We've got one million Premier League seasons.
So what's happened is me and me mate Adam, we've got together, and we've come up with a mathematical model and we've simulated
one million seasons in the English Premier League, which is the Football League that we have here in England, just to see what happens basically.
Okay, so for those of you that don't know, eh this is how the, the, the Premier League works,
it's the top flight of English football or soccer as eh, Americans like to call it.
And basically there are twenty teams, everybody plays each other home and away,
and if you win the game you get 3 points, if you draw you get 1 points if you lose you don't get any points.
It, you basically just tot up the points and see who's got the most points.
If there's any sort of ties, so some teams have the same number of points, there's no playoffs or anything like that.
It goes down to something called goal difference,
which is basically you take the number of goals that a team has scored and take off the number of goals
they've conceded. After that you go - it goes on goals scored. And
after that, it's just, they just agree a tie,
there's no ranking. And you can actually have literally two teams with identical records, in principle, and
literally, they won't be ranked. They'll just say, well, equal.
Obviously the goal is to is to win, win the championship.
But it's also really important to get into the top four
because the teams that get into the top four, they go into - there's something called the Champions league the next season.
Which is really lucrative, loads of money.
The big thing you want to avoid is
relegation, so that's finishing in the bottom three.
If you finish in a bottom three
you actually drop down
to the division below - to the league below - the subsequent season and that's really bad because
obviously
it's nowhere near as glamorous, far less income - all together a whole lower standard of football and you don't want to be there basically.
So that's the thing to avoid.
So football fans everywhere, you know, we like to argue about you know,
how many points do you need to win the league, for example? I mean that's a, that's a big issue this season because you know
there's two teams that have got really great records,
they're Liverpool and Manchester City. And it looks like you're gonna need a lot of points to win the league this season.
It's a thing you can ask: normally how many points would you need to win the league? How many points do you need to guarantee
entry into the Champions League the next season, to finish in that top four?
And of course the one that people really worry about is how many points do you actually need to avoid relegation?
What's - people talk about the magical forty point mark. So this is why we got interested,
we were interested in asking these questions from a mathematical point of view. So, of course we could answer some of these questions
theoretically, but in not very interesting way. So for example, if you get 64 points you're guaranteed not to be relegated.
That's a fact, right? You can show that quite easily.
But of course anybody who gets 64 points, or 63 points actually, is not going to get relegated in any reasonable season.
So we wanted to think more about probabilities and what, you know, what's likely to happen. But mathematically that's pretty much impossible to do
what we call analytically. So you really have to run computer simulations, use this idea of a Monte Carlo simulation.
And you use sort of randomness to sort of try to create random seasons. And then over a lot of seasons the sort of
probabilistic
scenarios sort of play out. This idea of Monte Carlo simulations,
they go back to the development of the atomic bomb actually. So we had a bit of a journey in
building up, building our model. We started off with some simpler models and then developed a quite sophisticated one
which is kind of based on the kind of thing that bookmakers use to predict outcomes of games.
We used something called a Poisson distribution to sort of get the expected goals we said a given team would have in a given game,
and built the model from that. And that used data from, from last season's Premier League actually.
It's kind of a weird season in as much as Manchester City had an anomalously good season. They got 100 points.
We're at the mercy of that, but we had to use something. And we literally played out the games in the simulation.
So we did it, as I said, 380 games over a season - a
million seasons. It is quite quick. I mean, I'm not going to take the credit for this,
I'm sure if I wrote a bit code that tried to do this it would take forever,
but my friend Adam is much better at that sort of thing than me and was able to write a very efficient code
which did it in about 20 minutes, half an hour or so.
And so we were really able to get out some fun statistics out of it.
Basically how many points do you need to win the Premier League, on average, based on this simulation?
Well,
it turned out that the mean number of points that finished second place
was eighty five point two. So basically that's telling us that you if you get 86 points,
chances are you're gonna win the league. In reality,
you know, the team winning the league was getting 95 points or so, in this simulation. Again
that's because City did so well last season and we were using last season's data. To get the Champions League for example, on
average you would need 72 points according to this simulation, which is a reasonable figure. There are some
circumstances where you would, you would need a lot more or a lot less, but that was generally the ballpark. Now the crunch,
to avoid relegation.
Well, we can look at the, at the number of points on average scored by the
the 18th team
so that's the the top team that did get relegated. And they got
32 and a half points was the mean. So that basically means that 33 points should be enough to avoid relegation
based on the sort of the simulations you would get from from from last season's data. That's quite low,
I think that's bit on the low side.
But again, you know, if we'd averaged over more seasons with our data, probably we would have maybe got a higher figure there.
So over a million seasons what sort of things happened?
