College World Series (#1 Vanderbilt v. #3 Michigan): Will BOTH TEAMS record an EXTRA-BASE HIT during Innings 5-6?

8:25 PM
Yes: Both teams record XBH during Innings 5-6
No: At least 1 team doesn’t record XBH during Innings 5-6

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Inputs To Solve

XBHs per Game by Team (Vanderbilt and Michigan)

##### User Estimates #####
Vand_XBHperG = (163+19+68)/69
Mich_XBHperG = (148+15+72)/70

print("Vanderbilt's XBH per Game is %s" % round(Vand_XBHperG,3))
print("Michigan's RUNS per Game is %s" % round(Mich_XBHperG,3))

Vanderbilt’s XBH per Game is 3.623
Michigan’s RUNS per Game is 3.357     

## Inputs Defined in the Problem
period_of_innings = 2
XBH = 0

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Method to Solve

• Estimate lambda (arrival rate - XBH per 2 innings) for each team
• Use the Poisson Distribution to compute the probability of zero XBH being hit in any 2 innings for each team
• The probability of both teams recording an XBH hit during Innings 5-6 is:     - 1 - the probabilty that Vanderbilt records zero XBHs muliplied by     - 1 - the probabilty that Michigan records zero XBHs

lambda_vand = Vand_XBHperG * period_of_innings / 9
print("lambda_vand = the total expected XBHs recorded by Vanderbilt over %s innings" % period_of_innings)
print("lambda_vand = %s * %s / %s" % (round(Vand_XBHperG,2),period_of_innings,9))
print("lambda_vand ~ %s" % (round(lambda_vand,2)))

lambda_vand = the total expected XBHs recorded by Vanderbilt over 2 innings
lambda_vand = 3.62 * 2 / 9
lambda_vand ~ 0.81     

lambda_mich = Mich_XBHperG * period_of_innings / 9
print("lambda_mich = the total expected XBHs recorded by Vanderbilt over %s innings" % period_of_innings)
print("lambda_mich = %s * %s / %s" % (round(Mich_XBHperG,2),period_of_innings,9))
print("lambda_mich ~ %s" % (round(lambda_mich,2)))

lambda_mich = the total expected XBHs recorded by Vanderbilt over 2 innings
lambda_mich = 3.36 * 2 / 9
lambda_mich ~ 0.75     

import math

p_v = math.exp(-lambda_vand)*(lambda_vand**XBH)/(math.factorial(XBH))

print("The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)")
print('where k = 0 and lambda = %s' % round(lambda_vand,2))
print('')
print("p = e^(-%s)*(%s^%s)/%s!" % (round(lambda_vand,2),round(lambda_vand,2),XBH,XBH))
print("The probability that Vanderbilt records zero XBH during Inngs 5-6 is %s" % round(p_v,3))

The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 0.81

p = e^(-0.81)*(0.81^0)/0!
The probability that Vanderbilt records zero XBH during Inngs 5-6 is 0.447     

p_m = math.exp(-lambda_mich)*(lambda_mich**XBH)/(math.factorial(XBH))

print("The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)")
print('where k = 0 and lambda = %s' % round(lambda_mich,2))
print('')
print("p = e^(-%s)*(%s^%s)/%s!" % (round(lambda_mich,2),round(lambda_mich,2),XBH,XBH))
print("The probability that Michigan records zero XBH during Inngs 5-6 is %s" % round(p_m,3))

The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 0.75

p = e^(-0.75)*(0.75^0)/0!
The probability that Michigan records zero XBH during Inngs 5-6 is 0.474     

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Solution

print("The probability of both teams recording an XBH during Innings 5-6 is (1 - %s) * (1 - %s)" % (round(p_v,3),round(p_m,3)))
print("The probability of both teams recording an XBH during Innings 5-6 is %s" % round((1-p_v)*(1-p_m),3))

The probability of both teams recording an XBH during Innings 5-6 is (1 - 0.447) * (1 - 0.474)
The probability of both teams recording an XBH during Innings 5-6 is 0.291

Posted on 6/25/2019