Written by Mark Cohen.

When Leicester won their simply astonishing title in 15/16, my mind was immediately cast back to a discussion I had with a friend following Brazil’s opening 3-1 win over Croatia in the 2014 World Cup on home soil.

I had lamented Brazil’s poor defending, and the fact that Croatia had worked the ball through the lines very easily, and I said that it wouldn’t surprise me if a strong team beat them by five goals during the tournament.

My friend asked if that had ever happened to Brazil, which it had not, of course, and he wondered what the odds of such an event would be, since it had never occurred. He imagined about 300-1, especially given they were at home.

A few weeks later, and Brazil were indeed five nil down, after 29 minutes, to a rampant Germany at home in the semi-final. They would lose 7-1, a result which sent shock waves throughout the footballing world.

The event had quite an effect on my thinking. Unless a 300-1 event had actually happened, it seemed that the true odds of something occurring were very different from the market odds. That is to say that people are very good in calculating fair odds in events which occur often, but struggle to apply their collective wisdom to outlier events where all the dynamics become difficult to fathom.

The outlier here was that Brazil were demonstrably terrible at defending and were coming up against a pressing German team designed to move the ball rapidly on the counter. Consider that Brazil, at home, were supposed to take the game to the Germans and you had a recipe for disaster for the Selecao – they would try and stamp their authority on the match, over-committing forward with their rapturous fans in full fervour urging them on but would be picked off like shooting fish in a barrel once the Germans turned the ball over.

Forward to Leicester two years later, and the same would happen – given 5000/1 odds at the start of the season and then winning the Premier League. The odds they were given meant that they would win the title with that team, roughly once, every 5000 years.

Try and let that sink in. Leicester, with Mahrez, Vardy, Kante, a horde of quality defenders and midfielders and a game plan well suited to beating the established powers, would have had to wait for a period about as long as recorded human history, before the maths would be in their favour for a title win!

The folly of that is laid bare even by looking at this season. Without Liverpool, who we shall discuss shortly, 5000-1 Leicester would be second just two points behind City, having only 13 games left, just four years after their first 5000-1 triumph.

Of course, they are no longer 5000-1, because we now have better information than we had before. We know that outlier teams are capable, in rare circumstances, of 80+ point finishes, and that sometimes that is enough to challenge as the big boys might all be in a rebuilding stage. It’s rare, but clearly it happens a lot more often than may seem.

The important take home here is that information is crucial in determining true odds. The more information you have, the better your capacity to calculate events.

If we’d have known how good Leicester really were in 15/16, their individual players, their camaraderie, their cunning counter-attacking strategy, and we’d have coupled that with the rest of the league’s general malaise, we’d have probably put them at around 75-1 for the title, or roughly once and a bit per century.

Interesting.

Anyway, all this brings me neatly to my new friend ‘Expected Goals’ or xG.

One of the sticks used to beat Liverpool 19-20 with, is that if you look at our xG differences, our goals for vs goals against, you get a strange picture:

Our expected points, by a carefully modelled engine (this time Understat, but they are all similar), puts us 5 points behind City on approximately 52 to their 57 (see last column xPTS).

That is a swing of 27 league points, and also suggests our performance levels are pretty close to that of Chelsea and even Manchester United on 47 and 45 respectively! Manchester United? I have had the morbid pleasure of watching many of their matches this season, and if we are mathematically only two wins and a draw better than them this season, well, then, football is indeed a senseless sport!

We’ll get back to that later, but first, let’s consider Liverpool’s market odds of having the points we do. The picture becomes even more stark …

I’ve guesstimated our market odds of winning in each game for this season (not a difficult excursion, can be done on excel, the calculations at the bottom for perusal) and then added the odds of a draw in the United game at Trafford, multiplied them through, and found this:

This season, our results, are about a 1/3333 chance. If we add our 9 wins at the back end of last season to the sequence, it becomes staggering – Liverpool’s record of 33 wins and a draw in our last 34 games are 1 in 10 000 000.

One. In. Ten. Million.

Now either you think that this run is so lucky, so unlikely statistically, that we’d need to go back to a point in time before humans existed to see it occur, or it could be that something’s amiss. It boils down to this – either the run we are on is statistically the luckiest to ever be seen in sport, never mind football, or the odds are wrong.

Could it be, that we are working with imperfect information?

It could be, could be.

Could be that you haven’t reckoned for Jürgen Klopp.

