(upbeat music) - There are some things in life that you just don't see coming. The world is random, unpredictable. (ice cubes crashing) 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. (upbeat music) (air whooshing) (upbeat music) (audience applauding) - 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 go you there. If you want to come down I picked you. Round of applause as she
comes to the stage, thank you. (audience applauding) What's your name? - Meghan.
- Meghan, okay Meghan. Meghan, how are you feeling
today, are you feeling lucky? - Yeah.
- Okay, good all right. If you just wanna come here
and just stand just there. Now Meghan, above your head (audience laughing) we've got a bag of gunge and there's this a little rope just there. What'd you reckon we're gonna do Meghan? - For some reason I feel
like it's gonna fall on me. (laughing) - Well, we thought about it. We thought about it going out but actually it's not gonna fall on you. You're gonna be the one
who's going up there to help us cut the rope. So if you wanna niff up
there just stand there. Now instead, I'm gonna 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 Meghan cuts the rope, the gunge is gonna fall down this way. And then either I've
done my sums correctly. in which case the gunge is gonna stop once it hits about here or it's gonna drop all the
way to the floor go splat. And then everyone in the first row is gonna be covered in gunge. Definitely one of those two things. Now, if we managed to get
through this unscathed, I want you all to burst
into spontaneous applause. And if this doesn't work, I'm just gonna do the rest of
the lectures covered in gunge. Okay, all right sound good. Okay, Meghan, how are
you doing, you up there? - Yep
- Okay. You ready to cut the rope, are you ready? Do you wanna give us a countdown? - Okay, five, four, three, two, one. - Whoa. (audience applauding) Thank you very much Meghan,
you haven't ruined the lectures so well done for that, that was great. Okay, so what happened there? We had a bag of real gunge there, which genuinely almost did
in fact splat all over us. Oh no. (audience laughing) It's fine. Something quite special happened there. Something quite
extraordinary there happened to stop that gunge from
spurting everywhere. You wanna 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 gonna
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 okay, we didn't get splattered. 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. And you all knew surely
that I knew that for sure. But still it's inevitable that
you feel a little bit worried and that I think is something
that you have to accept. We're all humans. 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 math 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. And we're gonna 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 entrance way to the RI. If you'd like to come out and join me. - [Hannah] 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. How fortunate, this
must be the new fashion. So we're gonna try and
experiment with all of you in a moment to see what happens when you're moving through a crowd. - Okay, when you were moving in a crowd, I mean everyone's making
their own decisions, its random surely, Matt. - It feels very random,
very chaotic, unorganized. You're being bounced around. However, there are some patterns and actually we may want
them to walk naturally. So we're not gonna tell them
when the experiment starts. So better watch this. Actually I'm really sorry, everyone. We've just realized don't move yet that we wanted the yellow hats on this side. We wanted, I know the red hats on this... It's not me it's coming from upstairs. So I think we're clear. Okay, If you can, as quick as you can, if you just swap over sides. Exactly what you are but opposite across. Okay 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. - There not all jumbled up. - It's not random, is it? Look at this, there having
some wild issues here. - Everyone's just following each other and you end up with
these very clear lines. - So if these were random,
it'll be a complete mix. Instead we've got these fantastic stripes. Come on everyone, let's keep it moving. You end up over these fantastic
stripes, look at that. So everyone, that was fantastic. Thank you so much and
that was the experiment. So thanks very much for getting involved. - Thank you Matt. Now it turns out there are
actually a lot of similarities between the maths of how people... (participants laughing) 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 math 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 math 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 you go, if you wanna go on this. 'Cause you only do this, go for it. (cracker opening) A few times a year you may not notice. Here you go you can have that one. And 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
that I can explain to you. So what you do we have to, I'll teach you and then I can show you. So what you wanna do, you
wanna hold your end lower than the other person. Use two hands with a really
sort of steady, firm hold. And you don't wanna do
any twisting or pulling. You don't wanna 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 you end
up winning, well done. You can have the hat now, enjoy. (audience applauding) Now, I've gotta be straight with you. This isn't gonna work every single time, especially not if you're 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 gonna 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 School
Teacher, Bobby Seagull. (audience applauding) There you go Bobby. - How are you - It's very good to see you. Okay Bobby. (audience applauding) What have you been doing there Bobby? - So I've been flipping
coins hundreds of times. On a sort of fair unbiased coin, you'd expect the chance of
a head or tail to be 50-50. 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 at 2000 times. No, I had to enlist the
help of school students. - Nice.
