OK, so today we’ve got exclusive

access to Nottingham Forest football ground here. Two-time European Cup winners

who have given us the access so that we can talk about a

very important number in football, and a very important

number in probability, which is the number 23. OK, so 23. So why is 23 an important

number in football? Some of you may know

this already. That’s the number of people

that you will have on the pitch during the game. That’s two teams of 11

and the referee. So there are 23 people

on the pitch. Now, here’s my question today. What’s the probability that two

of those people will share a birthday? The answer may surprise you. So we’re not talking about the

year, we’re just talking about the date itself. Maybe it’s the 14th

of January, maybe it’s the 5th of June. We’re talking about

the date itself. So let’s work this out. I can make this slightly

easier if I ask the opposite question. I’m going to work out the

opposite, which is, what’s the probability that no one on that

pitch shares a birthday. That’s an easier question

to answer. Let’s do this. OK, so your first player. OK, it doesn’t matter what

birthday he has. But when your second player gets

on the pitch, what’s the probability that he doesn’t

share a birthday? Well, he will have, out of the

365 days to choose from, he can have a birthday on 364

of them out of 365. So we’re not including February

the 29th, no leap years here. And we are assuming that all

days are equally likely. OK, so your second player has

to have one of these days. Your third player, when he comes

on to the pitch, will have a choice of 363

days out of 365. And then what next? The fourth player. Out of those remaining days, he

will have 362 out of 365. And you can keep going. Eventually, you’ll get

to the 23rd player. Let’s call him the referee. So your 23rd player, how many

choices does he have? He will eventually get 343

days left out of 365. So this is the number of days

that you’re allowed to have for that referee’s birthday. Because we are looking at no

one sharing a birthday. Now, if you want to find out

the probability that no one shares a birthday, you multiply

all these together. And you’ll get a number. And that number is around

about 0.493. And if you’re not happy with

probabilities like that, that’s 49.3%. Just slightly under half. We were interested in the

opposite question. The opposite question was,

what’s the probability that someone does share a birthday. That’s the opposite thing of

what we’ve worked out. So the probability that someone

does share a birthday will be 50.7%. It’s slightly over a half. You’re more likely for two

players to share a birthday than if they don’t

share a birthday. And that’s quite surprising. And people want to think,

well it must be something like 100 people. You must need 100 people

for that to be true. Or 200 people. If you think of it this way,

think of all the pairs of people you could make out of

23 people on the pitch. All the possible pairs of

people– in fact there are 253 pairs of people you

could make. And, well, think of it that

way– you start to see why it’s quite likely, that

two of those people will share a birthday. So next time you’re at a

football match, think of it– you have a greater than 50%

chance that two of those people share a birthday. OK, so here’s another way

to think about it. Imagine you’re watching

the game. And well, if you need to go to

the toilet, you get up and you have to move past all

the other people. By the time you’ve moved past 23

other spectators, there is a greater than 50% chance that

two of those people you walked past will have shared

a birthday.

March 5 is my birthday too!

If we include February 29 as a possibility how does it affect the outcome?

The probability is reduced from around.50729 to around .50686. if leap years are assumed have a 1 in 4 chance of happening in any given year (which isn't really true).

Thanks Brandon A, I know leap years have slightly less than a 1 in 4 chance of occurring in any year (as 3 in every 400 don't happen) but looking at your figures I don't think it will make a significant difference.

Sorry! That should be 3 in every 400 years not 3 in every 400 leap years.

march 23 mate

WTF man,14th Jan i had a big test, and 5th June is my birthday…NOW CALCULATE THAT PROBABILITY

I calculated it for what we across The Pond call football ("gridiron," or whatever you prefer). In the NFL, there are 7 officials in addition to the 11 players per team. So with 29 people, it's better than a 2:1 chance, 68.1 % to be, well, specific.

I don't actually care about sport(s) and things like that.

23 is a important number in Basketball, because of Michael Jordan 😛 🙂

23 October people,jelly?

Vsauce??

Only American cunts call it Soccer, the rest of the world calls it football

Mole day?

