke15).

## [1]

lambda_bc = bc_expected_pts

## [2]

lambda_du = du_expected_pts

## [3]

import math

m = first_to_bc
n = first_to_du

p_duke15 = 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_du/(lambda_bc+lambda_du))**k
    ans2 = (lambda_bc/(lambda_bc+lambda_du))**(n+m-1-k)
    p_duke15 += (ans*ans1*ans2)

Solution

print("The probability of Duke scoring 15+ points before BC scores 15+ points is ~%s" % round(p_duke15,3))

The probability of Duke scoring 15+ points before BC scores 15+ points is ~0.707

Info

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Posted on 2/4/2020