There are some things in life that you just don't see coming.
The world is random, unpredictable.
Unlikely things can happen.
So, are you blessed with good fortune?
Or are you...
..one of the unlucky ones?
But maybe there is a way through this mess of chance.
Maybe the secret to being lucky is in trusting the maths.
APPLAUSE
CHEERING
Good evening, everyone!
My name is Hannah Fry.
Welcome to the Royal Institution Christmas Lectures.
And let's start as we mean to go on.
So, who wants to be our first volunteer for the evening?
Let's get you, there. If you want to come down. In the pink jumper.
Round of applause as she comes to the stage! Thank you!
What's your name? Megan. Megan.
OK, Megan, how are you feeling today? You feeling lucky? Yeah.
OK, good. All right. If you just want to come here,
just stand just there. Now, Megan, above your head...
AUDIENCE LAUGHS NERVOUSLY
..we've got a bag of gunge and there's just a little rope,
just there. What do you reckon we're going to do? Megan?
For some reason, I feel like it's going to fall on me!
Well, we thought about it. We thought about it quite hard.
But actually, it's not going to fall on you.
You're going to be the one who's going up there to help us
cut the ropes, so if you want to nip up there with Fran, just there.
Now, instead, I am going to stand maybe not quite underneath it,
but what we've got here, the bag of gunge is attached to a rope.
And just at the other end of the rope there, there's a tiny, little
weight that's balancing it there.
And once Megan cuts the rope, the gunge is going to fall
down this way.
And then, either I've done my sums correctly, in which case the gunge
is going to stop once it hits about here, or it's going to drop
all the way to the floor, go splat,
and then everyone in the first row is going to be covered in gunge.
OK? Definitely one of those two things.
Now, if we manage to get through this unscathed, I want
you all to burst into spontaneous applause.
And if this doesn't work, I'm just going to do the rest
of the lectures covered in gunge. OK?
All right? Sound good? All right, Megan, how are you doing?
Yeah! OK. You ready to cut rope?
Are you ready? Do want to give us a countdown? OK.
Erm, five, four...
Three, two, one... ALL: Two, one...
Whoa!
Ha-ha!
APPLAUSE
Thank you very much, Megan.
You haven't ruined the lectures, so well done for that.
That was great. OK. So what happened there?
We had a bag of real gunge there,
which genuinely almost did,
in fact, splat all over us.
Oh, no.
LAUGHTER
It's fine.
Something quite special happened there, something quite
extraordinary there happened, to stop that gunge
from splatting everywhere. If you want to watch this back
in a little slow-mo. So the weight was just enough to make the rope
swing around that bar
and wrap around enough times to cause the friction to stop
the gunge from dropping.
We've got another angle of this.
So here's the second angle.
Now you think it's going to drop all the way down. Just the last minute,
there's just enough there for it to wrap around itself.
Unwrapped itself there for a second. But we were safe, we were OK.
We didn't get splatted. Now, here's a slightly smaller version here to
explain what happened.
Now, we calculated that if this weight here is 14 times lighter
than the item on the other end, then that is enough to make sure
that it would always stop itself from falling.
Now, I knew that for sure, of course. You all knew,
surely, that I knew that for sure.
But still, you know, it's inevitable that you feel a little bit worried.
And that's, I think, is something that you have to accept.
You know, we're all humans. We are...
We find it hard to override our instincts.
We're not built for calm and rational thought.
But that is the reason why we created mathematics. It's a way
to step outside of ourselves and be objective, a way to calmly
calculate something and be sure of the answer, rather than just rely
on what our messy minds might tell us.
And you know what? I'm a very big believer that maths can offer you
a new way of looking
at almost anything, because I think if you take the time to look,
thank you very much,
there are mathematical patterns hiding behind almost everything,
even things that feel like they are very far away from being
mathematical, even things that you think should be completely random.
Now, we're going to come back to this one in a moment.
But in the meantime, my fellow mathematician, Matt Parker, has got
a perfect example for us, haven't you, Matt? Hello. Yes.
I've got a huge group of people out here in the entranceway to the RI.
If you'd like to come out and join me. Sure thing.
So, thank you very much, everyone who came along.
Bizarrely, all wearing red hats. That's fantastic.
And all of you wearing yellow. Well, how fortunate!
This must be the new fashion.
So we're going to try an experiment with all of you in a moment
to see what happens when you're moving through a crowd.
OK. When you're moving in a crowd,
I mean, everyone's making their own decisions.
It's random, surely?
It feels very random, very chaotic, unorganised.
You're being bounced around.
However, there are some patterns and, actually, we...
WHISPERING: ..want them to walk naturally, so we're not going to
tell them when the experiment starts. OK. Watch this.
CONVERSATIONAL VOLUME: Actually, I'm really sorry, everyone.
We've just realised, don't move yet, that we wanted the yellow hats
on this side. We wanted, I know, the red hats on... It's not me,
it's coming from upstairs. So I think we're clear. OK. If you can.
Quick as you can. If you just swap over sides, exactly where you
are but opposite across. OK, so you can see here,
we've got an overhead camera rigged up so we can see.
Come on, everyone, as quick as you can.
Hurry up. Come on, faster, please.
We've got a TV show to do. Here we go.
So... They're not all jumbled up. It's not random, is it? No.
Right. Look at this. So, because everyone...
Having some mild issues here. Everyone's just following each other
and you end up with these very clear lines.
So if these were random, it'd be a complete mix.
Instead, we've got these fantastic stripes.
Come on, everyone. Let's keep it moving.
You end up with these fantastic stripes.
So, everyone. That was fantastic. Thank you so much.
And that was the experiment.
So, thanks very much for getting involved.
Thank you. Thank you, Matt.
Now, it turns out there are actually a lot of similarities
between the maths of how people...
AUDIENCE LAUGHTER
Be quiet down there! ..how people flow through a corridor
and how fluids behave.
And if you can understand how people move when they're in a crowd,
you can predict how they'll react
in the case of an emergency and that's something that's incredibly
important if you are designing buildings
or stadiums or train stations,
to make sure that your design is as safe as it could possibly be.