Alternatively, the way I've always understood it, is if you raise the likelihood of two people not sharing a birthday to the power of the number of possible pairs (in this case 253) you will get the 49.95%, or a 50.05% chance that someone shares a birthday.

HULL CITY!!!!!!

And of course it was Michael Jordan's number

When is this dude going to complete his transformation into The Joker?

23, 23, 23, what does it have to do with CLARA???? We have to wait so long until DW comes back!!!!

Came here after 42, kinda was expecting to see some references to Jim Carrey's film 🙂 Still interesting video.

Hey. This makes me wonder if you guys have done a video on the Monty Hall problem. I haven't looked at all 153 videos yet, so I don't know. But if you haven't, you should! It's really fun.

23 scares me… After watching the movie, that is.

23 is my D.O.B!!!GO TWETY THREE!

My math teacher used to always tell us this probability but I never understood it until now. That's pretty amazing. If only my calculus lecturer was as good at teaching as you!

If the rest of your message is in English then yes it is wrong

PARADOX: In a group of 23 people there is about 50% chance that there is a shared birthday. So 2 groups of 23 has a theoretical probability of about 100% of a shared birthday. However, in a single group of 46 people, there is only a 94% chance, even with many more possible combinations.

not necessarily true. There are people who grow up speaking multiple languages and they might use those languages interchangeably, possibly while writing things also.

LOGICAL FALLACY DETECTED! By that same reasoning, if you had two groups of 46 people, each with a 94% chance of having a shared birthday, then 2 groups of people would have a theoretical chance of 188% chance of a shared birthday. This is clearly not true and the problem lies with how the math is worked. each additional person you add increases the chance of having a shared birthday but the chances that are being added are getting smaller and smaller so you cannot add two probabilities like that

sorry about the triple message! my computer was saying there was an error so I tried till it went through!

I just liked this so that:

Likes = 1,111

Dislikes = 111

Let's call this the last "binary popularity" for a while. Next binary popularity would be, what, 10,000 likes if dislikes remains at this? Unlikely… oh, and it was a binary popularity before I liked it 🙂

Typo: not that many disliked it. Only 11, not 111.

that isnt right because he said that after you walk past 22 people it is a slightly larger than 50% chance that anybody you walked past shared a birthday with you or another person you walked past.

At first I was totally amazed. But, then, when I thought about it, if you imagine ropes between 23 people, all connected to every other person, if you counted the ropes it would be a large number, around half of 365

Question: Shouldn't the first fraction for odds no-one sharing a birthday be 365 over 365 (100% of not sharing) as there is no-one to share a birthday with?

If you like it better that way, that's fine, since the answer still comes out the same. You could even go a step further and say that before the 365/365, you should start with 1, since no one can share a birthday if there are zero people, either. So, 1 * 365/365 * 364/365 * ….

Very interesting, so it is a 58.7% chance that a player or ref on the field will share a birthday. I lea

Very interesting so 50.7% chance that a player or ref on the field will share a birthday. If one person was on the field wouldn't there be a 365/365 chance?

Why are you sorry?

Wow, that's pretty amazing. How come there is more of chance for players to share a birthday than not?

Is there also a possibility that none of the 23 players have the same birthday

This blows my mind. I never thought that there is such a good chance that I have the same birthday as someone else on the field.

If the number was even would it still work out that way?

"This blows my mind. I never thought that there is such a good chance that I have the same birthday as someone else on the field."

As I see it this is why this is so

apparentlyremarkable.The actual statement refers to

anytwo people, but I think we're programmed to consider it as "Me + 1 Other Person". The probability of that, of course, is much lower – no idea what though 🙂Maybe this video would be better placed in a psychologyphile channel.

theres 4 refs, so 26

im surprised that this is the only video by you guys about the number 23. i mean, theres a blockbuster movie about it.

that aside though.. ive always seen the number 343 appear in my everyday life to the point where it got annoying (just like the number 23 in the movie) and ive tried to ignore it.. but you just made me realize the the number of days in a year minus 23 is 343. i guess im not sleeping tonight.

cool I liked how you solved that

This is mind blowing. I didn't expect that, especially as a soccer player. Recently, we also did probability in my class…. Ahhh the memories. If you were to take the probability of two people in the whole stadium sharing a b-day, how would you work on the problem after you reach 1/365?

