Spanish Primera Division (Atletico Madrid @ Barcelona): Will Lionel Messi SCORE in the 1st Half?

4:00 PM
Yes: Messi scores in 1st Half
No: Messi doesn’t score in 1st Half

Inputs to Solve

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

p_anytime_goal = 1/2.05

print("The probability of a Lionel Messi scoring a GOAL is ~%s" % round(p_anytime_goal,3))

The probability of a Lionel Messi scoring a GOAL is ~0.488

Method to Solve

[1] Assume the probability of Messi scoring a goal in the 1st Half is approximately the same as the probability of Messi scoring a goal in the 2nd Half (p).

[2] Break Messi scoring down into halves:

1st Half	2nd Half
GOAL	GOAL
NO GOAL	GOAL
GOAL	NO GOAL

1st Half	2nd Half	odds
p	p	p^2
1-p	p	(1-p)*p
p	1-p	p*(1-p)

The sum of the odds of the above must equal p_anytime_goal

[3] Solve the quadratic equation p^2 - 2p + p_anytime_goal = 0 to estimate the probability Messi scores in the 1st Half

## [3]

import math

a = 1
b = -2
c = p_anytime_goal

d = b**2-4*a*c # discriminant

if d < 0:
    print ("This equation has no real solution")
elif d == 0:
    x = (-b+math.sqrt(b**2-4*a*c))/2*a
    print ("This equation has one solutions: "), x
else:
    x1 = (-b+math.sqrt((b**2)-(4*(a*c))))/(2*a)
    x2 = (-b-math.sqrt((b**2)-(4*(a*c))))/(2*a)
    print ("This equation has two solutions: ", round(x1,3), " or", round(x2,3))

This equation has two solutions:  1.716  or 0.284

Solution

print("The probability that Lionel Messi scores a GOAL in the 1st HALF is ~%s" % round(x2,3))

The probability that Lionel Messi scores a GOAL in the 1st HALF is ~0.284

Info

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3.6.5 (v3.6.5:f59c0932b4, Mar 28 2018, 16:07:46) [MSC v.1900 32 bit (Intel)]

Posted on 6/30/2020