And that, really, that is the point. That is what maths is all about.
It's all about discovering those invisible patterns
like this beautiful pattern left here by that swinging pendulum.
Isn't that gorgeous? Much neater, I think, than you would expect.
But, you know, maths isn't just about spotting patterns.
It's also about using them to your advantage.
So here is something that might look as though it's random.
Best part of Christmas, obviously. Who gets the toy?
Who gets to wear the hat?
Now, here you go, if you want to have a go on this,
because you only do this, go for it...
..a few times a year,
you may not notice, there we go, you can have that one...
..you may not notice that there is, actually, a pattern to this.
But luckily, I have done hundreds of these.
And there is a knack to winning. But I can explain to you.
So what you have to do - I'll teach you, right, then I can show you.
So what you want to do, you want to hold your end lower than the other
person, use two hands with a really sort of steady, firm hold,
and you don't want to do any twisting or pulling.
You don't want to really tear this.
So what you're trying to do, ultimately, you're trying to let
the other person do all of the work so that then...
Ahh! ..you end up winning.
Well done! You can have the hat, now. Enjoy!
Now, I've got to be straight with you.
This isn't going to work every single time.
Especially not if your opponent knows the same trick as you
and you're just steadily trying to get lower and lower
than the other person.
But the maths of prediction isn't about saying what's definitely going
to happen. It's about considering all of the possible outcomes and
working out what's likely to happen.
So, to show you what I'm talking about here,
join me in welcoming University Challenge mathematician
and schoolteacher Bobby Seagull.
Hey, Bobby! It's very good to see you!
APPLAUSE DROWNS HANNAH'S SPEECH
What have you been doing there, Bobby?
So I've been flipping coins hundreds of times.
OK. On a sort of fair, unbiased coin.
You'd expect the chance of a head or tail to be 50/50. Yeah.
So I thought, let me try and test this by flipping a coin six times
in a row. So you'd expect, six times in a row you'd expect three heads,
three tails, right? Yes.
But sometimes things don't quite work out the way we want them to.
So, have you been flipping a coin six times in a row,
many times in a row?
Yes, Mr Seagull's a true maths hero teacher, flipping it 2,000 times.
No, no, no. I had to enlist the help of school students.
Nice. So we went across London,
found students from Westminster Academy... Thank you.
..and students from my very own school, Little Ilford.
And that's these guys here, right? Yes, exactly. These students here.
So we got them to line up, all with a coin in their hand, and flipping
the coin six times. OK.
If they get a heads, they take one step in that direction.
And can you guess what happens when they flip a tail?
I'm going to go this direction. You're right.
And let's see what happens when they flip the coins.
So this is like a visual representation of the six flips.
OK, so that's the third flip there, is it?
Yep. And that's the fourth.
You can see wind blowing the ties about.
So, spreading out, every extra flip, they're spreading out more and more.
Exactly.
And now, if we get the students to move down towards the graph...
Oh, it's like a human bar chart!
..you start to see a pattern emerging.
Ah, those are very good. So there's way more people in the middle there.
Yes. And roughly the same number on the tails and the head side.
And a few have got six tails and six heads.
So these are three heads, three tails on this side. Exactly.
All here, I mean, these guys must have thought they were very lucky.
And down here, all tails. Exactly.
But you didn't just do this once either, did you?
I mean, this is like nested, lots of levels to it.
Exactly. So many classes repeating it many times
to get us a better dataset. OK.
Here we see, this is Westminster Academy students.
So, I mean, pretty much every single time we're seeing most people
being in the middle. But you always get these bits at the end.
You always get the extremities.
But the beauty comes when we try and combine all the information.
So here we see all these little dots, they're a student,
a proud, hardworking maths student.
And you put them together and we get what looks
like a normal distribution curve. Ahh!
And this is what the maths would have predicted from the beginning.
Exactly. Very lovely. Thank you very much.
Bobby Seagull. Thank you!
APPLAUSE
The point that we're trying to make here
is that life is full of randomness.
But even in the midst of chance, maths can still tell you what might
happen and also tell you just how likely that might be.
Which, of course, is precisely what predictions are all about.
So, OK. Let's take a prediction about the future
that we are all very familiar with -
what the weather is going to be like tomorrow.
So I got this from my phone earlier. This is my weather app.
And this here, it says that tomorrow the chance of rain is 20%.
Question is, what does that 20% actually mean? When it comes
to talking about the chance of rain, what does that 20% actually mean?
Who wants to kick us off? You want to make a guess as to what you think
20% means in that context?
The chances are probably 20%, it's going to cover.
OK, yeah, 20% is going to cover.
So you think it's about 20% of the space will get covered in rain?
What do you reckon? 20% of what? Do you want to give me a guess?
Anyone here want to give me a guess? Yeah, go ahead.
How much of the country is going to have rain in it?
OK, good. Good response. OK. OK.
Well, let's ask someone who really knows.
I want to introduce you to someone who, as you will find out, their
life depends on correctly predicting the future.
I'd like you to join me in welcoming Professor Chris Jackson.
Hey, Chris. How are you doing? Hi. Good, thank you.
APPLAUSE DROWNS HANNAH'S SPEECH
So how did they do? In terms of understanding that 20%, how did
our audience do? They did pretty well, yeah. They did very well.
What does it actually mean?
It means that if I was to live
the same day over and over 100 times, it would rain
on 20 of those days.
Does it tell you whether you should bring an umbrella or not, though?
I'm a pessimist. You should always bring an umbrella.
Yeah. I'm the same. No-one likes getting wet, right? No.
No-one likes getting wet. But you don't predict the weather, do you?
No, I don't. Something much more risky.
Yeah. I try and understand when, how volcanoes behave
and when they might erupt.
And you use those predictions to actually go in volcanoes?
Yes, I do. And we've got some of your photos here.
I mean, that's pretty close, right?
Yeah, it's pretty close. But it's important work we're doing
as scientists. You know, we handle the risk.
And so you're calculating this risk at all times, are you?
Yeah. We have visual observations on the volcano, how active it is.
But also, we have an idea of what the likelihood is
that this volcano may erupt while we're there.
