Jun 05 2019

MLB 5:00 PM
MLB (Dodgers @ Diamondbacks): Will the Dodgers SCORE a RUN during Innings 5-6?

Yes: Dodgers Score 1+ Runs during INN 5-6
No: Dodgers Score 0 Runs during INN 5-6

Inputs To Solve

Runs per Game by Team (Dodgers)

##### User Estimates #####
Dodgers_RperGame = 5.45

print("Use %s as total expected Runs for the Dodgers for the game." 
      % (round(Dodgers_RperGame,2)))

Use 5.45 as total expected Runs for the Dodgers for the game.    

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

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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 runs being scored by the Dodgers any 2 innings:

lambda_ = Dodgers_RperGame * 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(Dodgers_RperGame,2),period_of_innings,9))
print("lambda ~ %s" % (round(lambda_,2)))

lambda = the total expected Runs scored by the Dodgers over 2 innings
lambda = 5.45 * 2 / 9
lambda ~ 1.21    

import math

p = math.exp(-lambda_)*(lambda_**Runs)/(math.factorial(Runs))

print("The probability of k events occuring in an Poisson interval = e^(-lambda)*(lambda^k)/k!")
print('where k = 0 and lambda = %s' % round(lambda_,2))
print("p = e^(-%s)*(%s^%s)/%s!" % (round(lambda_,2),round(lambda_,2),Runs,Runs))
print("p = %s" % round(p,3))

The probability of k events occuring in an Poisson interval =
e^ (-lambda)(lambda^k) / k!
where k = 0 and lambda = 1.21

p = e^ (-1.21)(1.21^0) / 0!
p = 0.298    

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Solution

print("The probabilty of zero Runs being scored by the Dodgers in a %s inning interval is ~%s" % (period_of_innings,round(p,3)))

    The probabilty of zero Runs being scored by the Dodgers in a 2 inning interval is ~0.298

Posted on 6/5/2019