NCW (Rhode Island @ Fordham): Will EITHER TEAM SCORE 35 POINTS or MORE in the 1st Half?

Inputs To Solve

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

# over / under
expected_total_pts = 119.5

# point spread (Fordham favored)
spread = 10.5

ri_expected_pts = (expected_total_pts - spread)/2
fu_expected_pts = expected_total_pts - ri_expected_pts

print("The expected points scored by RI is %s" % round(ri_expected_pts,3))
print("The expected points scored by FU is %s" % round(fu_expected_pts,3))

The expected points scored by RI is 54.5
The expected points scored by FU is 65.0

## Inputs Defined in the Problem

half_pts = 35

Method to Solve

[1] Estimate lambda_ri - expected arrival rate of a point by RI in one half
[2] Estimate lambda_fu - expected arrival rate of a point by FU in one half
[3] Use the Poisson Distribution assumptions to find the probability that RI (p_RI35) and FU (p_FU35) score less than 35 points.
[4]The probability that neither team scores 35 POINTS OR MORE (p_no35) is (p_RI35) * (p_FU35)

## [1]

lambda_ri = ri_expected_pts/2

## [2]

lambda_fu = fu_expected_pts/2

## [3]
from scipy.stats import poisson

p_RI35 = poisson.cdf(half_pts-1,lambda_ri)
p_FU35 = poisson.cdf(half_pts-1,lambda_fu)

## [4]

p_no35 = p_RI35 * p_FU35

Solution

print("The probability NEITHER team SCORES 35 POINTS OR MORE in the 1st HALF is ~%s" % round(p_no35,3))

The probability NEITHER team SCORES 35 POINTS OR MORE in the 1st HALF is ~0.591

Info

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import sys
print(sys.version)

3.6.5 |Anaconda, Inc.| (default, Mar 29 2018, 13:32:41) [MSC v.1900 64 bit (AMD64)]

Posted on 2/5/2020