Have you ever had a close call?
I've never had a close call. Not yet, at least.
OK. All right.
Well, of course, because this is the Christmas lectures,
we've got a model of a volcano to demonstrate.
So you can tell us a bit about how your predictions
work, using this thing here. OK.
Yeah. So, the thing with volcanoes is they're very difficult to see
inside and underneath.
So we have to rely on a number of observations while we're looking
at the volcano.
So one thing we can use is analysis
of the gas that comes out of the volcano.
So by looking at the amount of gas and the type of gas, because gas
is contained in magma,
if we measure that, we can have an idea if magma's moving
into the volcano and the volcano
might be about to erupt.
And so if you see this kind of gas, you're calculating the risk
of an eruption all the time? Yes, exactly.
How much gas and what type of gas may actually kind of give us
an indication of what the nearness of an eruption is, yeah.
And are there other things that you're looking out for?
Yeah. So another thing we can look for is,
magma moves into the volcano, it pushes against the rock,
the rock fractures and releases energy in the form of earthquakes.
So, if we can measure the earthquakes, where they are in the
volcano, then we can actually measure the earthquakes in terms
of how strong they are as well.
With the gases together, we may be able to use that in some
sort of like forecasting sense, so, what's the likelihood?
Are there some signs that are sort of absolute no-nos, where you won't
enter a volcano after that point?
Yeah, I think if, you know, there's lots of gas, lots of earthquakes,
maybe even lava coming out the top of it, that's probably time
to leave! Time to...
Time to take a bit of a step back. Time to step back, yes.
Maybe let's do that! Let's do that.
So this one looks like it's imminent. OK?
NERVOUS LAUGHTER
Thank goodness you've got big glasses on then, huh?
Have you ever been at an actual volcanic eruption?
I have. Yes. Because this stuff is really serious, right?
This is not just playful... Absolutely serious.
It's serious for the people who work in and around volcanoes.
But it's even more serious
for the people who have to live with them every single day.
Yeah.
So this one looks like it's imminent.
This one looks like it's imminent.
I'm going to say, you know, probably 90% chance at the moment
it's going to erupt. OK.
NERVOUS LAUGHTER
Whoa!
AUDIENCE GASPS
That's 100% chance! Yeah. Impressive!
AUDIENCE WHOOPS
Fantastic! Thank you very much! Cheers. Thank you!
There is something that's important to say about a 90% prediction.
10% of the time that volcano won't explode.
And while it sounds like I'm saying something quite obvious there,
when you are dealing with the messy world of uncertainty,
you need to understand that being wrong is sometimes part
of prediction, because sometimes errors can have unexpected
consequences. Now, let me show you what I'm talking about here,
because we have just had a delivery of 100 Christmas presents
and the rumours are that, hiding amongst these hundred presents,
there are five brand-new smartphones.
And one of you gets to come down and open one
of these presents at random.
So, who wants to come down?
LAUGHTER
What a surprise. Perfect.
All right. Let's see who we can find.
If you want to come down there, yeah. Perfect. Round of applause.
What's your name? Yee-ling. Yee-ling, perfect.
OK, Yee-ling. All right. So if you want to stand just over there. Now,
you're going to get to pick one of these presents completely at random.
Five of them are phones, the other 95, they're kind of rubbish presents
like socks and satsumas. No-one wants any of them.
And because you only get to pick one present, we want to give
you the best possible chance at getting a phone.
But luckily, Matt Parker has invented
a very special present scanning machine to help you.
Haven't you, Matt?
Look at this! All right. Yeah. Amazing!
This is my Xmas Ray Detector .80.
And what we can do is we can put these presents
through the scanner. Actually, do you want to come with me
around over here? If you want to stand behind like the conveyor belt
over here where they come out, if I turn this machine on and I start
putting the presents in the top here, it will try and detect if
there's a phone in them.
If there's no phone, it just spits them out the same way they went in.
If it thinks there's a phone, it rewraps it. Look at that!
Ooh! That's a winner.
So, if it says 'phone', you put it on the table.
If it doesn't say 'phone', we don't care. Right?
Just down there somewhere. Is that OK? Are you ready?
I'm going to start piling them in here.
You sort them out. Here they come.
You seem pretty happy with this machine, Matt. I'm very proud.
It is a... How accurate is it?
This machine is 80% accurate. OK. 80% accurate. That's pretty good,
Matt, 80% accurate.
OK. So, then, one of these, then,
that's rewrapped as a phone,
what do you reckon are the chances that this is a phone?
Shout out what you think it is.
AUDIENCE OFFERS SUGGESTIONS
OK. All right. Let's think this through, then.
So, your machine, how accurate is your machine?
80% accurate. OK.
So your machine is 80% accurate.
There are five phones in total.
80% accurate means that it's only going to find four of them, right?
Which does, Matt, that does mean one
phone's going to end up on the floor.
Yes. The downside to 80% accurate is it's 20% inaccurate. Ahh!
But on the upside, 80% accurate. OK.
So, I mean, you make a good point.
Thank you! OK, one phone on the floor.
It's not the end of the world. Still gives you a really good chance
at finding a phone.
There's something going on there, though.
Hang on, hang on, hang on, hang on. Stop the machine.
Whoa-whoa-whoa. Whoa-whoa-whoa. OK. Hang on. Matt...
Yeah? There are way more than four phones on that table.
Yeah. It's 80% accurate
at both detecting a phone
and detecting NOT a phone.
Are you saying, hang on, are you saying this machine is taking socks
and satsumas and wrapping them as phones when they're not? Yeah.
20% of them.
I don't know if I brought this up earlier, Hannah,
but it's 80% accurate.
AUDIENCE CACKLES
Yeah, but Matt, there's 95 socks and satsumas here. Yeah.
20%, that's not, that's 19 rubbish presents in that pile of phones.
Yeah, but 80% of them are down here.
So, the problem is like, this is 80% accurate,
it doesn't mean these are going to be 80% phones. Yeah.
It just means, I'd like to recap, that my machine is 80% accurate.
OK, OK, OK. But right, by the time you're finished, you're going to
have, what, 23 presents over here?
