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[OC] The Birthday Paradox at the World Cup: how often do teammates share their birthday? (Hint: way more than you think). Also, do kids born in January have better chance of going to the World Cup than those born in December?
Let's do some shitty maths: 23 is just 6% of 365. Imagine you pick 6 random numbers from 1 to 100, and ask a friend to guess another 6 random numbers. What are the odds that both of you picked the same number? Pretty low, right? After all, your friend had a 94% probability of not picking any of your numbers.
So, at the World Cup, two teammates sharing their birthday, like our Polish friends do, must be quite unlikely. As said, it happens at least once, but could there be more cases? Now, if a single coincidence in a team seems unlikely, what about two? Or three, or even four? Impossible, right? As it turns out, the probability is much higher than what we estimated (the math above, or its logic, is wrong). The correct answer is a surprising 50%. Yes, 50% of the teams in Russia have at least two players born on the same day. And no, it's not a weird coincidence. It's exactly what mathematics predicted. This unexpected result is called the Birthday Paradox. But more about it later.
Now, here is another scenario. Let's take two kids from the same town and similar backgrounds: Albert, born on January 1st, 2014, and Zac, born on December 31st, 2014. Next September both will start kindergarten and join the town's club's youth academy (let's assume that, as usual, the cut-off date is January 1st, which means that all kids at both the class and the youth team were born in 2014). By then Albert will be 4 years 9 months old, and Zac only 3 years 9 months old. In other words, Albert is 27% older than Zac. At those ages, that's a massive difference, which means that Albert's brain and body are far more developed than Zac's, giving the former a huge advantage. The question is: 15 or 20 years later, does this advantage still exist, or did it disappear, becoming more irrelevant than other factors (e.g., health and injuries, money and access to proper training materials, genetics, "luck", personal motivation...)?. In short, does Albert have better chances of becoming a professional player and going to the World Cup, just because he was born in January?
Since two kids in a town is statistically insignificant, I analyzed the 736 players at the WC, from 32 countries in the five continents and so very different backgrounds. The result, as the previous one, might surprise you.
Let's start with the Birthday Paradox. From Wikipedia:
In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people.The wiki tells us that in a group of 23 people -like each of the 32 teams at the World Cup- the probability of at least two of them sharing their birthday is 50.7%. Mind you, this is not some bullshit you read online, but a bulletproof theorem that can be easily demonstrated using high-school mathematics. If you know how to code, you can check it yourself: here's a simulation I posted yesterday on /dataisbeautiful. As you can see, the results nail what the math predicted: https://old.reddit.com/dataisbeautiful/comments/8pce4t/simulating_the_birthday_paradox_in_a_group_of_23/
So, the question is: is this paradox true at the World Cup? Answer: yep. Exactly, 16 of the 32 teams (50%) have at least two teammates who have the same birthday. Not only that, but in several teams this happens not just once, but twice or even four times! In total, there are 23 coincidences (23 couples of players sharing a birthday with a teammate). Here's the full list of shared birthdays, per country: https://pastebin.com/jjnSedik
As said, this result, while surprising, it's perfectly normal. I analayzed the last 4 WCs, and the number of coincidences was even bigger in the past:
Thread on /dataisbeautiful:
Full list of shared birthdays in the last 4 WCs:
Some other birthday data: -The most common birthdays are March 5th, February 25th, and May 11th, with 7 players each. Here's the list of the 10 more common birthdays (do you see a pattern?):
-With 732 players and only 365 days, I expected (almost) all days to have at least one player celebrating his birthday on that day. However, that's true for only 310 of them. In other words, there are 55 days on which no player was born (no one was born on February 29th), despite being twice as many players as there are days in the year. Weird.