In the 17/18 Champions League Final, apart from the wanton shithousery of a certain Real Madrid defender, and the unfortunate keeping of Loris Karius, my over-riding analysis was that we looked completely out on our feet.

The chaotic, swashbuckling swarm of red attackers, the gegenpress that made Klopp famous, that inimitable style which had put us 5-0 up against Roma, 4-1 up against City in the league, and then 3-0 in the Champions League QF, was gone. In its place, a more tepid, cautious, slower game, and one which would fall agonisingly close at the final hurdle.

Watching City that season too, had been a total eye-opener. They had played with such precision, such speed and skill in battering 100 points, that it seemed nigh on impossible for anybody to come close to them in 18/19.

That said, I still believed that Klopp was building something special, and in my pre-season preview I posited that if City were to come off a little in their pursuit of CL glory, and we went all out for the 38 game league title, and had lots of luck, we could come close.

We had the luck, no doubt. Think of Origi’s derby goal in the 96th minute, surely a 1/500 event. What about Townsend’s amazing net-buster at the Etihad – or Studge’s incredible point saver at Chelsea? Even Shaqiri’s great double against the old enemy at Anfield, the last of Mourinho’s in the dugout, were checkered by massive deflections. The winner v Spurs at Anfield – frankly absurd.

We had loads of moments in the league and we made the best of them all, but City were better still.

The key to the 18/19 challenge, and subsequent Champions League win, was that Klopp had evolved tactically. I like to think of this evolution as an ability to play through the gears in a match, both up and down.

In previous seasons, we had essentially had two speeds, in layman’s terms, ‘gegenpress at full throttle’ and ‘hang on bravely’. This simplification is, of course, a tad reductive and unfair, but it only serves to highlight the sheer brilliance in Klopp’s evolution into the 19/20 season and the reason we have won 33 from our last 34 league games.

Where we had previously burst into leads, like a 2-0 away at Southampton, only to later lose the game 3-2, Klopp had managed to find the times in a match when pressing was most effective, his ability to find a way to conserve energy in a game without the loss of control, surely his magnum opus in management.

Klopp understood that, in order to challenge and be in a position to win multiple trophies, he would need to create a system of play which allowed for maximum in game control, in order to allow for us to rest whilst still winning.

Anyway, it was clear we’d learned how to play game context brilliantly last season, moving up and down the gears as needed, but that was just an appetiser for the main course.

In 19/20, Klopp has perfected the art of controlling the game state.

Let’s have a look at the numbers;

If you recall earlier, we noted that in 19/20, xG has us as being ‘expected’ to have just 52 points in the league, and City 57. The fact that we have 73 points is playing very well to the narrative around the season that Liverpool are generationally lucky. Indeed, we calculated the market odds of us being at these consecutive wins at 1 into the millions…

I would argue that there is very little luck about it.

Firstly, a ‘game state’ could be re-written as the ‘game’s current score line’, because that’s what it means. When judging how a team performs at different game states, we look at how they did in terms of xG performance when they were level, how they did if they were one up, two up, one down, two down etc.

Secondly, I also believed there are, broadly speaking, two type of managers – an ends domination manager, and an environmental domination manager.

The first would be a Mourinho type. This is a manager that typically tries to procure (by coaching, but usually by purchasing) the right type of traits in a player, which should allow the player to dominate his surroundings. If he is a goal scorer, he will be the best at goal scoring, a specialist type of forward who can dominate the one on ones with a defender and emerge victorious.

If it is a keeper, Mourinho would look for one that has better and faster reflexes than the strikers he will face, in order to dominate those exchanges – a striker shoots, and Mourinho’s keeper must make the save.

The ’ends’ domination manager looks to dominate the ends of the pitch, in defence and attack where the action happens. He tries to limit the conceding of chances through the players at his disposal, their inherent skills, and then tries to maximise the chances they create, again through their individual traits, in order to create xG opportunities.

An environmental manager, like Klopp, tries to dominate the environment. They will coach methodically and with huge repetition, systems which they believe will allow their team to control the match they are playing. They hope that this control will lead to chances at the attacking end, whilst nullifying the threat defensively.

It might be summarised by saying an ‘ends’ manager wants great players to make a great team, whilst an ‘environmental’ boss wants the team, its system, its ethos, to make its players look great.

Up to 19/20, I believed the managers were more or less one or the other, I didn’t see or understand the possibilities of a manager who was able to synthesise the two. What if a boss was able to purchase excellent players, and then coach them into great players, all whilst pairing them, into a great system?

