1
00:00:15,810 --> 00:00:20,550
Well, thank you for that excellent introduction, it's going to be hard to compete with that.

2
00:00:20,550 --> 00:00:26,790
So this is my question then and will the mathematician ever manage a football team?

3
00:00:26,790 --> 00:00:33,390
And I probably mean a little bit more than that because maybe a mathematician has managed an amateur football team,

4
00:00:33,390 --> 00:00:37,830
but will a mathematician at some point manage a Premier League team?

5
00:00:37,830 --> 00:00:45,690
That's my question. So let's start with our prejudice because I think a lot of my title plays on those prejudices.

6
00:00:45,690 --> 00:00:54,000
This is a football manager. Now this one in particular,

7
00:00:54,000 --> 00:01:03,990
who I didn't like for many reasons because I'm a Liverpool fan and he has a style which is probably the antithesis of mathematics.

8
00:01:03,990 --> 00:01:08,850
It's all about getting the players to be as passionate as possible and disregarding

9
00:01:08,850 --> 00:01:13,500
any kind of statistics which say that he's failing and he just keeps going and going,

10
00:01:13,500 --> 00:01:17,340
and he uses this sort of least mathematical approach to football.

11
00:01:17,340 --> 00:01:21,060
I think that might be. That's my prejudice. I'm going to own up.

12
00:01:21,060 --> 00:01:28,300
This is my prejudice. So we'll put that against another person who we might have some prejudices about.

13
00:01:28,300 --> 00:01:38,050
And this is Andrew Wiles, of course. And when we think of mathematicians, we think of a very logical structure to everything,

14
00:01:38,050 --> 00:01:44,740
very carefully thinking through and answering questions in a very, very precise type of way.

15
00:01:44,740 --> 00:01:51,280
And so our prejudices really tell us that Moreno and Wiles are somehow polar opposites.

16
00:01:51,280 --> 00:01:59,200
So how can we expect to unite these two and have a mathematician manage a football team?

17
00:01:59,200 --> 00:02:05,320
Well, I've got some suggestions or I'm going to work towards some suggestions.

18
00:02:05,320 --> 00:02:10,420
This is a starting point. This is another type of managerial style that we've heard about.

19
00:02:10,420 --> 00:02:15,820
This is Pep Guardiola and Guardiola. He's certainly passionate about the game,

20
00:02:15,820 --> 00:02:21,430
but he likes to sort of portray himself more as the kind of intellectual the man who's opening

21
00:02:21,430 --> 00:02:27,370
up space for his team and planning carefully about tactical decisions against the opposition.

22
00:02:27,370 --> 00:02:36,210
So there is this kind of idea also of the football manager as the intellectual who's trying to solve a problem.

23
00:02:36,210 --> 00:02:44,070
And then there's also a type of mathematician, not the pure mathematician, but there's also the type of applied mathematician.

24
00:02:44,070 --> 00:02:51,180
And this brings us to Philip, who's sitting up there in the back row and this is Philip Hare, and he's very kindly.

25
00:02:51,180 --> 00:02:53,760
This is this is the team he's been playing for.

26
00:02:53,760 --> 00:02:58,720
He's very kindly instructed the rest of the team exactly how you should stand when you have a photograph.

27
00:02:58,720 --> 00:03:05,550
So he's got his managerial style here, and he's got most of them seem to have listened to his advice.

28
00:03:05,550 --> 00:03:12,780
And Philip is just one of several mathematicians who are accomplished football players.

29
00:03:12,780 --> 00:03:17,370
I don't know what league it was. You played in, Philip, can you tell us?

30
00:03:17,370 --> 00:03:25,870
OK. But we actually have another professor at Oxford who has played at a much higher level.

31
00:03:25,870 --> 00:03:31,710
So this is Ruth Baker, who's also a professor of applied of applied mathematics mathematical biology,

32
00:03:31,710 --> 00:03:37,440
and she wears the number eight shirt or has worn the number eight shot for Oxford.

33
00:03:37,440 --> 00:03:44,430
So this must be a vast was Ruth. OK, this must be a varsity match, and this was the one you won.

34
00:03:44,430 --> 00:03:51,270
I take it. Yeah. Did you get the ball in that run? Can you remember what happened?

35
00:03:51,270 --> 00:03:57,840
So it is possible to be a mathematician and to be a successful football player.

36
00:03:57,840 --> 00:04:03,120
You have been you were described to me earlier today as the most successful football player in the whole maths institute.

37
00:04:03,120 --> 00:04:07,640
So very impressive.

38
00:04:07,640 --> 00:04:19,100
And I'm going to describe a little bit about my own background, so how I have gone from being a mathematician to becoming more involved in football,

39
00:04:19,100 --> 00:04:25,310
I thought I'd start with a picture of myself when I was a kid. I'm I'm the one.

40
00:04:25,310 --> 00:04:29,150
This one has this cute one. That's my little brother, Colin, and this is me.

41
00:04:29,150 --> 00:04:34,010
I think I must have been about eight or nine when this photograph was taken.

42
00:04:34,010 --> 00:04:38,180
And unfortunately, I wasn't any good at football.

43
00:04:38,180 --> 00:04:41,660
I liked having the strap on and I thought I looked very good in it.

44
00:04:41,660 --> 00:04:46,220
But I found out that I wasn't particularly talented football player.

45
00:04:46,220 --> 00:04:55,520
But what? I was much better at with mathematics, and I have this picture of myself a few years later when I, as Alan, said,

46
00:04:55,520 --> 00:05:00,230
I worked here as a Royal Society Research Fellow and I was particularly interested

47
00:05:00,230 --> 00:05:06,290
in one type of mathematics how you could apply maths to understand the real world.

48
00:05:06,290 --> 00:05:11,150
And a lot of my research here, I was only half time based here at the maths department.

49
00:05:11,150 --> 00:05:19,310
I was also based at the zoology department, and I work together with people who were studying locusts who were studying ants and pigeons.

50
00:05:19,310 --> 00:05:24,250
Think of a picture of the pigeons here. These are actually pigeons from from just outside Oxford.

51
00:05:24,250 --> 00:05:29,390
This Mr Ribeiro, who was one of my biologist colleagues who took these photographs and I studied

52
00:05:29,390 --> 00:05:35,090
how they interact and how they produce different types of collective behaviour.