This was very interesting, not only as a fan of football, but also as a math student. Probability is a key aspect and important part of our day to day lives. As humans, we continually put ideas, themes, and occurrences into quantitative values. Probability is one of the more favored way to measure aspects of our day to day lives. Realizing the importance and realities of these probabilities is also very important. And as we see in this video, things in our day to day lives are much more probable than we may have otherwise expected. How did the idea of using a full manned pitch as an example come about? What are other ways in which probability can be better applied to our daily lives?

birthdays arent evenly distributed throughout the months and days though.

Ha, March 5th's my birthday as well…go figure.

You should also take in account the line judges. But, its interesting that you found a way to apply math to the beautiful game. Well done.

This was definitely an interesting application of probability. I do have to wonder how to answer might vary if leap years and the likelihood of birthdays occurring in certain months over others was taken into account. (Which obviously for the purposes of this video was completely unnecessary, but would still be interesting to consider).

I didnt know that 23 was such an interesting number.

How cool! The relation between the game and the math was so interesting! I liked how you showed the players birthdays and showed who shared one. Awesome video!

There seem to be a disproportionate number of players born in January… This looks like something out of Malcolm Gladwell's book Outliers.

What is the probability of 180 people in a group sharing a birthdate? Please answer ASAP

This seems counter intuitive but the math never lies! Great video 🙂

How can I calculate the probability in a group of 23 (or n) people of another person having the same birthday as me? In other words what is the probability of me being one of the two people sharing the same birthday?

I like how you guys related the birthday problem to football to make it more interesting, which works perfectly well if we ignore the various assistant referees (linesmen, 4th & 5th officials, etc).

I wonder why it happens to be the number 23 that this probability is true. I guess it makes sense when you think that there is an 100% to people share a birthday if there are more than 365 people in a given group.

I showed this to a statistics class of 21 lower sixth and then checked to see if there was a pair among them. Well, there was a pair of twins. And the first two pupils on the register were a pair. And there were two other pairs. So what is the probability of two pairs, or more pairs? I think we can express it in terms of nCr and factorials.

This video was shocking to me! I had no idea that the probability of two soccer players sharing a birthday was so high. It at first seems so unlikely. Has there been any data collected on this topic? How often do two people on the pitch share a birthday in real life?

This video was very interesting and left me thinking about that it is more likely for out of 23 people 2 of those people share a birthday. I was confused at the start of the video but by the end numberphile had fully explained why his claim is true

You need to do a video on the 23 enigma

Mmm, seems to me that the formula would be 364/365 x 363/364 x 362/363, etc. Strange, since I have never met someone that I share a birthday with and I am 50 🙂

The number 23 is very important in soccer because that is how many people are on the field at once, including referees. I really enjoyed learning how to find the probability of something, like birthdays. It is quite shocking that is it more likely for two of the 23 players to share a birthday than for all of them to have different birthdays. This video showed me an easy way of how to determine probability. All you do is take the number 364 out of 365 days and multiply it by the second guy which is 363 out of 365 days and so on… Then you add multiply the bottom and the top of the fractions and divide and you will have a decimal. Move the decimal two places to the right to get your answer. Thank you!

Ron Lancaster was a great CFL Quarterback and he wore Number 23.

My math(s) class (plus a few random kids from the hallway) compared birthdays and all 40 or so of us did not have any birthdays in common! That must be pretty rare! (My teacher bought us pizza for this!)

Its amazing how you can figure out someones birthday just from number 23 and the number of days in a year.

There are 7 000 000 000 people on Earth. There are 365 days in a year. There are 366 days in a leap year. 7 000 000 000 / 366 = 19 125 683 That means that roughly over a 19 million people shares a birthday with you.

justin trudeau is now 23rd prime mininister of canada

Wow I never would thought that would be true.

that is so cool

I share my birthday with the referee, Keith Stroud!!!

it was very interesting to see that there's a more likely chance that there is a person with the same birthday as you.