Only four of them are going to be phones.
That gives you a four in 23 chance of finding a phone.
It's about 17%. So it wasn't... OK.
Well, do you want to pick one at random?
I mean, you can open it, have whatever's inside.
It's overwhelmingly likely to be a satsuma.
Well, you can keep it, though. Merry Christmas.
Thanks for your machine, Matt. My pleasure. Amazing!
80% accurate!
That kind of error, mislabelling satsumas as phones,
it's something that's called a false positive.
And it goes to show how maths can sometimes really prove
your intuition is wrong.
Now, false positives, they're everywhere.
You see this every time you go through an airport.
Think about all of the people that are pulled over from the scanner
for having lip balm and hair straighteners in their luggage.
And the number of people who are false positives massively
overwhelms the number of real weapons that the security team
are looking for.
But there is a really dark side to this kind of error, too,
because imagine if, instead of scanning for presents,
we were screening for cancer.
Now, even if a cancer screening test, like a blood test
or a mammogram, the ones that work with 89% accuracy
because they are not perfect, there will always be false positives.
There will always be people who believe that they have cancer
when, in reality, they actually have nothing to worry about.
This is kind of present scanning,
but from the perspective of the gift box and you can imagine
just how much pain and anxiety it might cause to be mislabelled.
Now, this doesn't mean that you shouldn't be screened,
but it's really important to understand
what these results mean.
But OK, if you can accept that being right isn't always possible,
if you can really understand these numbers, then you can still use
them to your advantage, because sometimes luck
really is a matter of life and death,
or in this case, zombies.
So to explain this properly, I would like you to join me in giving
a warm welcome to an epidemiologist
from the London School of Hygiene and Tropical Medicine, Ros Eggo.
OK, Ros, you study the mathematics of disease, right?
How much of it is luck and chance?
Well, there's a lot of chance that's involved
in the transmission of disease.
So if there's an epidemic happening at the moment, the chance
of you getting it depends on how many other people
there are that have the infection at the time.
And then if you happen to meet one of those, which is more likely
when there's a lot of people who have it,
there's also a chance you'll get it from them or not.
And if you have some pre-existing immunity, maybe
you've been vaccinated or you've had it before,
then the chance of them passing it to you also goes down.
So there's a lot. So, then, how can maths help you? Mmm.
It's really difficult to predict, on an individual level, if somebody
will get it. But on a population level, with these nice, big numbers,
there's some things we can predict - when the epidemic will go
up and when it will come down. We try and predict the peak.
And we try and predict which groups might be at risk of infection.
Well, talking of epidemics, there are some rumours
of a zombie apocalypse about to hit.
OK, so, everyone here, underneath your seats,
you should have a zombie mask
and you should have some ping pong balls.
Now, these are your zombie germs. Mm-hm.
So how it works is, if a zombie germ touches you, you become a zombie.
You put up your zombie mask and then you take your zombie germs
and you throw them straight up in the air as high
as you possibly can. OK.
And in a moment, I'm going to start off this infection.
So everyone start with your mask down to kick us off,
but you can make a prediction about what might happen here. Um.
So over here, nobody has any protection against zombies,
zombie infection.
So we're going to expect a lot of cases and possibly quite quickly.
OK. All right. Let's give it a go. Is everyone ready?
Everyone got their balls in their hand? All right. We're going to
start this infection. Here's the zombie germs coming at you.
I'm going to... I'm directly targeting people.
OK. Oh, already.
So, we've got little, actually, a few different patches here.
We do, yeah.
In fact, they're starting to get a little bit frightening around here.
And it's travelling backwards through, and now a big cluster of
zombies there, right in the middle. Uh-huh!
How realistic is what they're doing, compared to how normal, real
diseases spread?
Well, obviously, for real diseases, it's not quite so frightening
as what's happening up here.
But we use similar type of methods, using chance to pass on infection
to understand how real diseases spread around.
But for zombie infections, nobody ever recovers.
Nobody, OK. And that's, in the real world,
people usually recover.
I think there are, in fact, OK,
so if you...
..it's still going! It is still going!
And if you are not a zombie,
could you stand up for us? How many people are there?
Oh, we've got some!
Three people who managed to escape the zombies!
You also can't target people directly with your zombie germs.
That wasn't part of the rules. OK. Everybody, sit down.
Thank you very much. Well done. Now we can do this again, but this
time, we can use some kind of zombie defences. Exactly. Yeah.
So over here, there's going to be some protection against
infection, and these people are going to be completely protected.
OK. So those of you who have, you've got protective masks
under your seat and this makes you
completely immune from zombie infection. It does, yeah. OK.
So if the zombie germs touch you and you're wearing a face mask,
you're wearing a protective mask, don't worry about anything.
Don't put up your zombie mask, don't throw any germs around.
You're completely immune. And we'll see what happens now.
And what's your prediction about what will happen in this case?
Well, there's a lot of protection up here. So I think the epidemic will
be over very quickly and maybe not many people will be infected.
OK, let's give it a go. Here we go.
OK.
So, it's still started. We've got a few.
Oh!
OK, I mean, that stopped almost immediately.
OK. So those of you who are not wearing a protective mask, but also
not a zombie, could you stand up?
Oh, goodness me. Look at that! Wow, that's a lot.
And there's a point to it. Thank you very much, everyone.
You can sit down. There's a point to all of this, right?
Yeah, exactly. So the protection that we had in the population
from the people wearing masks who are vaccinated against infection
has protected everybody in this part of the audience
from getting infection.
And is this the same thing that happens
when we're vaccinated against diseases?
Exactly. It is.
So we have here, kind of, this community
has immunity from infection.
And so, even the people who weren't themselves vaccinated
have been protected by the protection
in the whole community.
So how much does the maths of modelling disease
make a difference back in the real world?
So we take experiments kind of like this, but in the computer,
take things that we know about how infection spreads
and about the population in general,
and the goal is to use the computer, use our simulations, to figure out
ahead of time what would be the best interventions.
What should we do to decrease the number of cases in everybody,
without it having to happen?