- So we went across London, found students from
Westminster Academy, thank you. And to use 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. 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 gonna go with 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. So that's the third flip there is it? - Yep, and that's the fourth. You can see wind blowing
the ties about, fifth time. - So it's 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. (laughing) - Oh, there's a very good... So there's way more people
in the middle there. - Yes, and roughly the
same number on the tails and the heads side. And a few, who've got
six tails and six heads. - So these are three heads three
tails in this aisle, is it? - Exactly.
- All that. I mean, these guys were
certainly 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 this. - Exactly, so many classes
repeating it many times to get us a better dataset. So 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 ends. - 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 there are a student, a proud, hardworking math
student and we put them together, and we get what's looks like
a normal distribution curve. - And this is what the maths
would have predicted would happen from the beginning.
- Exactly. - Very lovely. Thank you very much,
Bobby Seagull, thank you. (audience applauding) The point that we trying to make here is that life is for the 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 okay, 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 wanna make a guess as
to what you think 20% means in that context. - The chances are probably
20% it's gonna cover. - Okay, yeah, 20% is gonna 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 wanna give me a guess? Anyone here wanna give me a guess? Yeah, go ahead. - How much of the country's
going to have rain in it? - Okay, good response. 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. (audience applauding) Hey Prof, how are you doing?
- Awesome. (audience applauding) - Okay, good. 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. - [Hannah] What does it actually mean? - It means that if I
was to live the same day over and over a hundred 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. (laughing) - Yeah, I mean I understand, no one likes getting wet. No one likes getting wet. But you don't predict the weather, do you Chris? - No I don't. - Something much more risky. - Yeah, I try and understand
how volcanoes behave and when they might erupt. - And you use those predictions
to actually go in volcano. - Yes I do.
- I've got some little photo here. I mean, that's pretty close, right? - Yeah, it's pretty close
but it's important work we're doing as scientist. 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 that this volcano may
have while we're there. - Have you ever had a close call? - I've never had a close
call, not yet at least. - Okay, 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. - Okay, yeah so the thing with volcanoes is there 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 and what 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 for. - Yeah, so another thing we can look for as Magna 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. And we can actually
measure the earthquakes in terms of how strong they are as well and 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 there's lots
of gas, lots of earthquakes, maybe even lava coming out the top of it, that's probably time to leave. (laughing) - Time to take a bit of a step back. - Proper time to step back. - Maybe let's do that then
- Let's do that. - So this one looks like it's imminent. (laughing) - Thank goodness we got
glasses on then, huh? (laughing) Have you ever been at an
actual volcanic eruption. - I have, yes. - 'Cause this stuff is really serious. This is not just playful. - It's 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 eminent. - This one looks like it's eminent. I'm gonna say, probably
90% chance at the moment it's gonna erupt. (laughing) (model exploding) - [Audience] Whoa. - [Chris] That's a 100% chance. - Yeah, crazy. (audience applauding) Fantastic, thank you very much Chris. (audience applauding) There is something that's important to say about 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 a
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 rumors are that hiding
amongst these 100 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? (audience laughing) What a surprise. Perfect all right, let's
see who we can find. If you wanna come down there. Yeah, perfect, round of applause. (audience applauding) What's your name? - Eling.
- Eling perfect, okay Eling. All right so if you wanna
stand just over there. Now, you're gonna 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 and
no one wants any of them. And because you only
get to pick one present, we wanna 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. Come in Matt. Look at this.
