College World Series (#3 Michigan v. #1 Vanderbilt): How many RUNS will be SCORED during Innings 3-4?

7:45 PM
0 or 1
2 or More

Inputs To Solve

RUNS per Game by Team (Michigan and Vanderbilt)

##### User Estimates #####
Vand_RUNSperG = 570/70
Mich_RUNSperG = 485/71

RUNS_perGame = Vand_RUNSperG + Mich_RUNSperG

print("Vanderbilt's RUNS per Game is %s" % round(Vand_RUNSperG,3))
print("Michigans's RUNS per Game is %s" % round(Mich_RUNSperG,3))
print('')
print("Use %s as total expected RUNS for the game." % round(RUNS_perGame,3))

Vanderbilt’s RUNS per Game is 8.143
Michigans’s RUNS per Game is 6.831

Use 14.974 as total expected RUNS for the game.     

## Inputs Defined in the Problem
period_of_innings = 2
RUNS = 1

---

Method to Solve

• Estimate lambda (arrival rate - RUNS scored per 2 innings)
• Use the Poisson Distribution to compute the probability of 2 or RUNS being scored by both teams in Innings 3-4

lambda_ = RUNS_perGame * period_of_innings / 9
print("lambda = the total expected RUNS scored by both teams in Innings 3-4")
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 3-4
lambda = 14.97 * 2 / 9
lambda ~ 3.33     

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

p = 0
for i in range(RUNS+1):
    p += math.exp(-lambda_)*(lambda_**(i))/(math.factorial(i))
    
    if(i<RUNS):
        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 occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = [0,1]

e^(-3.33) * (3.33^0)/0! +
e^(-3.33) * (3.33^1)/1!

0.036 + 0.119     

---

Solution

print("The probability that 1 RUNS or Fewer will be scored in Innings 3-4 is ~%s" % round(p,3))

The probability that 1 RUNS or Fewer will be scored in Innings 3-4 is ~0.155

Posted on 6/26/2019