College World Series (#1 Vanderbilt v. #3 Michigan): How many RUNS will be SCORED during Innings 1-3?

7:08 PM
3 Runs or Fewer
4 Runs or More

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Inputs To Solve

RUNS per Game by Team (Vanderbilt and Michigan)

##### User Estimates #####
Vand_RUNSperG = 566/69
Mich_RUNSperG = 484/70

RUNS_perGame = Vand_RUNSperG + Mich_RUNSperG

print("Vanderbilt's RUNS per Game is %s" % round(Vand_RUNSperG,3))
print("Michigan's RUNS per Game is %s" % round(Mich_RUNSperG,3))

print("Use %s as total expected RUNS for the game." % round(RUNS_perGame,3))

Vanderbilt’s RUNS per Game is 8.203
Michigan’s RUNS per Game is 6.914

Use 15.117 as total expected RUNS for the game.     

## Inputs Defined in the Problem
period_of_innings = 3
RUNS = 3

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Method to Solve

• Estimate lambda (arrival rate - RUNS scored per 3 innings)
• Use the Poisson Distribution to compute the probability of 3 or RUNS being scored by both teams in Innings 1-3

lambda_ = RUNS_perGame * period_of_innings / 9
print("lambda = the total expected RUNS scored by both teams in Innings 1-3")
print("lambda = %s * %s / %s" % (round(RUNS_perGame,2),period_of_innings,9))
print("lambda ~ %s" % (round(lambda_,2)))

lambda = the total expected RUNS scored by both teams in Innings 1-3
lambda = 15.12 * 3 / 9
lambda ~ 5.04     

import math
str_ = ""
print("The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!")
print("where k = [0,1,2,3]")
print(' ')

p = 0
for i in range(RUNS+1):
    p += math.exp(-lambda_)*(lambda_**(i))/(math.factorial(i))
    
    if(i<3):
        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 = [0,1,2,3]

e^(-5.04) * (5.04^0)/0! +
e^(-5.04) * (5.04^1)/1! +
e^(-5.04) * (5.04^2)/2! +
e^(-5.04) * (5.04^3)/3!

0.006 + 0.033 + 0.082 + 0.138     

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Solution

print("The probability that 3 RUNS or Fewer will be scored in Innings 1-3 is ~%s" % round(p,3))

The probability that 3 RUNS or Fewer will be scored in Innings 1-3 is ~0.26

Posted on 6/25/2019