A Saint Patrick's Day Special | The Luck Of Finding Four-Leaf Clovers Using Odds Ratios

TOP OF THE MORNIN’ TO YA LADDIES! 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 the 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 or even how this idea came to be. This brought up a question: Are four-leaf clovers all that lucky?

First of all, let us start off with how four-leaf clovers are even genetically possible. Like every trait on every living thing, the fourth leaf that sprouts comes from DNA. But since the clover’s genome are surprisingly complex, four-leaf clovers are still somewhat of an unsolved biological puzzle. Amongst the over 300 species of clovers, the one that is most associated with having four leaves is the Widespread White Clover. Native to three continents, the white clover’s genomes tell 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’ meaning chromosomes, white clovers have double the number of chromosomes that humans, mangoes, and most other organisms have. The prefix ‘Allo’ which means that each pair of the white clover’s chromosomes comes from a different species.

Wayne Parrott, a professor at the University of Georgia, studies crop genetics and whose lab has been the closest as to figuring out the rare genotype of the fourth leaf. Through an amount experimental research and 178 clover plants grown and recorded, three leaves on a clover could and seem to be an adaptation for colder or wetter climates, as Parrott and his group figured out that four-leaved stems favoured warmer climates.

Now, on to 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 the event occurs divided by the probability 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 rather 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. 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.

Here is an example: Suppose you are analyzing data from people who have found four-leaf clovers to decide whether the finder’s gender and age affect their finding abilities. The ‘Find’ variable would be a binary response, which equals 0 if the person did not find a four-leaf clover, and 1 if the person did find one. The ‘Gender’ variable would also be a binary response. Being that it equals 0 if the person is male, and 1 if the person is female. ‘Age’ would be our continuous predictor is this example, which equals the person’s age.

Suppose the logistic regression procedure declares both predictors to be significant. If ‘Gender’ has an Odds Ratio of 2.0, you can conclude that the odds of a woman finding a four-leaf clover is twice the odds of a man finding one. If ‘Age’ has an Odds Ratio of 1.05, you can conclude that for each added year of the finder’s age, the odds of finding a four-leaf clover increase by 5%.

Now, do age and gender pertain to your chances of finding a four-leaf clover? Not necessarily. Honestly, it could have nothing at all to do with finding a four-leaf clover. It is truly all up to luck. Which is honestly pretty tough to quantify, as we all have different experiences with luck. Happy Saint Patrick’s Day laddies!

17.03.2022