-Things get (IMHO) weirder if we consider the full birthdays (days/month/year). The youngest player at the WC is Arzani (Australia), from 1999. The oldest one is Egypt's GK El-Hadary, from 1973. There are 9500 days between the two. Even if you consider most players to be between, say, 20 and 34 years old, that's still a 5000 days difference. With just 732 players, the odds of two players being born on the very same day, just hours apart, should be pretty low, right? Again, it happens way more often than I expected: there are 55 days (DD/MM/YYYY) on which more than one player were born. If you're curious, here's the full list:
Let's go now with the second question. Statistics show that all over the world slightly more people are born in the second part of the year -especially during summer- than in the first semester. There are exceptions, of course, but overall this seems to be a global trend. Some sources:
In general, if you were to analyze the birth months for all the players at the WC, you'd expect them to be more or less evenly distributed over the year, perhaps with more of them during the summer (e.g., 8% of the players were born in January, 9% in July, and so on) . However, numbers say otherwise. I counted how many players were born each month of the year, and the results speak for themselves:
As you can see, more players are born in the first months than later in the year.
Amazingly, despite more people all over the world being born in the second half of the year, at the World Cup, there are 72% more players born in the first quarter (Jan-March) than in Q4 (Oct-Dec). In absolute numbers, 231 in Q1 (32% of the total, well above the expected 25%) against 134 in Q4 (18%, well below the expected 25%).
Remember how a couple of minutes ago I asked you if you could see a pattern in the list of the 10 most common birthdays? Note now how 7 of them are in January , February and March.
Going back to our little friends, it seems that Albert has indeed better chances of becoming an elite player than Zac. Surprisingly, that gap during the early childhood seems to play a big role in players many years later, during their teenage years as they start playing for big teams or their countries, and even during their professional careers.
Again, this happens at every World Cup. Here is the data for the last 3 tournaments:
As you can see, the difference this years is bigger than usual, but the trend persists. This happens not just in football but in many other fields, including academics and the job market. It's called the Relative Age Effect. From Wikipedia:
The term relative age effect (RAE) is used to describe a bias, evident in the upper echelons of youth sport and academia, where participation is higher amongst those born early in the relevant selection period (and correspondingly lower amongst those born late in the selection period) than would be expected from the normalised distribution of live births. The selection period is usually the calendar year, the academic year or the sporting season. The difference in maturity - which can be extreme at young ages: a six-year old born in January is almost 17% older than a six-year old born in December in the same year - causes a performance gap that persists over time. A 2006 study finds that relative age affects student performance and has long-lasting effects on life outcomes. The authors find that "the youngest members of each cohort score 4–12 percentiles lower than the oldest members in grade four and 2–9 percentiles lower in grade eight... data from Canada and the United States show that the youngest members of each cohort are even less likely to attend university. A 2014 study finds that Italian students born in the early months of the year "are more likely to be tracked in more academic schools rather than in vocational schools.A Wikipedia user did something similar: teenage players at U-17/19 Euros (blue) vs general population in Europe (red): https://upload.wikimedia.org/wikipedia/en/thumb/3/37/Month_of_birth_distribution_UEFA_youth_tournaments_2010.pdf/page1-800px-Month_of_birth_distribution_UEFA_youth_tournaments_2010.pdf.jpg
I took a look at which countries have the most players born early in the year, looking for cultural/geographical/religious/economic… patterns, but found nothing.
So, in short, if you want your son to play at the World Cup, you should convince your wife to plan the pregnancy, so that the kid is born early in the year. Of course, this might get you a divorce, but, hey, you’d do anything for football, wouldn’t you?
Source for the data: https://en.wikipedia.org/wiki/2018_FIFA_World_Cup_squads
Tools: some python code I wrote and way too much free time being wasted.
Match Thread: SS Lazio - AS Roma (Derby della Capitale)
Venue: Stadio Olimpico, Roma
If I have made any mistakes, PM me or include my username in a comment
|Temperature||73 F / 23° C|
All streams were found at www.rojadirecta.me if you have a stream post it in the comments and ill add it to the match thread (:
|SS Lazio||AS Roma|
- This will be the 142nd Derby della Capitale in Serie A: Roma lead by 48 wins to 36; however, the most frequent result is a draw, occurring 57 times..
