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I’ve heard a lot of people claim not to believe in luck. Allow me to demonstrate that this belief, while psychologically satisfying to some, is tantamount to disbelief in Pi or milkshakes.

Luck is not some sort of ethereal faith-based system of wish-granting priority. Luck is the result of a simple calculation and luckiness is the sum of a series of luck calculations.

The Formula

Luck = Benefit / sqrt(Probability)

The basic unit of luck measurement is under some debate, but for our discussion, we will refer to the unit as Л or “El.”

You can see the formula in action with my online luck calculator.

Benefit:

A numeric value with min and max centered about 0 and range set to an arbitrary scale (ex.: winning a free bagel = 0.8 and getting a lethal papercut on the giant novelty check handed to you by Ed McMahon = -99). For our purposes, the benefit scale ranges from -100 to 100, inclusive.

Note: The benefit value is subjectively determined value on a scale where -100 is the worst possible, 0 is neutral, and 100 is the best possible outcome. Refer to table 1a for some examples.

Probability:

A ratio of the number of times an event will happen over a number of attempts. This value will always range from zero to one, inclusive.

Formula In Action

Assuming your assessed benefit value of finding a $20 on the street is 5 and the odds of doing so are 1:400 (1/400 = 0.0025 = 0.25%), the formula would work out like this:
Л = 5/sqrt(0.0025)
Л = 5/0.05
Л = 200

Homework

Everyone loves story problems, so here’s one for you:
Lucy values her life more than anything in the world except for that of Mr. Turtle, her cat. She places the benefit of losing her life at -99. After a friend of a friend perished in a tragic futon accident, Lucy found out that the odds of such a thing happening to her are 1:4,473. Aside from the toilet, Lucy owns no furniture with a seat or table top higher than 18 inches because she feels this will ensure her safety. However, a fateful visit to Sears nullifies all of her protective efforts as she trips over a footstool and suffers a fatal concussion.

Calculate the Л for Lucy’s untimely death. Show your work.
Hint: Surprisingly, the value is negative.

Luck Calculator

Use this simple tool to quantify the luck for a particular event.

Benefit _{(range: -100 to 100)}

 

Probability _{(range: 0 to 1)}

 
OddsPercentRatio

Calculate My Luck!

Л:

 
_{Table 1a.: Example relative benefits}