MLB (Yankees @ Athletics): Which TEAM will record MORE EXTRA-BASE HITS during Innings 4-6?

11:10PM
Yankees: More XBH during Innings 4-6
Athletics: More XBH during Innings 4-6 or Tie

Inputs To Solve

##### User Estimates #####

NYY_XBHperGame = (225+13+227)/123
HOU_XBHperGame = (245+20+212)/125
                #(2B+3B+HR) / GAMES 

expected_total_XBH = NYY_XBHperGame + HOU_XBHperGame

print("Use %s + %s = %s as total expected XBH to be hit for the game." 
      % (round(NYY_XBHperGame,3),round(HOU_XBHperGame,3),round(expected_total_XBH,3)))

Use 3.78 + 3.816 = 7.596 as total expected XBH to be hit for the game.

## Inputs Defined in the Problem
period_of_innings = 3
difference = 0

Method to Solve

[1] Estimate mu_NYY (expected arrival rate of XBH per 3 Innings for the Yankees)
[2] Estimate mu_HOU (expected arrival rate of XBH per 3 Innings for the Astros)
[3] Use mu_NYY and mu_HOU as parameters in the Skellam Distribution (the difference between 2 independent Poisson processes) to compute the probability of the Yankees recording more EXTRA BASE HITS during Innings 4-6 (p_NYY).

## [1]

mu_NYY = NYY_XBHperGame * period_of_innings / 9

print("mu_NYY = the total expected XBH recorded by the Yankees in 3 Innings is ~%s" % round(mu_NYY,3))

mu_NYY = the total expected XBH recorded by the Yankees in 3 Innings is ~1.26

## [2]

mu_HOU = HOU_XBHperGame * period_of_innings / 9

print("mu_HOU = the total expected XBH recorded by the Astros in 3 Innings is ~%s" % round(mu_HOU,3))

mu_HOU = the total expected XBH recorded by the Astros in 3 Innings is ~1.272

## [3]

from scipy.stats import skellam

p_NYY = skellam.cdf(difference,mu_NYY,mu_HOU)

print("Recall the cdf (cumulative distribution function) is P[X<=x] where X is the 'difference' in this example")

Recall the cdf (cumulative distribution function) is P[X<=x] where X is the 'difference' in this example

Solution

print("The probability the Yankees will record MORE EXTRA BASE HITS during Innings 4-6 is ~%s" % round(p_NYY,3))

The probability the Yankees will record MORE EXTRA BASE HITS during Innings 4-6 is ~0.637

Info

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import sys
print(sys.version)

3.6.5 |Anaconda, Inc.| (default, Mar 29 2018, 13:32:41) [MSC v.1900 64 bit (AMD64)]

Posted on 8/20/2019