- All right, yeah. - How amazing. - This is my X-mas ray detector 0.80 and what we can do is we
can put these presents through the scanner Actually, do you wanna come
with me around over here. If you wanna 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. (audience applauding) Oh, 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 just down there somewhere. Is that okay? Are you ready? I'm gonna start piling them
in here and you sort them out. Here they come. - [Hannah] You seem pretty
happy with this machine, Matt. - I'm very proud it is a... - Yeah, how accurate is it? - This machine is 80% accurate. - Okay, 80% accurate,
that's pretty good Matt. 80% accurate, okay. So then one of these then
that's re-wrapped as a phone. What do you reckon are the
chances that this is a phone? Shout out what you think it is. - [Audience] 20% - Okay, all right let's
think this through then. So your machine, how
accurate is your machine? - 80% accurate. - So your machine is 80% accurate. There are five phones in total. 80% accurate means that it's
only gonna find four of them. Matt, that does mean one phone's
gonna end up on the floor. - Yes, the downside to 80%
accurate is it's 20% inaccurate, but on the upside 80% accurate. - I mean, you make a good point. So, okay one phone on the floor, it's not the end of the world. It still gives you a really
good chance at finding a phone. There's something going on there though? Hang on, hang on, hang on. Stop the machine. - Whoa whoa.
- Whoa whoa. Okay hang on, Matt. 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 applauding) - Yeah but Matt, there's
95 socks and satsumas here. 20% that's 19 rubbish presents
in that pile of phones. - Yeah, but 80% of them are down here. (audience applauding) So the problem is like
this is 80% accurate. It doesn't mean these
are gonna be 80% phones. It just means and I'd like to recap that my machine is 80% accurate. - Okay, but right. By the time you're finished
you're gonna have what, 23 presents over here. Only four of them are gonna be phones. That gives you a four in 23
chance of finding a phone. - It's about 17%. So it wasn't... Okay, would do you wanna
pick one at random? (audience laughing) I mean, you can open it and
have whatever is inside. So overwhelmingly likely to be a satsuma. Well, you can keep it
though, Merry Christmas. (audience laughing) Thanks for your machine Matt. - My pleasure.
- Can't believe it (audience applauding) - 80% accurate. (audience applauding) - That kind of error
mislabeling satsumas as phones is something that's
called a false positive. And it goes to show how math 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 mislabeled. Now, this doesn't mean that
you shouldn't be screened, but it's really important to understand what these results mean. But okay, 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. (audience applauding) Okay Ros, you've studied the
mathematics of disease, right? How much of it is luck and chance? - 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 preexisting 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? - 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 somethings 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 rumors of a
zombie apocalypse about to hit. Okay, 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. 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. And in a moment, I'm gonna
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. - So over here, nobody has any protection against zombie infection. So we're gonna expect a lot of cases and possibly quite quickly. - Okay all right, let's give it a go. Is everyone ready? Everyone got their balls in their hand. All right, we're gonna
start this infection. Here's the zombie germs coming at you. I'm directly targeting people. Oh, already. So we've got actually a
few different patches here - We do, yeah. But it starting to get a little
bit frightening around here. - And it's traveling backwards
through and now forwards. A big cluster of zombies
they're right in the middle. How realistic is what
they're doing compared to how 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. And that's in the real world
people usually recover. - I think there are in fact. So if you... It's still going.
- It is still going. - If you are not a zombie
could you stand up for us? How many people are there? - Oh we've got some.
- Just three people who managed to escape the zombie virus. (audience laughing) you also can't target people
directly with you zombie germs, that wasn't part of the rules. Everybody sit down, thank you very much. Now we can do this again, but this time we can use
some kind of zombie defenses. - Exactly, yeah. So over here there's
gonna be some protection against infection and these people are gonna be completely protected. - 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. - So if the zombie germs touch you and you're wearing a face mask, and you 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. - Let's give it a go, here we go. Okay, so it's still started. I mean that stopped almost immediately. So those of you who are not
wearing a protective mask but are also not as 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 modeling disease make a difference back in the real world? - So we take experiments kind of like this but in the computer and
take things that we know about how infection spreads and about the population in general. And the goal is to use the computers, 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 TB in cows, you can use these mathematical ideas. - 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. 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. (audience applauding) - 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. We got team manager there,
obviously 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. (audience applauding) That's you on 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 the 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
that the darker the color, the darker the red, the more
likely you are to score. I mean, from there it's pretty easy. To score is easy from there.
