Minus Log Two — An Actuarial Poem
y company received updated model results, and several individuals thought the modeled tail was too high. They complained that the one-in-a-hundred-year event was ~50% larger than anything we had observed in the last 25 years. That argument didn’t sit well with me. Just because we haven’t observed a thing in 25 years doesn’t mean it couldn’t be a one-in-a-hundred-year event. But then I thought, “How many years of data would we need to have a 50-50 chance of witnessing a one-in-a-hundred-year event?”
And that is how the nonsense below was born.
Without further ado, I present to you, “Minus Log Two.”
And I’ll say it again
Whether it’s one in a hundred or one in ten
When you need 50-50 and nothing else will do
The thing to remember is Minus Log Two!
(Chorus)
Minus Log Two!
Minus Log Two!
You need 50-50, so what do you do?
Minus Log Two!
Minus Log Two!
You need 50-50, so what do you do?
(End Chorus)
Sixty-nine years
Is how long you’ll wait
For a 50-50 chance
To observe a one percent fate
How do I know this?
The log of one half
Which is Minus Log Two!
(Chorus)
Jim is flipping coins
Sarah is flipping cards
Tails versus heads
Blacks versus reds
What’s coming next?
Which one is due?
Actuaries Know! — Minus Log Two!
You don’t need e
And you don’t need pi
When you’re thinking 50-50
That’s not mono, that’s bi!
The calculus is clear
To both me and to you
Say it with me now —
It’s Minus Log Two!
(Chorus)
(1.0 − 1%)x = ½
x log (1.0 − 1%) = -log 2
x ≈ -log 2 / log (1.0 − 1%) ≈ 69