53
00:05:35,090 --> 00:05:38,000
And oh yes, this gets onto the next picture.

54
00:05:38,000 --> 00:05:43,670
And I needed to put this in because I was at Wolfson College and this is a picture of my daughter blowing bubbles in Wolfson College.

55
00:05:43,670 --> 00:05:51,680
I just wanted to have that in there as well. And then I became a professor in Uppsala.

56
00:05:51,680 --> 00:05:59,660
And then it turned out that my son Henrik, who's this one here, he started playing a lot of football,

57
00:05:59,660 --> 00:06:04,130
and it turned out that he had a lot more talent in the game than I did.

58
00:06:04,130 --> 00:06:06,890
And they needed people to manage or manage his team.

59
00:06:06,890 --> 00:06:18,380
So I ended up partly with a bunch of other dads who were, like, overly enthusiastic, trying to relive their own failed dreams through their children.

60
00:06:18,380 --> 00:06:23,000
We started training as a team and I'm still actually training his team.

61
00:06:23,000 --> 00:06:30,080
He's now 14 years old and he's still still plays football on a regular basis, despite me embarrassing him and talks like this.

62
00:06:30,080 --> 00:06:38,510
He's still involved with that. And then I ended up because I became interested in football again, and I'd always had that in the background.

63
00:06:38,510 --> 00:06:47,390
I ended up writing the book Soccer Mattox, thinking about how we can use maths to explain different parts of football.

64
00:06:47,390 --> 00:06:53,000
And in the book, I look at game theory for strategy. I look at randomness in the game.

65
00:06:53,000 --> 00:06:57,680
I look at passing networks, all aspects of mathematics that I knew.

66
00:06:57,680 --> 00:07:03,920
I tried to break down into the into the soccer maths textbook, but this was mainly an academic.

67
00:07:03,920 --> 00:07:09,620
That was part of it was how you might apply it in reality, but it was mainly an academic exercise.

68
00:07:09,620 --> 00:07:15,710
And then I, as you'd get asked to do, you get asked to do kind of talks when you write a book like this?

69
00:07:15,710 --> 00:07:21,920
I got asked to do a TED talk. And in that TED talk, or it was a TED talk, you should make a distinction here.

70
00:07:21,920 --> 00:07:29,660
But in that talk, I put my hand up to with the telephone and told Jürgen Klopp Being a Liverpool fan,

71
00:07:29,660 --> 00:07:38,990
I told you again, Klopp, Well, you know, you can ring me any time. I'm I'll help Liverpool get promoted or win the Champions League or whatever.

72
00:07:38,990 --> 00:07:51,070
And he didn't call. But strangely, actually, quite a few other clubs did call me and I have had a visit in Uppsala from two Premier League clubs,

73
00:07:51,070 --> 00:07:55,390
they made me write non-disclosure agreements. I can't say which.

74
00:07:55,390 --> 00:08:07,030
And I've also visited a few clubs here in the UK, and another club that called me is the club Hammarby and in Stockholm.

75
00:08:07,030 --> 00:08:12,550
And they were very open and they said that I can actually go and work their work together

76
00:08:12,550 --> 00:08:19,630
with the coaches and with the players and help them develop their play with analytics.

77
00:08:19,630 --> 00:08:28,150
And so now I'm actually working part time together with a big football club trying to improve their game with mathematics.

78
00:08:28,150 --> 00:08:36,310
So that's a kind of brief history of me. But what I'm now going to answer is I don't think I'm quite there.

79
00:08:36,310 --> 00:08:40,210
I'm not actually managing Hammarby. I'm a long way from there.

80
00:08:40,210 --> 00:08:48,580
But what I want to get at is the basis of why applied mathematics is useful to to a football team.

81
00:08:48,580 --> 00:08:57,240
Why? What is it that applied mathematicians have got that allows them to get somewhere and in helping a football team?

82
00:08:57,240 --> 00:09:04,320
And I think I've been told that when you do a talk like this, you should like be extremely clear what your messages.

83
00:09:04,320 --> 00:09:10,230
And so I've just written down precisely what my messages and I'm going to repeat it at the end of the talk.

84
00:09:10,230 --> 00:09:16,010
This is precisely what an applied mathematician has to has to give.

85
00:09:16,010 --> 00:09:24,410
We base what we say on data. When we talk about something, we collect data and we we base what we see on data.

86
00:09:24,410 --> 00:09:27,740
We formulate models to understand that data.

87
00:09:27,740 --> 00:09:36,680
It's a essential part of everything that we do, that we have a model which describes how we think the data works and how we understand the data.

88
00:09:36,680 --> 00:09:42,030
And then we fit our models to the data in order to make predictions of the future.

89
00:09:42,030 --> 00:09:46,530
So that's the rules that we follow, is applied mathematicians.

90
00:09:46,530 --> 00:09:53,520
What I'm going to spend the rest of the talk doing is explaining how we put this into practise exactly in football.

91
00:09:53,520 --> 00:10:02,570
And hopefully by the end of our persuade you that well may be applied, mathematicians can be trusted to run a football team.

92
00:10:02,570 --> 00:10:05,860
So let me get to the get to the base of this idea, right?

93
00:10:05,860 --> 00:10:20,830
Let's start with some goals. So I'm going to ask you a question then out of these two goals, which do you think is the best goal?

94
00:10:20,830 --> 00:10:24,460
So let's put our hands up hands up for the top goal.

95
00:10:24,460 --> 00:10:32,520
Is that the best goal? And who thinks that the bottom one is the best goal?

96
00:10:32,520 --> 00:10:42,180
OK, so we've got a I think, a slight majority for the top, the top goal now, the top goal is a very long distance shot.

97
00:10:42,180 --> 00:10:46,500
There is a mistake by the goalkeeper here left in the end. I don't like this goal.

98
00:10:46,500 --> 00:10:51,270
Obviously, being a Liverpool fan, this was the reason we didn't win the Champions League last season.

99
00:10:51,270 --> 00:10:55,500
And but the Boston one is a very, very messy goal.

100
00:10:55,500 --> 00:11:00,300
There's a lot of sort of things. There's a claim there by the goalkeeper that was a foul.

101
00:11:00,300 --> 00:11:07,080
It clearly wasn't a foul and the ball bumps into the into the back of the net.

102
00:11:07,080 --> 00:11:12,420
And so it's a much more messy type of goal. Well, what does maths have to say about this?