- 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 math says is the probability of a particular shot going in. So I think we have a little clip. - So we call this the expected goals game. - Okay, so what game are we watching here? - So this is a friendly
between Tranmere Rovers and Liverpool which a preseason friendly. - And you pause the footage just... 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? - So we have some options.
- Do you reckon it's 50%, 75% or 99%. Shout out your answers,
what do you think it is? What do you reckon the
maths says is the chances. - [Audience] 75 - 75 came up quite clearly there. All right, what's the answer? What does the math say? - Well, the actual answer here is 99%. (audience applauding) - So that means in
exactly the same position, with exactly the same surroundings, if you rerun this a hundred 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. - Okay, all right let's try one more. We got another clip for you, here we go. Oh, okay so he's much further 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 gonna be a lower chance. - It's gonna definitely be a lower chance. - But what does the math
actually calculate it to be? So we've got some options for you. All right, do you reckon the math says that this is 4%, 7% or 10%
chance of getting a goal? What do you reckon, shout at me. - [Audience] Seven. - Everyone's going in the middle of there, What's the answer?
- Everyone is going in the middle and you spot on, It's actually 7%. - And let's see what
actually did happen, miss. - One the reasons that that it was only 7% and not any higher was
because he shot it straight at the goalkeeper. - I think 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 anytime a ball is passed, for example. - Okay, so to help us to demonstrate this, I'd like to invite onto
the stage Bertie and Jamie from a London youth team. (audience clapping) Thank you very much guys. So Bertie and Jamie are just gonna have a bit of a kick about. 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
to click and click and click. I mean 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. - Bertie and Jamie, thank you
very much for the help there. Thank you. (audience clapping) So what do you end up with
once you've done all of this. - So for every game we get approximately 2000 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 a 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 one of the gigantic spreadsheets actually. - This is just one game. - And you're watching a game
of football where basically-- - Yes exactly.
- through numbers. It's an interesting, I
mean maybe less exciting than watching the match in the day. - Well, it depends on
your perspective, yes. - But you're not just collecting
these numbers, are you? What do you do with them? - So this data can gives us a goal value for every position and
for every player on pitch. - And what does it end up looking like? I think we've got a little example. - Yap, we have a little animation. - Okay, 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 represents the direction and speed that they can travel in. - [Hannah] And you've got
a blue team and a red team. - [Tim] Yep, so the red team
here is actually Liverpool. And the areas in red are
places that Liverpool players can get to sooner than the
players who are in blue - [Hannah] Based on how quickly people run 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 10, this is a Saudi 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 it 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. (giggling) 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 perfectly accurate. But we can play on this
game and see how it evolves. So the ball does get passed over. - It gets successfully received. - Still not very high chance
of scoring a goal from there. - Nope, but now Trent Alexandra-Arnold, his best option is to run
into this position here. So he's now dribbling the ball forwards. - 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 was 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 round about here and he scores a goal. - Which is exactly what you want. - Exactly. - So are you using this stuff
to just analyze your team or are you using it to
analyze other teams too? - So the advantage of this
is we see all of the players at the same time. Which means that we can
analyze 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 coming, thank you. (audience clapping) 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. So for this, I would like two volunteers who are willing to compete
against one another. Okay, perfect. If you wanna come down
here and that's one. I'll get someone from over here. Round of applause as they come on stage. (audience applauding) What is your name? - Nat
- Okay, Nat thank you. And what is your name? - Jasmine.
- Jasmine, okay Nat and Jasmine. This game is called goodie or baddie. 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 baddie in which case you put on your purple hat. And what we're gonna do is
we're gonna 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 goodie bag. I mean, it's pretty special. So this is the way that it works. If both of you decide to be a goodie, then you will end up
getting three points each. If both of you decided 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. Remember four rounds, you
have to get to 12 points. You happy?