So it doesn't matter whether you're talking about flus or Ebola
or, I don't know, TB in cows, you can use these mathematical ideas.
Exactly. Yeah, for human diseases, for animal diseases, even for
plants, it's really useful. And demonstrates that vaccines
really do make a difference. It does. It does.
Would you rather live over here with all these zombies or over here?
Definitely over there. Definitely over here.
Ros, thank you very much. Thank you.
There is a really simple point in all of this. If you've got maths
on your side, it's not just about spotting patterns.
It's about using what the numbers tell you
to bend the world to your will.
And there is one game of luck, skill and stats that actually captivates
millions of us every single week, because believe it or not,
the Premier League is awash with mathematicians.
So, here's the staff photo from Liverpool Football Club.
You've got the team manager there, obviously a very important job,
but here, this is a group of mathematicians.
These guys are the unsung heroes of Liverpool football team
and it's their job to make the team as lucky as possible.
So please join me in welcoming Tim Waskett.
So, that's you in that photo, Tim? Yeah. That's me, just there.
All right. So how on Earth do you go about changing a football game
into something to do with numbers?
So the primary currency that every football game is based on is goals.
Obviously, that's the most important thing.
And it's our job to turn every action on pitch, every pass, every
throw in, every tackle, every shot, into a goal probability.
And I think we've actually got an image from your team.
So this is showing you the darker the colour,
the darker the red, the more likely you are to score?
I mean, from there, it's pretty easy, right? Yes. Exactly.
So this is taken from literally hundreds of thousands of shots
through major leagues all over the world.
And by looking at where the shots take place, how often they became
a goal, gives us a probability of a shot from a similar situation,
ultimately ending as a goal.
Now, I understand that there's a little game that you play
with all of this, of trying to guess what the maths says
is the probability of a particular shot going in. Yeah.
I think we have a little clip.
So, we call this "the expected goals game". OK.
So what game are we watching here?
So this is a friendly between Tranmere Rovers and Liverpool,
this is a pre-season friendly. And you paused the footage just...
Yep. So, he's about to do a header.
So he's about to do a header and he's right in front of the goal,
there, very close. So what do we think the probability of this shot
turning into a goal is?
What does the maths calculate the chances of this turning into a goal?
We have some options. Do you reckon it's 50%,
75% or 99%? OK.
Shout out your answers. What do you think it is?
What do you reckon the maths says is the chances?
AUDIENCE RESPONDS ENTHUSIASTICALLY
Oooh, 75 came out quite clearly there.
All right, what did the maths say?
Well, the actual answer here is 99%.
SIMULATED CHEERING
So, that means in exactly the same position with exactly the same
surroundings, if you reran these 100 times, it would only not
result in a goal once. Exactly.
So, 99 shots of a similar sort of position will end in a goal,
and only one will get saved by the goalkeeper. Oh, OK. All right.
Let's try one more. We've got another clip for you.
Here we go.
Oh, OK, so he's much farther out here. Much further out,
and he's also not central onto the goal, he's off to one side.
So we know it's going to be a lower chance.
It's going to definitely be a lower chance.
But what does the maths actually calculate it to be?
So we've got some options for you.
All right. Do you reckon
the maths says that this is 4%, 7% or 10% chance of getting a goal?
What do you reckon? Shout it at me.
AUDIENCE RESPONDS
Oh, everyone's going in the middle there.
What's the answer? You're spot-on. It's actually 7%.
And let's see what actually did happen.
Ah, a miss! One of the reasons
that that was only 7% and not any higher was because he shot
it straight at the goalkeeper.
I mean, that's always a big mistake.
But it's not just about strikers that you're translating
into numbers, is it? No, exactly.
So this is the easiest thing that we can do, but we can do
a similar calculation for every other event on the pitch.
So any time the ball is passed, for example.
OK. So to help us to demonstrate this,
I'd like to invite onto the stage Bertie and Jamie
from a London youth team.
Thank you very much, guys. Thank you. So...
Bertie and Jamie are just going to have a bit of a kickabout. Yeah.
Tell us how this works, then. So for roughly 200 games per weekend,
we get data involving every single ball touch in the game.
So, the way the data is collected, every time that a player passes
the ball, they'll mark it on the pitch and they'll say
this is the position on the pitch and the player who made that pass,
and then there'll be somebody watching for the other team
making their passes.
So two people will be going backwards and forwards, marking
up all of these events. So roughly every second or so, there's a new
pass, so it's pretty frantic.
So you just have someone there to kick and kick and kick. It doesn't
sound like the most exciting way to watch football. No. Well,
thankfully, it's not us who has to do this work. We actually have
a data supplier who provides us with these data, these files for us. OK.
Bertie and Jamie, thank you very much for your help there. Thank you.
So what do you end up with once you've done all of this?
So for every game we get
approximately 2,000 ball touch events.
And that tells us the position of the player who makes the pass.
But what that doesn't tell you is where all of the other players
are on the pitch at that moment.
But you can get hold of those numbers?
So we can. For the Premier League games, we get
what we call tracking data.
And so this is a set of cameras all around the stadium and that's
monitoring the position of all of the players.
So, 22 players plus the position of the ball.
And it does that for 25 frames a second for the full 90 minutes.
So you end up with approximately 1.5 million data points.
That is a lot of numbers!
And in fact, we've got here on the gigantic spreadsheet, essentially.
So, this is just one game. And you're watching a game
of football here, basically.
Yes, exactly. Through numbers.
OK. Interesting. I mean, maybe less exciting than watching
Match of the Day. Well, it depends on your perspective.
But you're not just collecting these numbers, are you?
What do you do with them?
So this data can give us a goal value for every position
and for every player on the pitch.
And what does it end up looking like?
I think we've got a little... Yeah, we have a little animation.
OK. So tell us what we're looking at here. So this is what we call
pitch control. So you can see the players are in the circles there,
and the arrows represent the direction and speed
that they can travel in.
And you've got a blue team and a red team. Yep.
So the red team here is actually Liverpool.
And the areas in red are places that the Liverpool players can get
to sooner than the players who are in blue. Ahh!
Based on how quickly people run. Yes.
And based on where the ball is. Exactly.