103
00:11:12,420 --> 00:11:17,610
Well, what we do is we start with this idea. We start by looking at the data.

104
00:11:17,610 --> 00:11:28,410
And now here is some data over lots and lots of goals in football matches, not just one these this is actually all in a season of La Liga.

105
00:11:28,410 --> 00:11:32,670
This was the season before Neymar went to PSG.

106
00:11:32,670 --> 00:11:42,660
All of these little dots are shots that have been taken by these players, Lionel Messi, Neymar and Luis Suarez, so this yellow is a shot from here.

107
00:11:42,660 --> 00:11:49,680
These are long distance shots and if there's a black circle around it, then that means that it was a goal.

108
00:11:49,680 --> 00:12:00,690
So this is where the goals were scored from. And the important takeaway message from this is that if you see where the shots are, where are the goals?

109
00:12:00,690 --> 00:12:07,950
Nearly all of the goals are very close to the goal mouth, even namely as close.

110
00:12:07,950 --> 00:12:11,130
Messi has to, which are slightly long distance,

111
00:12:11,130 --> 00:12:21,060
but almost every goal scored by Barcelona in La Liga is scored very close to the goal and that was exactly like Manhas goal at the bottom.

112
00:12:21,060 --> 00:12:28,500
And not like Gareth Bale's goal at the top. So typically, goals scored from much, much nearer to the goal.

113
00:12:28,500 --> 00:12:32,340
They're not scored at long distance. And this isn't just true of Barcelona.

114
00:12:32,340 --> 00:12:35,820
There are teams which shoot from a longer distance. This is for the same season.

115
00:12:35,820 --> 00:12:39,960
This is Real Madrid and Gareth Bale who scored the video.

116
00:12:39,960 --> 00:12:44,970
The goal in the video I showed you. You see, he's got two long, long distance goals.

117
00:12:44,970 --> 00:12:51,450
Cristiano Ronaldo, he has shot. I think it's 60 times from outside the box.

118
00:12:51,450 --> 00:12:53,340
And he scored twice.

119
00:12:53,340 --> 00:13:03,390
So when he scores these goals and you often see them as the highlights on on TV afterwards, he's actually scores only one out of 30 efforts.

120
00:13:03,390 --> 00:13:08,250
And you often see a YouTube compilation of all of the goals that he's scored.

121
00:13:08,250 --> 00:13:12,150
Well, they should really have in these YouTube compilations is all of the misses

122
00:13:12,150 --> 00:13:17,040
that he's made because he misses a lot of the time where Ronaldo scores a lot.

123
00:13:17,040 --> 00:13:23,260
It's actually very close to the goal. Most of his goals come from very nearby.

124
00:13:23,260 --> 00:13:27,310
And that's a that's our data.

125
00:13:27,310 --> 00:13:35,790
So we've got our data. Next step is the model. And I want to start, and I think this is always what applied mathematicians tried to do.

126
00:13:35,790 --> 00:13:40,920
We start with the simplest possible model and then we build from there.

127
00:13:40,920 --> 00:13:48,330
And I want to start with the idea of this angle and the angle is how much of the face of the goal can you see?

128
00:13:48,330 --> 00:13:53,370
So if you're looking if if we take this podium, for example,

129
00:13:53,370 --> 00:13:58,860
the people who are sitting straight on at that podium can see it much more clearly than the people who are sitting there.

130
00:13:58,860 --> 00:14:06,570
There's a much wider angle. The people who are sitting at the back, they have a narrower angle than the people who are sitting at the front.

131
00:14:06,570 --> 00:14:16,020
And so our basic idea is this angle to the goalposts is going to be the model of the probability that you can score.

132
00:14:16,020 --> 00:14:25,670
Bale's shot is a long way out. So here's a little angle. Money shot is very close in, so it has a very large angle.

133
00:14:25,670 --> 00:14:33,540
And so the quality of a chance in football can be assessed by the angle to the goalmouth here.

134
00:14:33,540 --> 00:14:36,090
And then you have this nice property that, well, you can go around,

135
00:14:36,090 --> 00:14:42,870
as I mentioned that people sitting out there looking at this thing have a very narrow angle, even though they're closer to me.

136
00:14:42,870 --> 00:14:47,580
But people sitting up there, they might have a similar somewhere around there. They would have a similar angle.

137
00:14:47,580 --> 00:14:56,820
And it's actually a circle which stretches out from the goal. All of those points on the circle are that this is a segment of the circle here,

138
00:14:56,820 --> 00:15:02,290
and there's a circle that goes all the way round, and all of those points are on the circle.

139
00:15:02,290 --> 00:15:05,230
And so now we can define basically this.

140
00:15:05,230 --> 00:15:11,250
This is the essential bit of applied mathematics and applied mathematicians are always going on about how many parameters they have in their model.

141
00:15:11,250 --> 00:15:19,470
Here we just have a one parameter model. This angle, which defines the probability of scoring.

142
00:15:19,470 --> 00:15:26,700
A little bit of trigonometry. This is something I did by hand, you can actually work out from the X y coordinates of the shot.

143
00:15:26,700 --> 00:15:37,550
You can work out the angle. I won't go through the calculation, but you end up finding that these circles all have exactly the same angle.

144
00:15:37,550 --> 00:15:44,450
And now the next thing we're going to do is we're going to actually take data into this, and what we do is we do a thing called logistic regression,

145
00:15:44,450 --> 00:15:50,720
where we take all of the shots that have been taken in LaLiga on the Premier League

146
00:15:50,720 --> 00:15:55,940
and we calculate the angle for them and we calculate using logistic regression.

147
00:15:55,940 --> 00:16:04,100
We calculate the probability of them scoring a goal as a function of this angle and by computer fitting, I get these two parameters three point five,

148
00:16:04,100 --> 00:16:13,040
four times the angle theta and then this constant here, and they can then tell us the probability of scoring from different angles.

149
00:16:13,040 --> 00:16:22,340
It turns out the one parameter model isn't perfect. It turns out you do need to actually put in the X coordinate to get the best fit to this data.

150
00:16:22,340 --> 00:16:33,050
But this roughly gives a universal rule for scoring in football that there is a 30 percent chance here, a 50 percent chance here.

151
00:16:33,050 --> 00:16:41,530
And then there's a seven percent chance out in this in this circle, and that's roughly true across a wide range of leagues.

