Papal Probability

This article contained some numbers which led me off on a tangent.

Pope Francis is the 266th pope. There have been 37 false popes.

Therefore, 37/(266+37) = 12.2% of papal claimants are antipopes.

The average Pope serves for 7.3 years (John Paul II, it turns out, had the second longest reign in history).

Now, the average US life expectancy is 79.8.

Therefore, on average, an American will see ceiling(79.8/7.3) = ceiling(10.93) = 11 popes in their lifetime.

So, given an antipope rate of 12.2% and 11 popes in a lifetime, what are the odds that you will see an antipope in your life?

My probability is very rusty, and I wasn’t exactly great at it back in school, either, but I’m pretty sure this boils down to a classic Probability Mass Function

f(k;n,p) = Pick(n k)(p^k)(1-p)^(n-k)

So, the probability of exactly one antipope in a lifetime:

f(1;11,.122) = Pick(11 1)(.122)^1(1-.122)^(11-1)
= 0.36534

In other words, the odds of you living through exactly 1 antipope are a little over 1 in 3.

But wait, there’s more!

What are the odds of at least 1 antipope in your lifetime? At this point, the maths get pretty long and repetitive, so let’s cheat using the internet:

Probability of success on a single trial: 0.122
Number of trials: 11
Number of successes (x): 1

The answer?

The power of Apostolic Succession and the great Tradition of the Catholic Church assures you of a lifetime of legitimate spiritual leadership 1 time out of every 4.

In other words 76.1% percent of us will live under an antipope (and very likely more).

So there you have it: mathematical proof that Martin Luther was probably correct. Happy Reformation Day!