So, for example, the ball, in this particular example,
is that yellow dot there.
And if this player, who is currently in possession of the ball,
this is number ten, this is Sadio Mane,
his best option at this stage, is to probably pass to one
of these red areas. And, in fact, he ends up passing the ball up into
this red zone here to be picked up by player 66,
which is Trent Alexander-Arnold.
So this is a real game and we can play on watching the game
through this heat map here.
So, this thing here, what's this telling us?
So, this is what I was talking about before, about turning
everything into a goal probability. So this value now, 1.3%,
this is the probability that a goal will be scored with the ball
in this position within the next 15 seconds.
It's quite hard from there. Really.
From there, yes. Because you're so far back. You've got a long way to
go before you reach the goal. It's very accurate.
But we can play on this game and see how it evolves.
So, the ball does get passed over.
Yeah. It gets successfully received.
Still not a very high chance of scoring a goal from there.
No. But now, Trent Alexander-Arnold,
his best option is to run into this position, here. Ahh.
So he's now dribbling the ball forward.
So, are you using this information to look at what did happen and work
out what should have happened? So, we use this in a number of ways.
The main way we use this is
to evaluate player performance after the game.
And in this particular game, if we play on one more time,
what was the result of this sequence?
So if we pause it right about now,
you can see Trent Alexander-Arnold
now has the ball very close to the goal.
He's in a good position, but his best option now is to pass
into this red area here, where it can either be received
by Mane or Shaqiri, who is number 23 down here.
One of these two players is most likely to get
to this red zone.
And in actual fact, what happens in this particular situation,
is that Mane receives the ball
right round about here, and he scores a goal.
Which is exactly what you want. Exactly.
So are you using this stuff to just analyse your team
or are you using it to analyse other teams, too?
So the advantage of this is we see all of the players at the same time,
which means that we can analyse all of the players
within the Premier League and a large number of players in all sorts
of other leagues around the world, using the ball touch event data.
And that gives us some really good information on which players
are doing well and who we might be able to sign in the future.
Ultimately, to give you the best chance possible at beating your
opponent. Exactly. Amazing.
Tim, thank you so much for joining us. Thank you.
APPLAUSE
That's the thing about being lucky.
Sometimes it's not just about what YOU do,
but also about who you're up against,
and if winning is what you're after, something rather intriguing happens
when you start to look at the maths of competition.
OK, so for this, I would like two volunteers who are willing
to compete against one another.
OK, perfect. If you want to come down here.
That's one, and we'll get someone from over here.
Round of applause. Welcome to the stage.
APPLAUSE
What was your name? Nat. Perfect, OK, Nat.
Thank you. And what was your name? Jasmine. Hm?
Jasmine. Jasmine. OK, Nat and Jasmine, right, OK.
This game is called Goodie or Baddie,
right, and the reason why is because in every round you have two choices.
You can either decide to be a goodie,
in which case you put on your red hat,
or you can decide to be a baddie,
in which case you put on your purple hat.
And what we're going to do is we're going to play four rounds,
and in each round you have a chance to win some points.
If you get to 12 points in those four rounds,
then you win an amazing goody bag, OK? I mean, it's pretty special.
So this is the way that it works, OK?
If both of you decide to be a goodie,
then you will end up getting three points each.
If both of you decide to be a baddie,
you will end up getting one point each.
But if one of you decides to be a goodie
and the other person decides to be a baddie,
then the baddie takes everything.
They get five points and the other person gets nothing.
OK? Remember, four rounds. You have to get 12 points.
You happy? OK, all right.
Turn around, so you can't see each other's choices.
Here we go. OK. Here we go.
So, red for goodie, purple for baddie.
Make your choices now.
Oh!
Turn around and have a look at each other.
Oh! OK. All right. Five points, five points there.
One, two, three, four, five.
OK. All right. Round 2. Round 2. Here we go. Here we go.
OK. Round 2.
He stole some points off you that time.
Let's go for Round 2.
Go.
Oh! Payback!
Turn around, turn around.
Only one point each. You blocked him there.
OK, right. Round 3, Round 3, here we go.
Make your choice for Round 3.
And turn around and have a look at each other.
Argh. Argh!
You got him back. You got him back.
OK. There's still one round left.
One round left, turn around.
Here we go. OK.
Do you want to take your hat off and make your choices?
Go for it.
LAUGHTER
What an unsurprising ending.
Turn around, have a look at each other. OK.
So neither of you... I'm afraid neither of you got up to the line.
Neither of you got into our points.
But you know what's strange, though?
There were four rounds.
12 points was all you needed to win a prize.
If both of you had just played goodie every single time,
then you both would have walked away with an amazing prize.
The fact you played baddy, you blocked each other.
But, you know what?
It's understandable, because, OK, let's say...
Mind if I take this hat off your head for a second?
Let's say your opponent had chosen to be a baddie.
In that situation, you've got two choices, right?
You can be a goodie, in which case you get no points at all.
Or you can be a baddie, in which case you get one point.
So, if your opponent's a baddie,
being a baddie is definitely the best thing to do.
But what if... Do you mind switching your hats for me?
If your opponent instead had chosen to be a goodie,
let's think about what was available to you.
Be a goodie - you get three points.
Baddie - you get five points.
So even in this situation it's best off for you to be a baddie.
So it turns out it doesn't matter what your opponent does.
In any one round, it is always best for you to play the baddie,
even though if you both just played goodie,
you both would have ended up getting a prize.
So thank you very much to my volunteers.
You're both very bad!
APPLAUSE
Not very Christmassy, is it? Being bad to each other.
Actually, this is a very famous game among mathematicians
and it goes to show that winning isn't always about luck,
but it also, I think, highlights one of the great tragedies of humanity
that sometimes the tempting thing to do right then and there,
doesn't actually lead to the very best outcome overall.
And actually, you see this time and time again,
the very tiny little selfish choices that we all make,
they add up to mean that eventually we can all lose out.
So it doesn't matter here whether you're talking about climate change
or plastic waste or North Sea fishing.
We often get sidetracked by the really small choices in front of us
rather than holding the big picture in our minds.