152
00:16:41,530 --> 00:16:49,690
And if you have if you have looked at things like football analytics, which has lots of this is the basis of what's called the expected goals model.

153
00:16:49,690 --> 00:16:58,120
Basically, this probability gives the probability on an average day of football that you'll score a goal in these different situations.

154
00:16:58,120 --> 00:17:02,090
So it's called the expected goals model.

155
00:17:02,090 --> 00:17:08,090
And it works very well, it turns out the teams that have the best expected goals in the long term, they do well.

156
00:17:08,090 --> 00:17:13,190
And so this is an example. There's an online app if you want to go in and look at your team's expected goals,

157
00:17:13,190 --> 00:17:18,110
it works for the Premier League, for the last few seasons, the Champions League and so on.

158
00:17:18,110 --> 00:17:24,290
You can go into our 12 football analytics app and you can actually look at the shots that the players have got.

159
00:17:24,290 --> 00:17:30,920
And here you see why Liverpool won the Champions League. Mané took so many shots from very close to the goal.

160
00:17:30,920 --> 00:17:35,330
Lots of them were misses, but lots of them with goals and the same thing with Mohamed Salah.

161
00:17:35,330 --> 00:17:39,950
So they've specialised in getting extremely close to the goal before they shoot,

162
00:17:39,950 --> 00:17:47,500
getting inside those circles and producing a lot of goals as a result.

163
00:17:47,500 --> 00:17:54,430
I've got something similar for an elder. Now I've got I've got one more thing here for Philip, who's a Leeds United fan.

164
00:17:54,430 --> 00:18:04,000
If you use this measure, Leeds United's last season they failed to qualify for the Premiership.

165
00:18:04,000 --> 00:18:10,960
But it turns out when I calculated or when Opta calculated the expected goals for Leeds United,

166
00:18:10,960 --> 00:18:16,150
it turns out they were extremely unlucky if it wasn't for randomness.

167
00:18:16,150 --> 00:18:19,570
Leeds United would have won the Championship last season.

168
00:18:19,570 --> 00:18:25,870
If you look at this chart, they scored more expected goals had better chances than any other team.

169
00:18:25,870 --> 00:18:31,180
They conceded fewer chances than any other team. But they still weren't promoted.

170
00:18:31,180 --> 00:18:37,390
So there's a lot of unfair randomness in football that we can't really get away from.

171
00:18:37,390 --> 00:18:45,580
But we can get an over overall underlying idea of how good teams are, and Leeds United are actually doing very well this season again.

172
00:18:45,580 --> 00:18:54,440
So I think that they because they're good in this measure, they will eventually if they can keep it up and get promoted.

173
00:18:54,440 --> 00:18:57,740
OK, so I want to go back to some of our pledges.

174
00:18:57,740 --> 00:19:05,420
This is because I think what's very interesting when you've got a statistical tool like this or a mathematical tool for understanding the world,

175
00:19:05,420 --> 00:19:12,680
how can you use it? Well, one way you can use it is the following. So this is Raheem Sterling, who plays for Manchester City.

176
00:19:12,680 --> 00:19:19,520
And this is the type of headline that you see about Raheem Sterling in certain newspapers.

177
00:19:19,520 --> 00:19:29,300
This is the headline from the Daily Mail. Manchester City star Raheem Sterling earns two hundred thousand a week but takes an £80 easyJet flight,

178
00:19:29,300 --> 00:19:33,860
and apparently this is somehow really bad behaviour on the part of Raheem Sterling.

179
00:19:33,860 --> 00:19:36,410
How dare you take an easyJet flight?

180
00:19:36,410 --> 00:19:45,800
But even worse, the son found out that Raheem Sterling he hired a private jet and headed out for two holidays in a week.

181
00:19:45,800 --> 00:19:51,410
So Raheem Sterling can't win if he goes on a cheap easyJet flight.

182
00:19:51,410 --> 00:19:57,890
That's really bad. You know, cheap football player. He earns so much money, but if he hires a private jet, then that's something.

183
00:19:57,890 --> 00:20:07,370
There's something wrong about that. And what you'll often hear is this sort of justification of why they say bad things about Raheem Sterling

184
00:20:07,370 --> 00:20:12,830
is that he's not playing very well or he's not doing all he can for the team that he plays for.

185
00:20:12,830 --> 00:20:19,250
I'm Vinnie. Jones came out and said if Raheem Sterling didn't have pace, he would be playing for Exeter and Vinnie Jones.

186
00:20:19,250 --> 00:20:25,730
So despite the fact they got to the semi the semi-final of the World Cup with Raheem Sterling playing in every match,

187
00:20:25,730 --> 00:20:30,310
Vinnie Jones was worried that he was wasting too many chances, so Raheem was to blame.

188
00:20:30,310 --> 00:20:36,650
And so you get these types of headlines about players all the time. And.

189
00:20:36,650 --> 00:20:41,510
What a collie or another person who's interested in football analytics.

190
00:20:41,510 --> 00:20:45,410
Bobby Gardner did, is he actually study this statistically?

191
00:20:45,410 --> 00:20:50,540
Is Raheem Sterling wasting lots of chances like Vinnie Jones says, and it turns out he is.

192
00:20:50,540 --> 00:20:55,700
And if you compare is expected goals with his actual goals, he's spot on.

193
00:20:55,700 --> 00:21:02,000
So the chances that he gets, he converts as an average striker or a top level striker would.

194
00:21:02,000 --> 00:21:07,880
So you have people who are overperform, for example, Harry Kane of overperformance.

195
00:21:07,880 --> 00:21:12,080
Mohamed Salah over performs. But Raheem Sterling plays out on the left.

196
00:21:12,080 --> 00:21:16,790
He isn't their top striker. That's actually a Guerra who's up there on the on the list.

197
00:21:16,790 --> 00:21:24,500
So Raheem Sterling is actually just slightly above average in conversion, so you can actually do that statistical test and show that.

198
00:21:24,500 --> 00:21:30,350
And we find actually this season that Raheem Sterling is the top striker who has the best chances,

199
00:21:30,350 --> 00:21:33,950
and he's scored quite a lot of them if we do the statistics.

200
00:21:33,950 --> 00:21:43,070
But even if you don't believe any of the statistics, I now have the final proof that Raheem Sterling actually is a good striker.

