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  • We've got one million Premier League seasons.

  • So what's happened is May and we may.

  • Adam, we've got together on.

  • We've caught with a mathematical model and we've simulated war 1,000,000 seasons in the English Premier League, which is the football league that we have here in England just to see what happens.

  • Basically, OK, so for those that you don't know, this is how the Premier League works.

  • It's the top flight of English football or soccer a zoo.

  • Americans like to call it on.

  • Basically, they're 20 teams.

  • Everybody plays each of their home in a way, and if you win the game, you get three points.

  • If you draw, you get one point.

  • If you lose, you don't get any points.

  • You basically just talked on the points and see who's got the most points.

  • If there's any sort of ties or some teams have the same number of points, there's no playoffs or anything like that.

  • It goes down Thio, something called goal difference, which is basically you take the number of goals 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 win win the championship.

  • But it's also really important to get into the top four because the teams to get into the top four, they go into that 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 the 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 his glamorous, far less income.

  • Altogether.

  • 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 how many points do you need to win the league, for example.

  • I mean, that's a big issue this season because you know, there's two teams that I've got really great records there, Liverpool and Manchester City on.

  • 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 you need to guarantee entry into the Champions League the next season to finish in the top four?

  • And of course, the one that people really worry about is how many points do you actually need to avoid relegation?

  • What people talk about the magical 40 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 not very interesting way.

  • So, for example, if you get 64 points, you're guaranteed not to be relegated.

  • That's a fact or a theory.

  • You can show that quite easily, but of course, anybody 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 on what 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 Monte Carlo simulation.

  • You sort of randomness to sort of try to career random seasons on then over a lot of seasons.

  • The sort of problem list probabilistic scenario 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 simple models and then developed quite sophisticated one, which is kind of based on the kind of thing that bankers used to predict outcomes of games.

  • We use something called a plus on distribution to sort of get the expected goals.

  • We said a given team would have any given game.

  • I'm built the model from that that used data from from last season's Premier League actually kind of a weird season.

  • Inasmuch, is Manchester City harder on anomalous, Really good season.

  • They got 100 points were at the mercy of that, but we have to do something and we literally played out the games in the simulation, so we did it.

  • As I said, 380 games over a season a 1,000,000 seasons.

  • It is quite quick.

  • I'm not gonna 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, that me and was able to write a very efficient code which did it in about 20 minutes, Self an hour or so.

  • And so we really able to get some food in statistics out of it.

  • Basically, how many points you need Thio in the Premier Li, on average, based on this simulation, well, it send out of the mean number of points that finish second place was 85.2.

  • So basically, that's telling us that you 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 will be using last season data Thio 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 need a lot more or a lot less.

  • But that was Germany, the ballpark now the crunch to avoid relegation, well, we can look at the at the number of points on average, scored by the thief 18th team.

  • So that's the top team that did get relegated and they got 32 a half points.

  • Mean so that basically means that 33 point should be enough to avoid relegation based on the sort of the simulations you would get from from last season there.

  • That's quite low, I think, bit on the low side.

  • But again, you know, you read, averaged over more seasons with dates and probably would have maybe got a high figure there.

  • So over a 1,000,000 seasons, what sort of things happened?

  • So, for example, what's the most points that somebody won the league?

  • Needless to say, Manchester City did on on actually, on 62 occasions, score or 114 points, which is where they won every single game.

  • So 62 times out of a 1,000,000 season city got a lot of points that were available.

  • The highest number of points.

  • Somebody got relegated with Okay, that would be a disaster, right?

  • Get relegated on the large number of points.

  • Actually, it wasn't that high in these simulations.

  • The highest number of points somebody got relegated within our 1,000,000 seasons was 44 on.

  • Actually, that's that's kind of close to this sort of probably data.

  • West Ham went down on 42 42.

  • There was a season when teams played a few more games where Crystal Palace went down on 49 which is considered the ultimate disaster.

  • So in the 1,000,000 seasons, there weren't any case is really where a team got relegated.