And part of that is a mathematical reason, as we've just seen
with that game, when the incentives aren't set up
to encourage really good behaviour.
But I think it's also worth remembering that as humans,
we are not these perfectly rational objects.
If you really want to be lucky,
then you have to take all of the weirdnesses of humans into account.
So, OK, let's have a look at some of your weirdnesses as an audience.
Underneath your seats, you should have a whiteboard and a pen.
What we're going to do, if you get those out and get them ready...
What we're going to do is when I say "go",
I want you to pick a number completely at random
between one and ten.
I want you to write on your whiteboard when I say go,
and then we'll hold them up. OK.
Number between one and ten, completely at random.
Go.
And then hold it up when you're finished,
and let's have a look at what you've got.
OK, OK, let's have a little look at what we've got.
OK. What can I see here?
OK, OK. All right.
I'll tell you what, if you wrote down a one, could you stand up?
Oh! Hardly...
Certainly not 10% of the audience, that, is it?
Thank you very much, sit down.
If you wrote down a ten, could you stand up?
Oh, again, only a smattering.
How intriguing. All right. Sit down.
If you wrote down a seven, could you stand up?
Ooh! I see!
All of a sudden...
Thank you very much. You can sit down.
Now, in fact, actually, if you play this with big groups of people,
it almost always happens that seven is the most common number,
to be chosen. Huge swathes of people will choose a seven.
And there's a kind of strange reason for that.
If you're picking a random number, one feels like it's too small.
Ten feels like it's too big.
Five is kind of too much in the middle.
Two's even - can't choose that one.
Eight's sort of too neat.
All the other numbers fall away, and you're left,
if you're picking a number at random,
with only seven really feeling like the random number.
I guess the point in all of this is that you have to remember
that human behaviour really isn't actually random.
Humans are not very good logical machines.
And what that means is that if you really want to make yourself lucky,
you've got to go beyond the world of maths,
because, you know, there is actually some evidence
that shows that just thinking you are blessed with good fortune
means you can actually make your own luck.
And there is someone who knows quite a lot about this.
This is Dr Michael Gervais in Los Angeles.
He's known as the secret weapon of top athletes around the world.
Hello, Michael. How are you doing?
I'm fantastic. Great to be here. Thank you, Hannah.
You have worked with a number of amazing people,
haven't you, Michael?
I've been fortunate, yes, for sure.
What is it that you do?
Well, by trade and training,
I am a sport and performance psychologist.
So you're trying to get people in the right mind-set to win?
Yeah. There's three things that we can train as humans.
We can train our craft, our body and our mind.
And world-leading thinkers and doers
are not leaving one of those three up to chance.
And the science is informing us of best practices to be able
to train our mind, to be able to adjust to the unfolding,
unpredictable, unknown.
So do you have any top tips for us
as to how to train our minds to get the best out of ourselves?
I wish I had tips and tricks and hacks and short cuts,
and there really aren't many,
and so if we can learn from the best in the world
how to fundamentally organise your life, to strengthen your mind,
to deal with the unknown.
And what we've come to find out is that there are a handful of skills
that people practice - mindfulness being one of them,
optimism being another.
And those are trainable skills.
Confidence is a trainable skill.
Being able to be calm in any environment is a trainable skill.
So there's a handful of a few that are most employed by most.
I hear that you've worked with a few daredevil skydivers.
I think we have a little clip of one of the people you've trained.
Just tell us what Luke Aikins did. He's here in the green. Absolutely.
So, Luke Aikins is one of the most extraordinary base jumpers,
aeronautical flight folks in the world.
And what he did - he was the first ever to do this -
is that he jumped from 30,000 feet, which in and of itself is a big deal
because you need oxygen masks to be able to carry enough oxygen.
But he did it without a parachute.
Without a parachute?! He was the first person...
Yeah, and he's the first person to do that,
and he jumped into a 16-storey net that he and his team built.
And so you were behind the scenes in advance of this event,
trying to get him to focus in the right way?
Yeah. When your life is on the line and the stakes are high
and consequences are real,
nobody leaves very much up to chance.
And so training your mind is one of the ways to help somebody
have great command of themselves under duress.
And so absolutely, yeah, this is one...
This is an incredibly dangerous project.
Do you think he's mad?
LAUGHTER
I get that question a lot.
No, he is actually just like some of the greatest mathematicians
in the world, just like some of the greatest historians,
is that they go to the edges of their potential.
And when somebody goes to the edges of their potential,
they're taking the next natural step.
And in some cases, it changes humanity.
In other cases, maybe it changes a family legacy.
But this is what the greats do, is they add to their body of work
by extending their capabilities.
Now, in those extended areas,
in that place where they're not quite sure
if they have what it takes,
that's where luck... We want to diminish the amount of luck involved
and make sure that we're increasing them out of skill.
And so is a lot of this about helping them overcome their nerves?
Well, certainly the emotional component to exploring one's
potential towards mastery, towards high performance
and achievement and success - emotions are part of it.
And emotions and thoughts and environment
are the three legs to the stool.
And while we might not be able to ever really manipulate our
environment, we can manage our thoughts
that influence our emotions.
So those are the three components
that we want to make sure we're investigating.
That's amazing. Dr Michael Gervais, thank you very much for joining us.
APPLAUSE
Feeling lucky - just feeling lucky - can change your chances of success,
and as Dr Michael Gervais was saying there,
it's all about fighting your instincts,
about overriding your gut,
stepping outside of yourself and being objective,
and I think there is something in there that maths can empathise with.
OK, how about those people who are really lucky?
So how about the ones... Not just ones who have maths and bravery
on their side, but how about people who walk away with the really big
prizes, the ones who stand out from the crowd, right?
The real one-in-a-millions?
Well, I'll tell you what.
Let's try and find one, because what we're going to do
is we're going to whittle down all of you
to find the luckiest person in our audience.
You know how we're going to do it?
We've got a game show.
APPLAUSE
So, are you feeling lucky?
I'd like to welcome my glamorous assistant, Matthew Parker.
Now, OK, everybody, if you would like to stand up
underneath your feet, you should have two hats.