201
00:21:43,070 --> 00:21:53,360
I take it back. Vinnie Jones admits he was wrong about Raheem Sterling after Manchester City put in a fantastic display against Southampton.

202
00:21:53,360 --> 00:22:00,290
And so that's a lot of the time. What we're up against this idea that, yeah, there's this idea that it's all about some sort of passion.

203
00:22:00,290 --> 00:22:06,440
And it's not just to do with with statistics, but there's often statistics underlying why certain players are the best players.

204
00:22:06,440 --> 00:22:11,930
And I would say Raheem Sterling is the best. Statistically, he's the best England player.

205
00:22:11,930 --> 00:22:22,160
We have just now. And this goes on, so it's another example, this is Paul Pogba and the son's Old Trafford correspondent,

206
00:22:22,160 --> 00:22:29,260
and he said that it basically compared Paul Pogba to Roy Keane and poor shows and said that he

207
00:22:29,260 --> 00:22:34,420
wasn't doing his job for the team and he should try harder and do better for Manchester United.

208
00:22:34,420 --> 00:22:40,960
And this type of thing is slightly more difficult to test because it's easy when it comes to goals.

209
00:22:40,960 --> 00:22:45,730
But how do you test a midfield player? Paul Pogba plays deep in midfield.

210
00:22:45,730 --> 00:22:49,750
He plays sometimes assists, but he doesn't always score all of the goals.

211
00:22:49,750 --> 00:22:51,280
So how do you test this?

212
00:22:51,280 --> 00:23:02,710
Well, a solution to this was suggested by Sarah Rudds, who has not sure if she's a mathematician, but she has a strong applied mathematics background.

213
00:23:02,710 --> 00:23:08,020
And her idea was to use something called a mark off chain to assess, assess midfielders.

214
00:23:08,020 --> 00:23:13,330
And the idea is you basically build up a model of that in a typical game of football.

215
00:23:13,330 --> 00:23:17,080
What's the percentage chance that a ball in midfield goes out to the wing?

216
00:23:17,080 --> 00:23:18,880
What's the chance that it goes into the box?

217
00:23:18,880 --> 00:23:27,520
What's the chance that it goes into the goal and you can build up an overall model, assuming that passes in the past don't affect the future.

218
00:23:27,520 --> 00:23:32,740
You can build up an overall model of the quality of different types of passes.

219
00:23:32,740 --> 00:23:37,560
And that framework is something that we've worked with quite a bit and developed.

220
00:23:37,560 --> 00:23:41,100
Again, coming back to the idea of modelling data,

221
00:23:41,100 --> 00:23:46,260
the idea is that we use all of the ball actions in the group and we group them into possession chains,

222
00:23:46,260 --> 00:23:52,440
so each one of these these messy lines here is a possession chain ending in a shot.

223
00:23:52,440 --> 00:23:55,260
So it might be a sequence of passes dribbles.

224
00:23:55,260 --> 00:24:01,380
The ball might be lost for a few seconds, but then regained, says a chain of a possession landing in the shot.

225
00:24:01,380 --> 00:24:10,920
Then what we do is we find the probability that a certain path in this chain ended in a shot and this is really extending.

226
00:24:10,920 --> 00:24:15,720
The expected goal was model over the entire pitch. So we're looking at all the passes.

227
00:24:15,720 --> 00:24:19,380
What was the chance that they ended in the shot? Then we work out.

228
00:24:19,380 --> 00:24:26,130
Was it a goal? If you have all of these past coordinates in the shot and then we did a similar thing,

229
00:24:26,130 --> 00:24:30,720
but in reverse, we did a similar thing for dribbles and then we do the reverse for tackles.

230
00:24:30,720 --> 00:24:39,900
So if you prevent a attempt on goal by the opposition, then you can actually evaluate how dangerous that type of attempt was.

231
00:24:39,900 --> 00:24:43,770
And this allows us to build up a model of the whole game of football,

232
00:24:43,770 --> 00:24:53,300
assuming that everything is memory loss that we go from just from one place to the other, not remembering the sequence that they were in before.

233
00:24:53,300 --> 00:25:01,370
And that could then find us we actually could find that Paul Pogba was one of the most important players at the World Cup.

234
00:25:01,370 --> 00:25:06,020
He made a lot of passes from deep here in midfield.

235
00:25:06,020 --> 00:25:09,140
And these are multiple evaluated is extremely valuable.

236
00:25:09,140 --> 00:25:14,960
If you can pass the ball from here to here, then you're going to be able to launch a very quick counterattack counterattack.

237
00:25:14,960 --> 00:25:22,360
And so he makes a lot of passes that are of extremely high value.

238
00:25:22,360 --> 00:25:26,680
And we made a ranking actually for last season based on this measure.

239
00:25:26,680 --> 00:25:33,190
The green one is the attack value, the red one is defence and the blue one is scoring goals.

240
00:25:33,190 --> 00:25:38,830
And I just wanted I wanted to really rub it into Manchester United fans about who the best players were.

241
00:25:38,830 --> 00:25:48,100
So I use this as an excuse. I just ran Liverpool and Manchester United players last season, ranked according to our Markov chain model.

242
00:25:48,100 --> 00:25:56,170
And it's interesting. See that Virgil van Dijk, who won European Player of the Year, came out top mainly because of his defensive contributions.

243
00:25:56,170 --> 00:26:00,280
But then in second place you have Paul Pogba and he does everything.

244
00:26:00,280 --> 00:26:07,540
He produces lots of effective passes. He defends very well and he has lots of very good shots and goals.

245
00:26:07,540 --> 00:26:12,250
Then you have a whole row of Liverpool players all the way down to market share.

246
00:26:12,250 --> 00:26:18,520
And so we can actually measure the scale of the players and this is what I like to think of.

247
00:26:18,520 --> 00:26:22,390
If you are, I'm going to come to Barcelona now where I went to visit.

248
00:26:22,390 --> 00:26:29,650
But Barcelona were for a while very interested in signing Paul Pogba and I don't think that they think, well, Pogba doesn't have as much passion,

249
00:26:29,650 --> 00:26:40,250
is keen, does what they're thinking in their mind is Pogba passes the ball up from midfield in a much more effective way than any other player.

250
00:26:40,250 --> 00:26:48,830
So now I'm going to come to my own contribution and how what I've been doing and in football, as I said before,

251
00:26:48,830 --> 00:26:54,530
I think we've gone over that a lot of my work was on collective animal behaviour, trying to understand the movements of animals.

