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A Saint Patrick’s Day Special: The Luck of Finding Four-Leaf Clovers Using Odds Ratios

Christopher Dimitriadis


Image via The Jacksonville Florida Times Union.

Top of the Mornin’ to ya! So, it is almost time for Lá Fhélie Pádraig, also known as Saint Patrick’s Day in English. This day is known for bringing the luck of the Irish into people’s everyday lives for a mere 24 hours, which got me thinking about four-leaf clovers. A rare variation of the common three-leaf variety, these clovers are said to bring in good luck, although it is not clear where this idea originated or even how it came to be. This theory raises the question: are four-leaf clovers all that lucky?

First, let us start with how four-leaf clovers are even genetically possible. Like every trait expressed by every living organism, the fourth leaf that sprouts is coded for by its DNA. But since the clover’s genetic code is surprisingly complex, four-leaf clovers are still somewhat of an unsolved biological puzzle. Among the over 300 known species of clovers, the one most often associated with having four leaves is the Widespread White Clover. Native to three continents, the white clover’s genome tells us the story of a plant that geographically tried and failed to split into multiple species. The white clover is an allotetraploid, ‘Tetra-’ meaning four and ‘-ploid’ referring to the number of chromosome sets present in a given organism’s cells. White clovers have twice as many chromosomes as humans, mangoes, and most other organisms. The prefix ‘Allo-’ means that each pair of the white clover’s chromosomes comes from a different species.

Wayne Parrott, a professor of agronomy at the University of Georgia, studies crop genetics. His lab has been the closest to figuring out the rare genotype responsible for the fourth leaf. Through substantial research involving the growth and experimentation of 178 clover plants, Parrott and his group figured out that three leaves on a clover seem to be an adaptation for colder or wetter climates, whereas four-leaved stems favoured warmer climates.

Now, onto the main focus. The estimated statistical odds of finding a four-leaf clover on your first try is around 10,000 to 1. If you want to find a five-leaf clover (yes, they exist), the odds skyrocket to 1,000,000 to 1. Let us assume you want to dive deeper into descriptive statistics and compare the odds of finding a four-leaf clover versus a five-leaf clover. You might want to use an Odds Ratio. With an Odds Ratio, you can compare the odds of two events, where the odds of an event equals the probability that the event occurs divided by the probability that it does not occur.

In this case, you would find that your Odds Ratio is 100, showing that it is much more likely to discover a four-leaf clover than a five-leaf clover. You can thus say that the odds of finding a four-leaf clover are 100 times greater than those of a five-leaf clover, even though both are relatively hard to find.

Odds Ratios are not plainly important for comparing the odds of two events. They also play a key role in logistic regression. By using binary logistic regression, we can investigate the relationship between a binary response and one or more predictors. We can then use the Odds Ratio for the predictors to quantify how each predictor affects the probabilities of each response.

Now, could independent conditions or traits such as age alter your chances of finding a four-leaf clover? Not necessarily. Honestly, it could have nothing to do with finding a four-leaf clover. It is all up to luck, which is arguably impossible to truly quantify, as we all have different experiences with luck. Happy Saint Patrick’s Day!



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