NCAA Baseball Super Regional (#1 Ole Miss @ #1 Arkansas):

How many RUNS will be SCORED during Innings 5-6?

5:30 PM
0 or 1
2 or More

Inputs To Solve

Runs per Game by Team (Ole Miss and Arkansas)

##### User Estimates #####
Ole_RperG = 482/59
Ark_RperG = 437/58

expected_total_Rs = Ole_RperG + Ark_RperG

print("Use %s + %s = %s as total expected Runs to be scored for the game." 
      % (round(Ole_RperG,2),round(Ark_RperG,2),round(expected_total_Rs,2)))

Use 8.17 + 7.53 = 15.7 as total expected Runs to be scored for the game.     

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

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Method to Solve

Estimate lambda (rate of runs scored per 2 innings) and use the Poisson Distribution to compute the probabilty of zero and one run being scored by both teams any 2 innings:

lambda_ = expected_total_Rs * period_of_innings / 9
print("lambda = the total expected Runs scored by the Dodgers over %s innings" % period_of_innings)
print("lambda = %s * %s / %s" % (round(expected_total_Rs,2),period_of_innings,9))
print("lambda ~ %s" % (round(lambda_,2)))

lambda = the total expected Runs scored by the Dodgers over 2 innings
lambda = 15.7 * 2 / 9
lambda ~ 3.49     

from scipy.stats import poisson

p_Runs_0or1 = poisson.cdf(Runs,lambda_)

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Solution

print("The probabilty of zero or 1 run being scored in any 2 innings %s" % round(p_Runs_0or1,2))

The probabilty of zero or 1 run being scored in any 2 innings 0.14

Posted on 6/10/2019