Jun 4 2019

MLB 7:07 PM
MLB (Yankees @ Blue Jays): How many EXTRA-BASE HITS will OCCUR in the FIRST 2 INNINGS?

0 or 1
2 or More ***

Inputs To Solve

XBHs per Game by Team (Yankees and Blue Jays)

##### User Estimates #####
Yankees_XBHperGame = (80+5+93)/58
BlueJays_XBHperGame = (90+5+69)/59

expected_total_XBHs = Yankees_XBHperGame + BlueJays_XBHperGame

print("Use %s + %s = %s as total expected XBHs to be hit for the game." 
      % (round(Yankees_XBHperGame,2),round(BlueJays_XBHperGame,2),round(expected_total_XBHs,2)))

## Inputs Defined in the Problem
period_of_innings = 2
XBHs = 2

    Use 3.07 + 2.78 = 5.85 as total expected XBHs to be hit for the game.    

---

Method to Solve

Estimate lambda and use the Poisson Distribution to compute the probabilty of zero or one XBH being hit in any 2 innings:

lambda_ = expected_total_XBHs * period_of_innings / 9
print("lambda = the total expected XBHs hit by both teams over %s innings" % period_of_innings)
print("lambda = %s * %s / %s" % (round(expected_total_XBHs,2),period_of_innings,9))
print("lambda ~ %s" % (round(lambda_,2)))

    lambda = the total expected XBHs hit by both teams over 2 innings     lambda = 5.85 * 2 / 9     lambda ~ 1.3    

import math
str_ = ""
print("The probability of k events occuring in a Poisson interval = e^(-lambda)*(lambda^k)/k!")
print(' ')

p = 0
for i in range(XBHs):
    p += math.exp(-lambda_)*(lambda_**(i))/(math.factorial(i))
    
    if(i<1):
        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_)
print(round(p,2))

    The probability of k events occuring in a Poisson interval = e^(-lambda)*(lambda^k)/k!          e^{(-1.3)(1.3^0)/0! +     e^(-1.3)(1.3}1)/1!          0.273 + 0.354     0.63    

---

Solution

print("The probabilty of zero or 1 XBHs being hit in a %s inning interval is ~ %s" % (period_of_innings,round(p,2)))
print("The probabilty of two or more XBHs being hitting in a %s inning interval is 1 - the probabilty of zero or 1 XBHs being hit, or ~ %s" % (period_of_innings,round(1-p,2)))

    The probabilty of zero or 1 XBHs being hit in a 2 inning interval is ~ 0.63     The probabilty of two or more XBHs being hitting in a 2 inning interval is 1 - the probabilty of zero or 1 XBHs being hit, or ~ 0.37    

Posted on 6/5/2019