I was surprised recently at hearing an interview with Olivier Giroud from Arsenal Football Club about a goal he scored New Year’s day against Crystal Palace. Giroud’s goal was an immediate candidate for Premier League goal of the year. Making a run inside the penalty box, Giroud received a waist-high cross behind his body. Reaching backwards with his left heal, Giroud deflected the ball forward and into the upper corner of the goal (a bodily contortion often called a “scorpion kick”).

After the match a reporter asked Giroud to describe the shot; Giroud replied that he “had maximum luck.” Bewildered by the candid acknowledgement, the reporter replied “luck?” Giroud affirmed “yeah, yeah, it’s just about luck.”

The interview had me wondering how much of Giroud’s success could be attributed to luck and how much credit should he take for himself? Would I be as “lucky” to make the same shot? I also wondered if it’s possible to quantify the amount of luck influencing any result.

I began with the English Oxford dictionary definition of *luck*: “success or failure apparently brought by chance rather than through one’s own actions.” The dictionary continued with a suitable example: “it was just luck that the first kick went in.”

This definition captures the role of chance but I wasn’t satisfied with the lack of quantitative guidance. Perhaps Giroud and I both need luck to make the shot but how could we need the same amount? I might attempt the shot 100 times and not score once. So I looked to probability theory and after some deliberation came up with the following definition*:*

“The amount of luck contributing to a result is the difference between the expected result and the actual result.”

For example, if the odds of winning a lottery are 1 in 100 and I win with a single ticket, then luck accounted for the difference between the number of tickets needed to expect a win (51 tickets) and the number of tickets I bought (1 ticket). Buying one ticket was the sum contribution of my efforts and luck had to account for the additional 50 tickets I should have had to buy. Whether the quantity of luck is “good” or “bad” is subjective but my hunch is that most people like to win the lottery.

I put my definition to the test in the following ways:

First, should we consider it* lucky* when an expected result happens? If there’s a 70% chance of sunshine on my wedding day, would I be lucky to enjoy a sunny wedding? I don’t believe we should call an expected result “lucky” no matter how strongly we feel about the outcome. We could, on the other hand, call it *unlucky* if unexpected rain were to fall on the wedding. It may seem fortunate when the sun shines as expected, but I wouldn’t consider it luck. You simply appreciate when the expected happens.

What about my quantification of luck? Is luck proportional to the probability of outcomes? I think it’s correct to say that people are luckier at winning when the probabilities against them are greater. You need more luck to overcome 5000:1 odds than 2:1 odds. And at the craps table it takes the same amount of effort to roll the dice but you’ll need more luck to roll a 12 than a 7. I find probabilities a compelling way to quantify luck.

So what about Oliver Giroud? How “lucky” was he to make the shot? His result is harder to quantify than dice rolls and lotteries, but it’s not a shot that professional players make every day. In my case, luck may not be enough to score the goal. It would take something more like…divine intervention.