- Roma are unbeaten in their last four league meetings against Lazio, winning one and drawing three – prior to this, the Biancocelesti had won three matches in a row.
- There has been only one 0-0 draw in the last 15 Serie A matches between these two sides, with the Giallorossi finding the net in each of the other 14 games.
|SS Lazio||AS Roma|
First Half0' KickOff
3' Candreva makes a fantastic run on the left side running all the ways to the edge of the box and then cuts in. He tries to place a shot across the goalie but the goalie deflects the ball. Lazio is knocking on Roma's door...
5' A Roma defender makes a horrible backpass inside of Romas own goal box. Lazio's Candreva recovers the ball and crosses the ball to Klose who amazingly misses the open header.
15' The match has calmed down a lot. After Lazios great start Roma is trying to slow the game down as much as possible and Lazio are happy to go along with it.
22' After a failed free kick Roma's Iturbe gets fouled on the counter attack by Lulic. The Roma players scream for the red but they will have to settle for a yellow.
31' Gentiletti gets a yellow after he fouls Roma's Keita and then tries to land a sneaky kick to Keita's gentlemen sausage.
35' Completely unnecessary foul by Biglia as Florenzi tries to start a counter. Thats three yellow cards for Lazio, 1 for Roma.
45 + 2' Halftime
|SS Lazio - AS Roma|
Fan Comments at Halftime"Florenzi and Candreva were the two stand out players that half. Plan pass the ball to Totti isn't working, Roma need a striker who will actually make a run into the box." - zeshie
"Nice result for us so far. Shite soccer from us so far." - Traxillion
"For the past few months Roma has been looking like someone who just started playing Fifa and can't hold the ball for more than 10 seconds so just tries to do a long cross here and there" - peesprinkler
"A rather boring first half but honestly that's how you have to play against Lazio, you can't let them counter-attack you. Too bad I can't see us scoring anytime soon..." -Ynimixer
Second Half45' KickOff
47' Lazio's Basta takes a crack at it from outside of the box and the ball just goes wide. Lets hope this increase in the tempo of the game continues!
51' Lazio's Lulic fouls Totti with a slight kick to the chest as they both try to go for the ball. Luckily for him the ref does not decide to give him a yellow which would've meant a red card for Lulic. Torosidis is given a yellow card for complaining to the ref
55' Lulic Cavanda
60' Totti Ibarbo
68' Keita Pjanic
68' Ibarbo has a clear chance as the ball is deflected to him after a corner kick, but he paces the ball wide. Its not going to get any closer for Roma to score than that.
74' Goooooooooal Roma! Iturbe slots the ball in after a great pass from Pjanic to Ibarbo to set him up to cross the ball in.
It looked like this:
Iturbe --- Goal ^ | | | Ibarbo74' Ibarbo (for taking his shirt off)
76' Mauri Djordjevic
76' Biglia Matuldi
80' Gooooooooooal Lazio!!!! Anderson crosses the ball in beautifully for Klose to re-center the ball with a header for Djordjevic to just slot it in. Lazio 1 - Roma 1
It looked like this:
Klose | | | Goal <----- Djordjevic84' Goal Romaaaaaa!!! Djanga heads the ball in beautifully to the left post. Commentators are saying it was offsides. But no Lazio player argued for offside.
It looked like this:
Mapou ---- Goal / / / / / / / / Pjanic86' Florenzi
90 + 3' Full Time Lazio 1 - Roma 2
Fan Comments at Halftime"God fucking damnit" - brutalpoonslayer
"The team dug out something within itself. To be honest, we didn't see the ball much, but we fought hard. Now we need to get some stronger ideas for next season, because Lazio are scary. We could've played for a draw if we had seen Lazio sit back more. They didn't and we hit them on the break." - Daniele De Rossi thanks camalittle
"Can't really believe roma won this. They had about 10 minutes of dominance in which they scored twice." - Red_Dog1880