- Yes. - Okay, all right turn around so you can't see each other's choices. Here we go. So red for goodie, purple for baddie, make your choices now. Turn around and have a look at each other. Oh, okay all right five points there. One, two, three, four, five. Okay all right, round two here we go again Round two, he stole some
points off of you that time. Let's go for round two, go. (laughing) Payback turn around, only 1 point each, you blocked him there. Okay, round three here we go. (laughing) And please make your
choice for round three. Turn around and have a look at each other. (grunting) you got him back, there's
still one round left. (balls clinking) One round left, turn around here we go. Don't take your hat off and
make your choices, go for it. (laughing) What an unsurprising ending, turn around and have a look at each other. So neither of you, I'm afraid. Neither of you got up to the line. Neither of you got 12 points. But you know what was 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 that you played
baddie you blocked each other. But you know what, it's understandable. Because let's say... Do you mind if I take this
out of your head for a second. Let's say your opponent
had chosen to be a baddie, in that situation you've got two choices. 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 is 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 is 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'd
both just played goodie, you both would have
ended up getting a prize. So thank you very much
to my volunteers there. You're both very bad. (audience applauding) Merry Christmas is it
say that to each other. And this 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 right 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 behavior. 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 Let's have a look at
some of your weirdnesses as an audience. Underneath your seat, you should have a whiteboard and a pen. What we're gonna do. If you can get those
out and get them ready. What we're gonna do is when I say go, I want you to pick a
number completely at random between one and 10 and
I want you to write it on your whiteboard when I say go, and then we'll hold them up. Number between one and
10 completely at random, go and then hold it up
when you're finished and let's have a look at what you've got. Let's have a little look of what we got. Come I see here. All right, I'll tell you what, if you wrote down a
one could you stand up. Oh, certainly not 10% of
the audience, that is it. All right, thank you very much sit down. If you wrote down a
10, 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. Oh, 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. A huge swathes of people
will choose a seven. And there's a kind of
strange reason for that. If you're picking around a number, one feels like it's too small, 10 feels like it's too big. Five is kind of too much in the middle. Two's even, can't choose that one. Eight 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 behavior 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. - And you have worked with
a number of amazing people, haven't you Michael? - I've been fortunate
in that, yes for sure. - What is it that you do? - Well, if I trade in training I am a sport and performance psychologist. - So you're trying to get people in the right mindset 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 shortcuts, and there really aren't many. And so we can learn from
the best in the world how to fundamentally organize your life to strengthen your mind
to deal with the unknown. And what we've come to find
out is that there are 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 those are 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 trained. So 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 is in and of itself is a big deal. Because you need oxygen mask to be able to carry enough oxygen but he
did it without a parachute. He was the first person to do.
- Without a parachute. - Yeah, and he was the
first person to do that. He jumped into a 16 story 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 of the chance. And so training your
mind is one of the ways to help somebody have
great command of themselves under duress. And so, absolutely this is an
incredibly dangerous project. - Do you think he's mad? (audience laughing) - 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 wanna diminish the
amount of luck involved and make sure that we're
increasing the amount 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. Emotions and thoughts and environment are the three lakes to the store. 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 wanna make sure
we're investigating. - That was amazing. Dr. Michael Gervais, thank you very much for joining us. Round of applause. (audience applauding) 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 some thing in there that maths can empathize with. But okay, how about those
people who are really lucky? So how about the ones, not just the 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. They're the real one in a millions. Well, I'll tell you what,
let's try and find one. 'Cause what we're gonna do is we're gonna whittle down all of you to find the luckiest
person in our audience. And you know how we're gonna do it? We've got a game show. (upbeat music) (audience applauding) So are you feeling lucky. I'd like to welcome my glamorous
assistant Mathew Parker. 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 gonna do is
we're gonna run a series of semi-random rounds. And 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're 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. - Okay, you ready to play? Let's go. (upbeat music) - [Announcer] Round one. - Which of these two
balloons is going to explode in a ball of fire. Is it yellow or blue? Make your votes now. (upbeat music) - Everyone's voted, It's quite loud. Cover your ears, here we go, ready? The blue one is not explosive. Which means the yellow one is.