One is yellow. One is blue.
What we're going to do is we're going to run a series
of semi-random rounds.
All you need to do is put on your blue hat or your yellow hat,
whichever you think is most likely to win.
If you are unlucky and you get one of the semi-random rounds incorrect
I'm afraid you then have to sit down.
You are out of the game.
If you get it correct, you stay standing up.
You're through to the next round.
OK, are you ready to play?
Let's go.
Round 1.
Which of these two balloons is going to explode
in a ball of fire?
Is it yellow or blue? Make your votes now.
Everyone's voted.
It's quite loud.
Cover your ears. Here we go.
Ready? The blue one is...
BALLOON POPS ..not explosive.
Which means the yellow one...
DEEP BOOM ..is!
Blue, you are wrong. Sit down.
Yellow, stay standing up.
Everybody, hats off.
Round 2.
APPLAUSE
Round two is a race.
If you think the blue channel cockroach will win,
put on your blue hat.
If you think the yellow cockroach will win, yellow hat.
Everyone ready?
And they're off.
LAUGHTER Come on!
SHOUTS OF ENCOURAGEMENT
FROM AUDIENCE: Come on, blue!
Blue, blue, blue!
Oops.
And the winner is...
Blue!
APPLAUSE
Yellows, sit down.
Blues, stay up. Hats off.
Round 3.
APPLAUSE
OK, everyone.
I've got a pancake here.
One side of it is yellow. One side of it is blue.
Once I flip the pancake, which side will land face up?
Yellow or blue? Make your votes now.
Here we go. Ready?
Oh! SHE CHUCKLES
It's yellow!
Blues, you lose. Sit down.
Yellow, you are through to the next round.
Everybody, hats off.
Round 4.
I found this person backstage.
Is their name Dave? Is it Tom?
If you think it's Dave, blue hat, Tom, yellow hat.
Look at him. That's the facial hair of a Dave,
but the shirt of a Tom. What do you reckon?
OK.
Hats on.
And the correct name is...
It's Tom!
Blues, sit down.
Yellows, stay up.
Hats off.
Round 5.
APPLAUSE
Who is tonight's extra special celebrity guest?
Is it Operation Ouch's Dr Xand van Tulleken
or Operation Ouch's Dr Chris van Tulleken?
Yellow or blue. Make your bets now.
And the answer is...
Hey, everybody!
Which one are you?
What?! We've known each other for years.
It's Xand van Tulleken! OK.
Yellow, you are through to the next round.
Thanks, Xand, that's all we need from you.
Blues, sit down. Everybody, hats off.
Round 6.
APPLAUSE
All right.
Am I wearing blue socks?
Am I wearing yellow socks?
Vote now with your hats. Blue or yellow socks?
Blue hats for blue, yellow for yellow.
Yellow, blue, blue, blue, yellow.
OK. Are you ready?
They are...
Have you ever...blue?
Ready?
Yellow!
Blues, you're down. Yellows, stay up.
Who've we got? One over there.
We've got two over there.
We've got one over there.
OK, everybody. Hats off.
Round 7.
APPLAUSE
Which one of my two party blowers is going to be longer when I blow it?
Is it going to be blue or yellow?
Make your vote now.
OK. They've made their bets. All right, here we go.
PARTY BLOWERS SQUEAK
And the answer was blue.
Yellow, you lose.
Blue, you're through to the next round.
Final Round.
APPLAUSE
OK.
We've got three people left.
This one is a straight run between me and Matt
as to who can get the balloon on their head to pop first.
Who wants to go... We need to...
You need to pick a team this time.
So who wants to go for me?
Thank you. And who's going for Matt?
Thank goodness that music doesn't get annoying.
We have got... Let's have a look.
We've got two blue and one yellow. Interesting.
Interesting. OK.
OK, ready, Matt? Ready.
Three, two, one.
Go.
AUDIENCE SHOUTS ENCOURAGEMENT
BALLOON POPS
CHEERS AND APPLAUSE
Right.
Tie breaker, will the blue/yellow coin land blue or yellow?
You've gone for yellow.
You're going to go for blue. Are you ready?
And the winner is...
Yellow! You're the luckiest person in the room!
The luckiest person!
APPLAUSE
Amazing!
The winner!
Abi, the luckiest person in our audience,
we've got a crown for you.
We've got a trophy for you.
We're not going to give these to you just yet
because we really want you to prove
that you are the luckiest person in the audience.
So what you've got to do, Abi,
is you have got to just land a ping pong ball into that, OK?
Now, we know you're lucky.
I mean, you just beat everyone in this room,
so we're not going to make it too easy for you.
Come and follow me.
We're going to shoot the ping pong ball from up here.
Let's see how lucky you really are.
We want you to get that crown.
We want you to get that trophy.
So if you just want to stand in there.
Your job now, Abi, is to try and fire it into there.
Let's give her some encouragement.
Yes! Come on!
CHEERS AND APPLAUSE
Come on, you're the luckiest person.
Not bad.
OK, we'll give it another go.
Come on. We really want to get the crown. Come on.
Oh, it's pretty close.
It's almost like they weren't lucky and someone just had to win!
We can speed this up if we bring in the string.
Thank you for the string!
Of course, because the more times that you do something,
even if it's really unlikely,
eventually it becomes a mathematical certainty.
Here we go.
Abi, we're going to put some safety glasses on you. OK.
We're going to give you a scary-looking glove.
OK, so this sets fire.
Can you give us a test click, make sure it's working?
OK. You're going to, in a second, we'll count down.
You're going to set fire to the string. Are you ready?
Count down from... Everyone. Three, two, one, go!
Whoa!
Surely one's going to go in!
Come on!
Whoa.
Hang on, hang on, hang on, hang on.
There's one in there!
CHEERS AND APPLAUSE
You're the luckiest person in the audience!
So, OK, everyone.
We have just discovered how we can use our understanding of maths
to get lucky, and in the next section, we're going to explore
how we can up our chances of winning at even bigger challenges,
and learn that bending the rules can sometimes be good.
Goodnight.
The luckiest person!
CHEERS AND APPLAUSE