NFL (Packers @ Bears): Will EITHER TEAM SCORE in the LAST 3 MINUTES of the 4th Quarter?
11:00PM
Yes: Points scored in last 3 mins of 4th Quarter
No: 0 points in last 3 mins of 4th Quarter
Inputs To Solve
Scores by Team 2018
Packers
Bears
##### User Estimates #####
GBP_Scores_perG = ((25+14+1) + 30 + 1) / 16
CHI_Scores_perG = ((28+16+6) + 30 + 1) / 16
# ((pass + rush + dst) + fg + safety) / games
total_observed_scores = GBP_Scores_perG + CHI_Scores_perG
print("The total observed SCORES per Game by the Packers is %s." % (round(GBP_Scores_perG,3)))
print("The total observed SCORES per Game by the Bears is %s." % (round(CHI_Scores_perG,3)))
print('')
print("Use %s + %s = %s as total observed SCORES per game for the Packers and Raiders." % (round(GBP_Scores_perG,3),round(CHI_Scores_perG,3),round(total_observed_scores,3)))The total observed SCORES per Game by the Packers is 4.438.
The total observed SCORES per Game by the Bears is 5.062.
Use 4.438 + 5.062 = 9.5 as total observed SCORES per game for the Packers and Raiders.## Inputs Defined in the Problem
period_of_game = 3/60
points = 0Method to Solve
- [1] Estimate lambda_pts - expected arrival rate of a SCORE per 3 minute period during a Packers and Bears game.
- [2] Use the Poisson Distribution to compute the probability of the 0 points being scored during a 3 minute period during a Packers and Bears game (p0)
## [1]
lambda_pts = total_observed_scores * period_of_game
print("lambda_pts ~ the total expected SCORES over a 3 minute period during a Packers and Bears game")
print("lambda_pts ~ %s * %s" % (round(total_observed_scores,3),period_of_game))
print("lambda_pts ~ %s" % (round(lambda_pts,3)))lambda_pts ~ the total expected SCORES over a 3 minute period during a Packers and Bears game
lambda_pts ~ 9.5 * 0.05
lambda_pts ~ 0.475## [2]
import math
p0 = math.exp(-lambda_pts)*(lambda_pts**points)/(math.factorial(points))
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_pts,2))
print('')
print("p0 = e^(-%s)*(%s^%s)/%s!" % (round(lambda_pts,2),round(lambda_pts,2),points,points))The probability of k events occurring in an Poisson interval = e^(-lambda) * ((lambda^k)/k!)
where k = 0 and lambda = 0.48
p0 = e^(-0.48)*(0.48^0)/0!Solution
print("The probability there are 0 POINTS SCORED in the LAST 3 MINUTES of the 4th Quarter is ~%s" % round(p0,3))The probability there are 0 POINTS SCORED in the LAST 3 MINUTES of the 4th Quarter is ~0.622Info
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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)]