College World Series (Florida State v. Michigan): How many HITS will be recorded in the 1st Inning?

Inputs To Solve

Hits per Game by Team (Florida State and Michigan)

##### User Estimates #####
FlST_HperGame = (500)/57
Mich_HperGame = (566)/59

expected_total_Hs = FlST_HperGame + Mich_HperGame

print("Use %s + %s = %s as total expected HITS to be recorded for the game." 
      % (round(FlST_HperGame,2),round(Mich_HperGame,2),round(expected_total_Hs,2)))

Use 8.77 + 9.59 = 18.37 as total expected HITS to be recorded for the game.

## Inputs Defined in the Problem
period_of_innings = 1
Hits = 1

Method to Solve

Estimate lambda (rate of HITS per 1 innings) and use the Poisson Distribution to compute the probabilty of 0 or 1 HIT being recorded by both teams in teh 1st Inning:

lambda_ = expected_total_Hs * period_of_innings / 9
print("lambda = the total expected HITS recorded over %s inning" % period_of_innings)
print("lambda = %s * %s / %s" % (round(expected_total_Hs,2),period_of_innings,9))
print("lambda ~ %s" % (round(lambda_,2)))

lambda = the total expected HITS recorded over 1 inning
lambda = 18.37 * 1 / 9
lambda ~ 2.04

import math
str_ = ""
print("The probability of k events occuring in a Poisson interval = e^(-lambda) * (lambda^k)/k!")
print("where k = [0,1]")
print(' ')

p = 0
for i in range(Hits+1):
    p += math.exp(-lambda_)*(lambda_**(i))/(math.factorial(i))
    
    if(i<1):
        str_ += str(round(math.exp(-lambda_)*(lambda_**(i))/(math.factorial(i)),3)) + " + "
        print("e^(-%s)*(%s^%s)/%s! + " % (round(lambda_,2),round(lambda_,2),(i),(i)))
    else:
        str_ += str(round(math.exp(-lambda_)*(lambda_**(i))/(math.factorial(i)),3))
        print("e^(-%s)*(%s^%s)/%s!" % (round(lambda_,2),round(lambda_,2),(i),(i)))

print(' ')
print(str_)

The probability of k events occuring in a Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = [0,1]

e^(-2.04) * (2.04^0)/0! +
e^(-2.04) * (2.04^1)/1!

0.13 + 0.265

Solution

print("The probabilty that 0 or 1 HITS are reorded by both teams in the 1st Inning is ~%s" % round(p,3))

The probabilty that 0 or 1 HITS are reorded by both teams in the 1st Inning is ~0.395

Posted on 6/17/2019