NCB (#8 Villanova @ St. John’s): How many POINTS will Villanova SCORE BEFORE St. John’s SCORES?

6:35 PM
3 Points or Fewer
4 Points or More

Inputs To Solve

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

# over / under
expected_total_pts = 143

# point spread (Villanova favored)
spread = 3

stj_expected_pts = (expected_total_pts - spread)/2
vil_expected_pts = expected_total_pts - stj_expected_pts

print("The expected points scored by St. John's is %s" % round(stj_expected_pts,3))
print("The expected points scored by Villanova is %s" % round(vil_expected_pts,3))

The expected points scored by St. John’s is 70.0
The expected points scored by Villanova is 73.0

## Inputs Defined in the Problem

first_to_vil = 2 #2 baskets ~~ 4 points
first_to_stj = 1 #1 basket ~~ >= 1 point

Method to Solve

[1] Estimate lambda_stj - expected arrival rate of a basket by St. John’s
[2] Estimate lambda_vil - expected arrival rate of a basket by Villanova
[3] Use the Poisson Distribution assumptions and the ‘first to’ equation to compute the probability of Villanova scoring 4 points before St. John’s scores 1 point. (p_vil).

## [1]

lambda_stj = stj_expected_pts/2

## [2]

lambda_vil = vil_expected_pts/2

## [3]

import math

m = first_to_stj
n = first_to_vil

p_vil = 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_vil/(lambda_stj+lambda_vil))**k
    ans2 = (lambda_stj/(lambda_stj+lambda_vil))**(n+m-1-k)
    p_vil += (ans*ans1*ans2)

Solution

print("The probability of Villanova scoring 4 points before St. John's scores 1 point is ~%s" % round(p_vil,3))

The probability of Villanova scoring 4 points before St. John’s scores 1 point is ~0.261

Info

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Posted on 1/28/2020