I had to watch this video for a school project we had to do and I was truly fascinated by the statistic that it was more likely that 2/23 people were more likely than not to have birthdays on the same day. I really like the way they tied this statistic together with soccer and then later used a specific example of two players that had the same birthday. This is almost as fascinating as the the stat that all three of the Dallas Mavericks point guards (Deron Williams, JJ Barea, and Raymond Felton) were born on the same day. The likeliness of this occurrence is 0.00182%. This means it would take statistically approximately 1270 years for this specific event to happen again.

Thanks for a gideo on 23

I am super surprised by the outcome of this video. It made me think hard! I would've never guessed that the probability of two people out of 23 people are more likely to share a birthday (by 50.7%) than it is for them not to share a birthday. It made complete since when the math was being done to show how this was possible. What would be the probability that two people out of a certain number had a birthday in the summer? How could you figure this out? Also, are there any other numbers other than 23 that this works for? Very cool video.

please explain me that "what is the probability if 3 players have the same birth day out of 23 players"

NOTTINGHAM FOREST FC WERE BY FAR THE GREATEST TEAM YOU'LL EVER SEE AND WERE NOTTINGHAM FOREST!!!

There was a slight mistake in how the problem was defined. He said "the chance that 2 people out of 23 share a birthday" but what he's really calculating is 2 or more sharing a birthday.

i loved this esp. since I was able to follow it all the way through!

I am really suprised by the outcome of this video. It made me question many things and made me think hard. I would've never guessed that the probability of two people out of 23 people are more likely to share a birthday (by 50.7%) than it is for them not to share a birthday. It made sense however when the math was being done to show how this was possible. What would be the probability that two people out of a certain number had a birthday in the summer? How could you figure this out?

Guys I made a formula

(1-(364/365)^((x(x-1)/2) )))*100

I was expecting a reference to a movie.

This video taught me more about probability and how it can be used in real life situations. Obviously there are many more ways of using probability, but it does put the world in a whole new view. Probability helps give us an idea of the risk of a chance before we take that chance which can be seen as very helpful when making large decisions.

This showed me that math was really important in real life. It taught me that math is a thing that we have to use in real life situations. It showed why we need to learn math and why it is important in life. This video will be helpful to the people that have a question like "why do we learn math if we don't use them in real life?"

I really enjoyed this video, because it shows us that math can be brought in to real life situation, it also showed me how probability can be used to figure a lot more than you actually think. Before watching this video, I would've never thought that there's a 50% chance that two players have the same birthday in every match, but all the rules of probability prove that it is possible. I really enjoyed this video!

To calculate it faster by hand: 364×363×…×343=364!/342! So just type (364!/342!)/365^22 and you get the same result. (your calculator might not be able to handle the factorials so try using wolframalpha)

I am super surprised by the outcome of this video. It made me think very hard! I would've never guessed that the probability of two people out of 23 people are more people are more likely to share a birthday (by 50.7%) than it is for them to not share a birthday. It made complete since when the math was being done to show how this was possible. What wold be the probability that two people out of a certain number had a birthday in the summer? How could you figure this out? Also, are there any other numbers other than 23 that this works for? Very interesting and cool video!

What is the probability that someone watching this video also has the same birthday as the two players! 5th march thats me!

Wes Morgan moved to Leicester City.

So Basically, in a group of 23 people, there is a 50.7% Chance someone shares a birthday with you and a 49.3% chance that someone does not share a birthday.

Big up aux DNL maths de Jeanne d'Arc

Barring any genetic anomalies between contributed egg and sperm, each [human] parent contributes 23 chromosomes to their resulting child when they reproduce

Since 2012 the Australian Football League season has 23 home-and-away rounds, followed by the finals series.

So if you get a group of 46 people the chance for 2 of them sharing a birthday is 100%?

pastebin ZaDVP0FH .

n = 10 : Probability = 0.117

n = 20 : Probability = 0.411

n = 30 : Probability = 0.706

n = 40 : Probability = 0.891

I absolutely love these videos, but the markers were a bad choice. Watching these videos with headphones is just killing me.

Hey so I made a probability-based football video on how likely you are to win the Super 6 jackpot, taking inspiration from these Numberphile videos