252
00:26:54,530 --> 00:27:04,070
And then when I started writing Soccer Matic's, I became very interested in exactly this type of movement on the pitch.

253
00:27:04,070 --> 00:27:10,790
So if you watched Barcelona, maybe on our show, this is the Barcelona team of 20, 10 11.

254
00:27:10,790 --> 00:27:19,050
Lionel Messi, you see him. But what you also see is some very, very nice, ticky tack of passing that they did during that time.

255
00:27:19,050 --> 00:27:24,640
And what we could do is we could break down those types of passes.

256
00:27:24,640 --> 00:27:32,230
By we used something called a de looney triangulation, and this is where you connect the nearest neighbours,

257
00:27:32,230 --> 00:27:39,130
the most direct neighbours, the neighbours who have a border with each other, whether with a line, and that gives you a triangulation.

258
00:27:39,130 --> 00:27:44,170
And what you see is that message opens up a lot of passing to John Vitol example.

259
00:27:44,170 --> 00:27:48,730
He has an open past in the East. He has one hair out to the right.

260
00:27:48,730 --> 00:27:56,230
And if they do this, if they stand in this way where they're kind of maximally distant from other players around them,

261
00:27:56,230 --> 00:28:02,980
they're still only triangulation opens up automatically. And so this is called a veterinary diagram.

262
00:28:02,980 --> 00:28:12,940
And it turns out that a lot of what Barcelona do is that they stand in a way which puts their opposition on the edges of the veterinary diagram,

263
00:28:12,940 --> 00:28:17,500
which means that they're maximally distant from them at any given point.

264
00:28:17,500 --> 00:28:24,130
And as a result, this triangulation opens up where they can actually pass the ball very effectively to each other.

265
00:28:24,130 --> 00:28:30,850
So there's a kind of mathematical principle underlying the Tic TAC of football that Barcelona have been playing,

266
00:28:30,850 --> 00:28:35,500
and I was very excited about this and I wrote a lot about it in schematics.

267
00:28:35,500 --> 00:28:45,730
And then I was lucky enough to be invited down to Barcelona and see this is Messi up close and personal, so I got to see Messi really near in action.

268
00:28:45,730 --> 00:28:50,650
I didn't get to meet him, unfortunately. I was probably at one point I was at the training group.

269
00:28:50,650 --> 00:28:56,830
I was at this training ground, so I was probably a few hundred metres away from Messi when he was training and 100 metres away.

270
00:28:56,830 --> 00:29:05,470
But I didn't get the introduction, unfortunately, but I did get to meet the data scientists who work at Barcelona and they actually have a team.

271
00:29:05,470 --> 00:29:09,790
It's a little bit like a sort of university department there with all the sports science they do,

272
00:29:09,790 --> 00:29:14,500
it's really impressive placed to see what they're trying to do.

273
00:29:14,500 --> 00:29:25,660
And I met this guy here. This is Javier Fernandez, and I was, of course, very pleased with all my glowingly triangulation and border noy diagrams,

274
00:29:25,660 --> 00:29:32,020
and I gave a presentation there and told them all about it. And they were like, Yeah, yeah, of course we know all of that.

275
00:29:32,020 --> 00:29:39,070
They're there. And I was very surprised to hear that they were they already use that type of technique.

276
00:29:39,070 --> 00:29:47,920
And what Javier had developed was an even better technique for measuring basically who's going to come to the ball first.

277
00:29:47,920 --> 00:29:57,010
So here is a here is Barcelona playing in a purple and the green areas show where a Barcelona player will come to first.

278
00:29:57,010 --> 00:30:01,240
The red area show where the opposition players will come to first.

279
00:30:01,240 --> 00:30:07,000
And this they track for every match and they're able to see how the team controls space.

280
00:30:07,000 --> 00:30:11,890
And the whole of Barcelona's game is built up about how you can control space.

281
00:30:11,890 --> 00:30:15,550
And Javier is sitting there after the match looking well.

282
00:30:15,550 --> 00:30:19,150
Have they controlled space in the way that they said they would control space and

283
00:30:19,150 --> 00:30:25,140
he can actually give feedback and so on about how they're controlling space?

284
00:30:25,140 --> 00:30:29,670
And so I took a lot of what I learnt to Barcelona,

285
00:30:29,670 --> 00:30:36,300
and now now I have a research project together with them and wanted to put that into work in Hammarby.

286
00:30:36,300 --> 00:30:44,690
As I said, this started with me phoning virtually, phoning you by the way, Juergen, you know, you can actually still come and contact me.

287
00:30:44,690 --> 00:30:48,600
I'm I am a Liverpool fan, so I would rather be working for you.

288
00:30:48,600 --> 00:30:55,920
So yeah. But so they started with me making this and Hammarby did ring me up, and they were local team in Stockholm,

289
00:30:55,920 --> 00:31:00,840
so it was much more easy for me to start working with them and their coach, Stefan Bellbottom.

290
00:31:00,840 --> 00:31:07,710
He was very open to this type of this type of collaboration, and now I often go to the trainings.

291
00:31:07,710 --> 00:31:09,870
We have development things here.

292
00:31:09,870 --> 00:31:18,750
And what's most fun is that we have a feedback cycle where we can present what we've learnt to the players and show the mathematical models.

293
00:31:18,750 --> 00:31:24,450
And they say whether they think that this works or that we can actually give them feedback on their performance.

294
00:31:24,450 --> 00:31:27,470
And I'm going to give a few examples of this.

295
00:31:27,470 --> 00:31:34,670
One is exactly as I said, this was Javier's method that he's been developing, we've we've been developing along that idea.

296
00:31:34,670 --> 00:31:42,310
This is a goal that we scored recently. Where the green team here.

297
00:31:42,310 --> 00:31:48,740
So you're cheering for the green team now, right? OK, so if the blue team score is bad, green team need to score.

298
00:31:48,740 --> 00:31:57,370
So oh good. We've got the ball back. This is Mojo Jankovic shoes our best ranked player just now, according to our system.

299
00:31:57,370 --> 00:32:01,330
Alex Kuczynski, who played for Fulham. Both of them play for Fulham at one point.

300
00:32:01,330 --> 00:32:06,820
Get the ball out to Nico. Nico gets it back into the middle and Moyo, who got the ball back in the first place.

