NCF (#19 Wisconsin @ South Florida): Will EITHER TEAM SCORE in the FIRST 5 MINUTES of the 2nd Half?

9:00PM
Yes: Points scored in first 5 minutes
No: 0 points scored in first 5 minutes

Inputs Needed To Solve

Scores per Game by Team

Wisconsin
South Florida

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

WIS_Scores = (51 + 10 + 0)/13
SF_Scores =  (43 + 15 + 0)/13
             #TD + FG + Saftie / Games
    
total_score_events = WIS_Scores + SF_Scores
    
print("The total expected Scoring Events per Game by Wisconsin is %s." % (round(WIS_Scores,3)))
print("The total expected Scoring Events per Game by South Florida is %s." % (round(SF_Scores,3)))

The total expected Scoring Events per Game by Wisconsin is 4.692.
The total expected Scoring Events per Game by South Florida is 4.462.

## Inputs Defined in the Problem

period_of_game = 5/60
score_event = 0

Method To Solve

[1] Estimate lambda_score - expected number of total scores per 5m interval for both teams
[2] Use the Poisson Distribution to compute the probability there are no scoring events in the 1st five minutes (p0_scores)

## [1]

lambda_score = total_score_events * period_of_game
print("lambda_score ~ the total expected scoring events for both teams during a 5m interval")
print("lambda_score ~ %s * %s" % (round(total_score_events,3),round(period_of_game,3)))
print("lambda_score ~ %s" % (round(lambda_score,3)))

lambda_score ~ the total expected scoring events for both teams during a 5m interval
lambda_score ~ 9.154 * 0.083
lambda_score ~ 0.763

## [2]
import math

print("The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!")
print("where k = 0")
print('')

p0_score = math.exp(-lambda_score)*(lambda_score**(score_event))/(math.factorial(score_event))
print("p0_score = e^(-%s) * (%s^%s)/%s!" % (round(lambda_score,2),round(lambda_score,2),(score_event),(score_event)))

The probability of k events occurring in a Poisson interval = e^(-lambda) * (lambda^k)/k!
where k = 0

p0_score = e^(-0.76) * (0.76^0)/0!

Solution

print("The probability NO TEAM SCORES in the FIRST FIVE MINUTES is ~ %s" % round(p0_score,3))

The probability NO TEAM SCORES in the FIRST FIVE MINUTES is ~ 0.466

Info

download md file
email: krellabsinc@gmail.com
twitter: @KRELLabs

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 8/30/2019