(ballon exploding) Blue you are wrong, sit down. Yellow, stay standing up. Everybody hats off. (air whooshing) - [Announcer] Round two. (audience applauding) - Round two is a race. If you think the blue
channel cockroach will win put on your blue hat. If you think yellow cockroach
will win yellow hat, everyone ready? And they're off. (audience laughing) Come on. (audience cheering) And the winner is blue. (audience applauding) Yellow, sit down. Blue stay up, hats off. (air whooshing) - [Announcer] Round three. (audience applauding) - Okay 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 we'll land face up, yellow and blue make your votes now. Here we go, ready? Oh, it's yellow. Blues you loose, sit down. Yellow you are through to the next round. Everybody hats off. (air whooshing) - [Announcer] Round four. (audience applauding) - 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? Okay, hats on and the
correct name is. it's Tom. Blue sit down, yellow stay up, hats off. (air whooshing) - [Announcer] Round five. (audience applauding) - 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. (audience murmuring) And the answer is... - Hey, hi everybody. - Which one are you? - What, we've known each other for years. - It's Xand Van Tulleken. Okay, yellow you are
through to the next round. Thanks Xand, that's all we need from you. Blue sit down, everybody hats off. (audience applauding) (air whooshing) - [Announcer] Round six. (audience applauding) - Al 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. Okay, are you ready? They are, you blue? Ready, yellow. (audience applauding) Blues your down, yellows stay up. Who've we got? One over there, we've got two over there. We've got one over there. Okay, everybody hats off. (air whooshing) - [Announcer] Round seven. (audience applauding) - Which one of my two party blowers is gonna be longer when I blow it? Is it going to be blue or yellow? Make your votes now. (upbeat music) Okay, they made their votes. All right, here we go. (party blower honking) And the answer was blue. Yellow, you loose. (audience applauding) (air whooshing) - [Announcer] Final round. (audience applauding) - 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? You need to pick a team this time. So who wants to go for me? Thank you, and who's going for Matt. - Okay, thank goodness that
music doesn't get annoying. - We have got, let's have a look. So we've got two blue and
one yellow, interesting. Ready Matt. - Ready? - Three, two, one, go. (audience cheering) (ballon popping) (audience applauding) - All right, tie breaker. Will the blue yellow
coin land blue or yellow. You've gone the yellow. You're gonna go for blue, are you ready? And the winner is yellow. (audience applauding) - The luckiest person, amazing. (upbeat music) - The winner.
- What's your name? - Abby.
- Abby, the luckiest person in our audience. We've got a crown for you. We've got a trophy for you. We're not gonna give these to you just yet because we really want you to prove that you are the luckiest
person in the audience. So what do you gotta do Abby, is you have got to just land
a ping pong ball into that. Now we know you're lucky. I mean, you just beat
everyone in this room so we're not gonna make
it too easy for you. Come follow me. We're gonna 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 Abby is to
try and fire it into there. Let's give us some encouragement
as she goes come on. (audience applauding) Come on, you're the luckiest person. Not bad, we'll give it another go. Come one, we really want
you to get you that crown. Oh, it's really close. - Hang on, it's almost
like they weren't lucky and someone just had to win. I tell you what, we can speed this up if we bring in the string. (audience laughing) Thank you for the string. (audience laughing) - Okay, 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. - Abby we have put some
safety glasses on you. We're gonna give you
a scary looking glove. So this sets fire. Can you give us a test click
make sure it's working. You're gonna in a
second, we'll count down. You're gonna set fire to the string. Are you ready to cut down from everyone, Three, two, one. - Whoa. (audience murmuring) (ping pong balls crashing) Surely ones gotta get in. Hang on, there's one in there. (audience applauding) So okay everyone. We have discovered how we
can use our understanding of maths to get lucky. And in the next lecture,
we're gonna explore how we can up our chances of winning
at even bigger challenges and learn that bending the
rules can sometimes be good. Good night, the luckiest person. (audience applauding) (upbeat music)