301
00:32:06,820 --> 00:32:15,430
He manages to score a goal and is very happy. And what I like about this goal in particular and now going to do the same thing,

302
00:32:15,430 --> 00:32:22,600
but analyse it from this top down view and I'll just let it play to start with so you can get a feeling for it.

303
00:32:22,600 --> 00:32:26,710
So this is the opposition. It's stones foul attacking. They take the shot, the ball comes back.

304
00:32:26,710 --> 00:32:31,300
Moyo is twenty two. He collects it. Nico opens up space here.

305
00:32:31,300 --> 00:32:35,710
Alex opens up space here. Nico still got this lovely space here.

306
00:32:35,710 --> 00:32:43,360
All the time, keeps it, keeps it keeps that. Then the attacking players come in and score a goal and so we can actually

307
00:32:43,360 --> 00:32:48,790
see how they're controlling and using space in the build up for those goals.

308
00:32:48,790 --> 00:32:54,460
These points are very important because one thing we talked about a lot was defence.

309
00:32:54,460 --> 00:33:01,150
You need to come back and defend. Even as an attacking midfielder, Moyo is a player who always wants to run up and score goals.

310
00:33:01,150 --> 00:33:03,520
But if he's standing around here,

311
00:33:03,520 --> 00:33:11,080
then we actually when when the shot comes in and it's controlled by the defender or it's headed away by the defender,

312
00:33:11,080 --> 00:33:15,910
we control a lot of the area outside our box and they don't control that.

313
00:33:15,910 --> 00:33:20,320
And so if you think of the ball is just sort of bouncing out a random direction,

314
00:33:20,320 --> 00:33:24,760
we're going to control a lot of the places where it could balance out, too.

315
00:33:24,760 --> 00:33:29,830
And here's another where a few seconds later, you see Alex controls the space in front of him.

316
00:33:29,830 --> 00:33:32,560
Alex is No. 20. He's running in this direction.

317
00:33:32,560 --> 00:33:39,310
Nico is number 40 running in this direction, and they've started to control the attacking space on their way out.

318
00:33:39,310 --> 00:33:43,690
And so you can actually get an idea about what spaces we're controlling.

319
00:33:43,690 --> 00:33:50,440
Another thing you can do is you can look at past probabilities. This is when Alex sent the pass out to Nico.

320
00:33:50,440 --> 00:33:54,820
This is basically 100 percent success rate expected from our model.

321
00:33:54,820 --> 00:34:03,850
We calculate all the possible passes he could make, and we could say Alex could have tried to play the ball through to Moyo straight away.

322
00:34:03,850 --> 00:34:11,590
We have a 60 percent on that, but he has a 98 percent chance if he passes through to Nico.

323
00:34:11,590 --> 00:34:19,030
Then a few seconds later, we have this situation, and then we found out that now Nico has a 65 percent chance to Moyo.

324
00:34:19,030 --> 00:34:25,270
He could have also taken the post further away, but if he takes the post further away,

325
00:34:25,270 --> 00:34:31,900
then he's got a worse angle for the striker that so the best decision is to take the 65 percent chance which he takes.

326
00:34:31,900 --> 00:34:38,890
And on this score. And so we can use this type of technique basically to improve the positioning.

327
00:34:38,890 --> 00:34:42,880
This is a project together with Fran Peralta, who did.

328
00:34:42,880 --> 00:34:49,990
This is a master's thesis. I've been I've become incredibly popular in my university when it comes to writing master's thesis.

329
00:34:49,990 --> 00:34:55,810
Like, I get a lot of requests to do this and I know that most of them do.

330
00:34:55,810 --> 00:35:01,390
I do manage to find the time for them because it's so many exciting cycling projects to do in maths and football.

331
00:35:01,390 --> 00:35:06,010
But Fran wrote a master's thesis doing this and what our idea was.

332
00:35:06,010 --> 00:35:15,760
We can actually feedback and improve the performance of play, and I feel I take another example from Barcelona.

333
00:35:15,760 --> 00:35:19,810
I think this is a lovely. So what do you think is the most important?

334
00:35:19,810 --> 00:35:25,520
Maybe I'll have? This is a sort of test. What's the most important thing that happens in this sequence?

335
00:35:25,520 --> 00:35:32,150
Have I got any suggestions, anyone? So the girl, the that guy in the left is very important.

336
00:35:32,150 --> 00:35:40,630
He runs and gets the ball. Is this the one? You mean it's going to spread the cost?

337
00:35:40,630 --> 00:35:51,440
Him here. Yes, he's very he gets the bullets, so he's very important, but I think that the absolute most important thing is this run here.

338
00:35:51,440 --> 00:36:00,350
Because what that run does is it opens up space for the for the player on the left so he can run through onto it,

339
00:36:00,350 --> 00:36:09,120
and you can actually see that in this picture. So here is the top down view again,

340
00:36:09,120 --> 00:36:19,140
the ball is coming from here in the past is going to there and you can see as the player as the player here moves inwards,

341
00:36:19,140 --> 00:36:28,820
it opens up a green space for an elbow on the left. And so it's the movement actually opens up for the other players.

342
00:36:28,820 --> 00:36:32,990
And we can actually simulate how the football players move.

343
00:36:32,990 --> 00:36:37,100
And this idea comes from a lot of what we worked on with animal behaviour.

344
00:36:37,100 --> 00:36:44,270
We can simulate one or two seconds into the future because when animals try and avoid colliding with each other,

345
00:36:44,270 --> 00:36:49,730
they tend to anticipate where other animals are moving to and move into open space.

346
00:36:49,730 --> 00:36:53,140
And so we can anticipate what happens into the future.

347
00:36:53,140 --> 00:37:01,280
We can say to the players, you can anticipate what's going to happen into the future, where should you move optimally in such situations?

348
00:37:01,280 --> 00:37:06,830
And we can simulate that. This is an example of a right back. He was quite a long way from the play.

349
00:37:06,830 --> 00:37:14,990
We have an optimal position. He should move out here. In fact, he moves quite centrally, so he doesn't really move in an optimal position.

350
00:37:14,990 --> 00:37:23,150
But what we actually find about the attacking midfielder here is he did move in a perfectly optimal way.

