Footballers Simone Boye Sorensen, Luna Jevitz, Sandra Sepulveda and Diana Ospina García, who competed in the recent Women’s World Cup, share March 3 as their birthday.
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If you’re in a room with 22 other people, there’s a greater chance that two of them will share a birth date than none of them will.
There was something strange about the Women’s World Cup that had just been held in Australia: several international teams had players born on the same day of the year.
There is a counter-intuitive phenomenon known as the “Christmas problem” or the “Christmas paradox.”
The problem is generally presented this way: “How many people would have to be together for the odds of someone sharing a birthday to increase to more than 50%?“.
Initially, when people encounter this problem, they tend to give a number like 180, which is about half the number of days in a year.
Starting from the reasonable assumption that birthdays are generally evenly distributed throughout the year, The answer is only 23 people.
This is because we are not worried about the exact day on which Christmas falls, we just want to know if there is a coincidence. By the time we reach 39, the chances of two people matching their birth date increases to approximately 90%.
To understand why such a low number is needed, we can start by looking at the number of pairs of people in the room: ultimately, what matters to us are pairs of birthdays that fall on the same day.
If we have 23 people in a room, there are 253 possible ways to pair them (As in the chart below).
The exact calculation of the probability of coincidence is a bit more complicated, but when we realize that 23 individuals give us 253 pairs, the probability that at least one of these pairs will have the same birth date increases to more than 50%.
If there are more than 50 people, the chances of someone sharing their birthday increases to over 97%.
Image source, Yeats/BBC Kate
If 23 people in a room shook hands with each other, the number of handshakes would rise to a very high number, very quickly.
From words to deeds…
A lot of theory, but can it be applied in practice? In the 2023 Women’s World Cup, there were 32 participating teams, each with exactly 23 players. It is the perfect ground to test the theory.
After analyzing the data I was able to find this 17 (just over half) of the 32 teams had at least two players who shared a birth date.
There has only been one couple born on the same day in the same year. (December 5, 2000): Panamanian Carmen Montenegro and Leneth Cedeño.
Three teams (Brazil, Colombia and Denmark) had two sets of shared birthdays while two others had three sets of shared birthdays (Morocco and Nigeria).
One Nigerian couple had the second most shared date of all the teams, Christmas Day, which was shared by seven people in the tournament.
During the second semi-final, a couple who shared a birthday faced off against each other: Alex Chidiac (Australia) and Chloe Kelly (England) share a birthday on January 15, although Kelly is exactly one year older than Chidiac.
Image source, Getty Images
At least 17 teams participating in the Women’s World Cup had players who shared a birth date. The statistics say something similar…
English midfielder Jordan Nobbs and her rival, Spanish striker Esther Gonzalez, were born on the exact same day, 8 December 1992. Despite being in their respective teams, neither played during the final.
In total, I identified 24 pairs of birthdays within the teams.
March 3 is the birthday of the Danish couple (Simon Boy Sørensen and Luna Jevitz) and the Colombian couple (Sandra Sepulveda and Diana Ospina García). This date became the most common birthday among all teams: nine players participated in one birthday.
DNA match?
Image source, Getty Images
The Birthday Dilemma explanation works to explain cases in which the DNA of two unrelated people matches.
Beyond football, the same logic behind the “Christmas problem” helps us explain what appear to be paradoxes in other disciplines.
In 2011, while scientists were searching Arizona’s DNA database (which includes more than 65,493 samples), Partial match detected between two unrelated DNA profiles (no family links).
For two unrelated people, this outcome would only be predicted once every 31 million pairs of profiles examined.
This surprising discovery sparked greater research into these types of coincidences. By comparing all profiles in the database, 122 pairs of individuals with a similar (or higher) level of chance were identified.
Lawyers in various parts of the United States have relied on this study to question the uniqueness of DNA identifiers She called for similar comparisons in other DNA databases, including the national database, which contains more than 11 million samples.
If 122 matches appear in a database as small as a database of 65,000 people, can DNA really be relied upon to identify suspicious individuals in a country with a population of 300 million people?
Are the odds associated with DNA profiles wrong, potentially jeopardizing convictions reached based on DNA evidence?
Some attorneys think so, and have presented Arizona’s results to cast doubt on the solidity of DNA evidence in their clients’ cases.
In fact, we can do the math and say that comparing the database’s 65,493 Arizona samples to each other gives us a total of over 2 billion unique pairs.
With a match probability of one in 31 million pairs of unrelated profiles, we should find 68 partial matches.
The difference between the expected 68 and the 122 that emerged can easily be explained by the profiles of close relatives in the database.
Family profiles tend to show partial matches more often than unrelated matches. Rather than making us doubt the DNA evidence, the database results match the “Christmas Calculations” very well.
The unexpectedly large number of combinations of pairs that cause problems such as Christmas, in general, is the force that explains the feasibility of improbable events that occur by pure chance.
It is worth noting that in such situations, when there are sufficient chances of something happening, even if they are low, it can make very unlikely events very likely.
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