So for example
what's the most points that somebody won the league with? Needless to say Manchester City did on a, on actually on 62 occasions score
114 points, which is where they won every single game.
So 62 times out of a million season City got, you know, got all the points that were available. The highest number of points
somebody got relegated with? Okay, that would be a disaster, right? You could get relegated on a large number of points.
Actually, it wasn't that high in these simulations. The highest number of points somebody got relegated with our million seasons
was
44.
And actually that's that's kind of close to the sort of Premier League data. West Ham went down on 42.
There was a season when teams played a few more games, where Crystal Palace went down on 49,
which was considered the ultimate disaster.
(Brady: So in the million seasons there weren't any cases, really, where a team got relegated having a really good season?)
Nah, nah, not really. So other things that you notice: the most number of goals scored by a team in a season,
Manchester City on one particular season scored 161 goals.
Which blitzes the, the actual record which was set by Aston Villa in 1931, where they scored
128 goals. Again that was in 42 games.
Somebody actually won the league in this as well only scoring 50 goals.
Obviously Man City did annoying well. Out of the 1 million seasons, they won the league nearly 900 thousand times,
they won it eight hundred ninety six thousand three hundred and thirteen times.
Actually the team that won the next most, this is kind of curious,
you probably would think given that we were basing our last season data that the second-place team from last season,
which was Manchester United, would win the next most. That's not what happened.
The team that won the next most, which kind of pleases me, was Liverpool.
Okay, who finished fourth last season. They won the league in this 45 thousand eight hundred sixty-two times out of our simulation.
So the reason the model favoured Liverpool was because when they won games they won by a lot. They scored a lot of goals,
they won spectacularly when they won last season. So the model kind of likes that. - (Brady: Over the million seasons in your model)
(was there a freak season like the famous Leicester season where it, where an underdog came through and won it?)
So, not really, okay? So not in our, in the model simulation I'm talking about here.
We did do a trial simulation where Leicester, and it was Leicester actually,
won the league three times out of a million. In this simulation, this sort of main one, the final one,
nobody outside of the top six won the league. Nobody. It's kind of depressing actually. - (Brady: Did any of the big super teams ever get relegated?)
They did yes. Yes, this is quite funny actually.
Chelsea, poor old Chelsea, got relegated five? Five times? They finished second from bottom twice and they finished third from bottom three times.
None of the other big six got relegated. There were a few sort of anomalous things. Southampton did surprisingly
well.
They finished second once and they got into the Champions League - get this they got into Champions League 22 times out of a million!
Okay, which is really, and they're completely anomalous. There's like, nobody else sort of that far down the table does anything like that
well. Again, it'll be because of the nature of it how their games played out,
they probably scored, they scored plenty goals - that kind of thing.
So there's sort of a general overview of the season data, but there's some more fun extremes sitting in there
which we've got to talk about. What's the biggest win that anybody had in our simulation in our million seasons?
Well needless to say it was Manchester City. And they beat Bournemouth 20 goals to 1.
So they scored 20 goals, Bournemouth got 1. That's blowing out of the water the sort of the kind of thing
we've actually seen in real life. The record
score in a top-flight game is 12 nil. Done by West Brom over 100 years ago, also Notting Forest
did it over 100 years ago.
(Brady: But over the course of a million years, it's reasonable that it'll happen one day) - It is, it is.
I mean, it's not so crazy that City might occasionally get those those kind of score lines over a million seasons,
absolutely not.
There were even more other remarkable score lines. Everton seemed to be heavily involved in some in some crazy score lines. The highest number of
goals by a losing team - ten. Chelsea played Everton at Goodison Park, Everton won 11-10.
Okay, so that's a quick - and Everton seemed to be involved in a lot of these games.
There was a Merseyside derby which was the highest scoring draw. That was Everton nine, Liverpool nine.
I don't think my heart would be able to cope with a game
like that. I went to see Liverpool and Everton play and it was, it was a 4 all draw and that was bad enough.
Nine all I don't think I could handle.
The most goals in a game, okay. So the most goals in a game, that was Manchester City beat - again -
Everton, 17-5.
22 goals in that game. There's actually, the record in English football that, in real English football not in our
simulation, was Tranmere Rovers Tranmere beat Oldham 13-4. So 17-5 is not
actually that far away if you think about it. You know the model's not perfect.
One thing it doesn't do very well, for example, is predict nil-nils. The reason for that is because a nil-nil draw is it's kind of - could be kind of a game of attrition.
We, you know once a team gets sort of set in like that then that dictates what happens
next. And the model doesn't do that because it's really, really about randomness, okay, so it doesn't really capture nil-nils very well.
So that's one of, one of the weaknesses of it. And actually it's not really clear how you would fix that, that's tricky.