  • Having a really good singer now, not really other things, that sort of thing 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 actual record 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 the well of the one million seasons.

  • They won the league nearly 900,000 times.

  • They want 896,313 times, actually, the team that won the next most.

  • This is kind of curious.

  • You probably would think, given that we're basing our last season data that the second place team from last season with Manchester United would win the next most.

  • That's not what happened.

  • The team that won the next most kind of pleases, May, was livable.

  • Okay, who finished fourth last season?

  • They won the league in this 45,862 times of our simulation.

  • So the reason a model favor Liverpool was because when they won games, they will buy a lot.

  • They scored a lot of goals.

  • They want spectacularly when they won that season.

  • So the model cannibal expat over the 1,000,000 seasons in your model, was there a freak season like the famous Lester season, where where an underdog came through?

  • So no, Really?

  • Okay, so no.

  • In in the model simulation of talking about here, we didn't have a trial simulation where less there, and it was less they're actually won the league three times out of a 1,000,000 in this simulation lists of Maine on the final one, nobody outside of the top six won the league.

  • Nobody kind of pressing.

  • Actually.

  • Did any of the big super teams ever get relegated?

  • Did?

  • Yes, yes, this is quite funny, actually.

  • Chelsea for old Chelsea got relegated 55 times.

  • They finished second from bottom twice and then finished third from bottom three times.

  • None of the other Big Six got relegated.

  • There were a few sort, anomalous things.

  • Southampton did surprisingly well.

  • They finished second once on they got into the Champions League.

  • Get this the guards and cameras in 22 times out of a 1,000,000.

  • Okay, which is really another completely anomalous.

  • There's like nobody else sort of that far down the table.

  • Does anything like that?

  • Well, again, it will be because of the nature of it, how their games played out.

  • They probably scored a sickle, plenty of goals, that kind of thing.

  • So there's a sort of general overview of the season, but there's some more fun extreme sitting in there, which we've gotta talk about.

  • What's the biggest win that anybody had in our simulation in our 1,000,000 seasons?

  • While Needless to say, it was Manchester City on they beat Born with 20 goals to 1 20 girls.

  • Bob got one.

  • That's blow it out of the water.

  • That sort of that kind of thing we've actually seen in real life at the record, scoring a topflight again.

  • 12 milk.

  • Don't buy West Brom's over 100 years ago.

  • Also, not Forrest did it over 100 years ago, but over the course of a 1,000,000 years, it's reasonable that it'll happen.

  • Wonder it is, it is.

  • I mean, it's not so crazy that sitting my occasional get those those kind of score lines over a 1,000,000 seasons.

  • Absolutely not.

  • There were even more other remarkable scorelines, evidencing to be heavily involved in some crazy scorelines, the highest number of goals by a losing team.

  • 10.

  • Chelsea played Everton.

  • Goodison Park, Evan won, 11 10.

  • It's okay, so that's it.

  • Again, Evan seem to be involved in a lot of these games.

  • There was a Merseyside Darby, which is the highest scoring drawer that was ever to nine Liverpool nine.

  • I don't think my heart would be able to cope with the game like I wouldn't see.

  • Look for 11 play and it was a four old drawer.

  • That was bad enough.

  • And I know all.

  • I don't think I could handle number seven 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.

  • Actually, that the record in English football that really English football.

  • Not in our simulation was Tranmere overs trying maybe older, 13 4 17 five's not actually that far away.

  • If you think about it, you know the models not perfect.

  • One thing it doesn't do very well, for example, is predictable nails.

  • The reason for that is because a nil nil draw or is it could be kind of a game of attrition.

  • We don't want a team get sort of set in like that, then that dictates what happens next on.

  • The model doesn't do that because it's really, really about randomness.

  • Okay, so it doesn't really capture nil nails very well.

  • That's one of one of the weaknesses of it, and actually, it's not really clear how you would fix those.

  • It's that's tricky.

We've got one million Premier League seasons.

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百万人のシミュレートされた季節 - Numberphile (A Million Simulated Seasons - Numberphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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