351
00:37:23,150 --> 00:37:29,690
So his run where he if you look at the run, it starts, he runs like this and then he stops like that,

352
00:37:29,690 --> 00:37:34,130
and you could classify that as being quite lazy that you then kind of, yeah, OK.

353
00:37:34,130 --> 00:37:39,410
But he actually, the way he stops when we calculated it in the model was optimal.

354
00:37:39,410 --> 00:37:46,500
He had the best stopping position. And this is the sort of thing that we can use with the players, and we've been doing this,

355
00:37:46,500 --> 00:37:55,140
how maybe we're basically starting doing this, maybe just now where we can give them feedback.

356
00:37:55,140 --> 00:37:58,650
Now I have to. Yeah, so this was this was a very nice example where we got the ball back.

357
00:37:58,650 --> 00:38:03,810
You shouldn't shoot from there, actually, but so we'll forget, we'll forget about the shot.

358
00:38:03,810 --> 00:38:13,080
We talked about that, too. What I'd like to point out here is that the press play here, so they've got the ball and we organised.

359
00:38:13,080 --> 00:38:15,330
So we've got man marking very nearby.

360
00:38:15,330 --> 00:38:22,860
But we also control all of the space so we can measure how we're managing to press them and how we're controlling the space around the team.

361
00:38:22,860 --> 00:38:30,060
And we could calculate with this was their actual position is a shadow picture, the shadow dot and their real position.

362
00:38:30,060 --> 00:38:36,150
And we could actually show the players afterwards that you were pretty much optimally positioned in that type of press.

363
00:38:36,150 --> 00:38:41,180
I'll take the question afterwards.

364
00:38:41,180 --> 00:38:48,770
There's lots we can do, this was this was this was one of my favourites, because can I say another thing about football players?

365
00:38:48,770 --> 00:38:56,090
They're so sweet, like you see them out on the pitch and they're like, really angry and angry, and I should have been a foul referee.

366
00:38:56,090 --> 00:39:00,770
But like, when you meet them, they're like the nicest people you left me.

367
00:39:00,770 --> 00:39:06,920
They're really sweet and mild mannered. And David's, you know, it's OK if you tell me about this or something.

368
00:39:06,920 --> 00:39:12,560
And this is an example. So this this what I was just showing here. This is Emad Khalili.

369
00:39:12,560 --> 00:39:18,490
He played the following pass. And it went out there and it didn't get to the player.

370
00:39:18,490 --> 00:39:26,800
And if you want to show this one more time, here we go.

371
00:39:26,800 --> 00:39:35,530
If you look at Moyo, there is like really annoyed with Armand because he wanted the ball and Imat didn't pass into.

372
00:39:35,530 --> 00:39:42,430
And so afterwards, Imad asked me, You know, did I make the right decision in making this pass?

373
00:39:42,430 --> 00:39:48,320
And you could actually see that given the percentages. There was a very small margin that he could get it to.

374
00:39:48,320 --> 00:39:55,210
Moyo And though the board didn't quite get to their left back, it was the right decision to play that pass.

375
00:39:55,210 --> 00:40:02,670
So you can actually use the model to evaluate how you're playing after after the game.

376
00:40:02,670 --> 00:40:10,910
Right. That's a lot in my experience and how it's been working out in using this type of mathematics, this type of applied mathematics.

377
00:40:10,910 --> 00:40:17,600
And now I come back to my major point, what is it that applied mathematicians have got in all of these examples?

378
00:40:17,600 --> 00:40:23,660
We start with data. We start building up models and then we try and fit our models to data.

379
00:40:23,660 --> 00:40:30,110
And that's basically how we cycle through in everything that we do, all of the projects that we study.

380
00:40:30,110 --> 00:40:34,940
And that's really what I think makes applied mathematicians quite quite special.

381
00:40:34,940 --> 00:40:43,310
And we have got one very special applied mathematician here, and I learnt I myself learnt a lot of this art from from Philip.

382
00:40:43,310 --> 00:40:54,290
And I had a room of Philip that you have actually written to Premier League clubs and said you've lost him or, you know, you've sacked your manager,

383
00:40:54,290 --> 00:41:01,940
you need a new manager and you have a collection of you don't have any any except unless you have a collection of rejection letters.

384
00:41:01,940 --> 00:41:09,500
Is that correct? They're not rejection letters. They're considered, Oh, they're considering it, right?

385
00:41:09,500 --> 00:41:15,110
Well, I think if anyone would like to pose the question we can ask, ask Philip about the contents and some of these letters afterwards.

386
00:41:15,110 --> 00:41:20,150
But I think unfortunately, Philip, I mean, we're here to celebrate your 40th birthday.

387
00:41:20,150 --> 00:41:25,640
Was it way? Unfortunately, I think it might be too late for you because one thing I've learnt,

388
00:41:25,640 --> 00:41:30,530
for example, Stefan Billboard, who's the manager of Hammarby, is quite an analytic person.

389
00:41:30,530 --> 00:41:35,330
Actually, I think Marino is a bit more analytic than I gave him credit for at the start.

390
00:41:35,330 --> 00:41:42,050
And certainly, Claudia is an analytic person. Plus, it's an incredibly difficult job.

391
00:41:42,050 --> 00:41:48,020
So we've probably got quite a lot of academics here in the room. And you know how it is when you get your paper rejected,

392
00:41:48,020 --> 00:41:53,840
how horrible it is for your fellow students who've written spent so much time working on it and so on.

393
00:41:53,840 --> 00:41:59,450
Think about being a manager and how you have to go into work after losing a match and get everyone.

394
00:41:59,450 --> 00:42:01,850
You've got twenty two students to take care of.

395
00:42:01,850 --> 00:42:08,300
In this case, 20 to 30 students and lift up their morals is a really, really difficult job to keep going.

396
00:42:08,300 --> 00:42:14,060
I've got a lot of respect now for being a football manager, but I do think.

397
00:42:14,060 --> 00:42:22,940
That there is this future, I think that there will be some point in the future where these types of mathematicians like Bob and Sarah and Javier,

398
00:42:22,940 --> 00:42:31,020
there is a chance that they might be managing football clubs or be very close to being an important decision making roles within those clubs.

399
00:42:31,020 --> 00:42:40,470
So I do think there's this inspiring possibility for a future where an applied mathematician can make a difference at a football club.

400
00:42:40,470 --> 00:43:04,404
And I think that was all I have to say. Thank you very much.