Liverpool 19/20 can be defined as THE most environmentally dominant team in world football, whilst simultaneously having the best ‘ends’ players.

And the numbers bear this out.

Let’s look at Manchester United first, a dismal team which purports to be an ‘ends’ domination outfit but has just one player on its entire roster who could be classed currently as a proper ‘ends’ domination player – Marcus Rashford.

Here are United’s game state figures so far;

Man Utd State Mins at State xG at State % Time at State GD at State Goal diff < -1 150 0.98 6% 1 Goal diff -1 383 0.51 16% -1 Goal diff 0 1089 0.4 46% 3 Goal diff +1 435 0.89 18% 1 Goal diff > +1 297 1.36 13% 3

What can be quickly deduced from using United’s numbers as a baseline, is that they are probably under performing at the ‘ends’. Reason being is that their xG at any game state is positive, but they are spending 81% of the game at a goal up, a goal down, or level – so with the game in the balance, and their actual GD at each state is negligible, so they can’t convert their chances.

This ‘ends’ under performance makes a great deal of sense, given the form of players like De Gea in defence and Martial up front. United can be on the front foot, if not quite bossing a match (you will see the difference in Liverpool and City’s numbers shortly), but they cannot make it count when it matters. If they concede chances, they can’t keep them out, and if they make chances, the ball doesn’t’ fly in.

The other huge issue for them, is that they cannot effect a game statistically until a goal has gone in. At the ‘Goal diff 0’ game state, they are just 0.4 goals better than their opponents, and this state of the game comprises 46% of their game states.

In other words, to summarise, United are level for half their games, during which they are not demonstrably on top. If they go ahead, they seem to be able to peg a team in quite well, without actually scoring, as their goal difference is just 4. If they fall behind, they also tend to up the tempo significantly, again, without being able to score, their GD here, zero.

Also, when at level or one behind, they struggle to be more than half a goal better than their opponents – a serious issue as this is the time in the game when you exert the most mental pressure. If you think about being at 0-0, for example, the game is on and everybody has belief. Even Southampton were feeling good after 9 minutes against Leicester at home on 25th October. 80 minutes later, they were 9-0 down.

The beginning or level state of a game is one where everybody is going full tilt and anything can happen.

Thus, if you are battling to impose your will on all or most of your opponents at this stage, it means you are not demonstrably better than them, and you are likely not very good.

Now, with this basis of understanding in mind, lets review City so far. On the surface, brilliant numbers:

Man City State Mins at State xG at State % Time at State GD at State Goal diff < -1 204 1.4 9% 3 Goal diff -1 191 0.53 8% -2 Goal diff 0 980 1.81 42% 13 Goal diff +1 482 1.41 21% 8 Goal diff > +1 491 1.86 21% 14

They have a nice, high proper goal difference, showing their individuals’ ability to actually finish the goals or save their opponents’ shots, and they have a very, very healthy xG in totality. Indeed, it’s at nearly two goals at the level segment, as well as when they are up more than one, showing an ability to thrash a team that’s being beaten.

The issues only come into focus when we look closer. City are spending 17% of their minutes behind in games, and when you see their GD of 13 at state ‘Goal diff 0’, understand that they’ve scored 23, but conceded 10 at that state. That’s a lot of goals to concede when level. Remember how teams feel anything is possible when the game is level? You don’t want to see teams able to take it to you with such alacrity. At some points last season, I remember thinking that nobody could even lay a glove on City in the run in, let alone knock them down, but that is clearly no longer the case.

Teams try and stay level with them now, knowing a first thirty minutes of difficulty will be followed by a much softer last hour, and if they can keep their shape and concentration, they know the chances at the other end will be there.

It seems to suggest they have brilliant goal-getters, a front three of sheer quality who are supported by one or two running midfielders capable of creating loads of chances.

Equally though, unfortunately for them, it all points to a team incapable of properly defending their goalkeeper, and one which offers up high quality chances at a rate unsustainable for a title winning team.

They have also failed to dominate the defensive ‘end’. When Ederson has been needed, or a defender has had a pivotal moment against an attacker, they have been found wanting.

Also, they appear mentally fragile. At the ‘goal diff -1’ stage, they are just 0.53 xG better than their opponents. This stands in stark contrast to the other states where they are all at nearly 1.5 or higher. It means they get mentally stung by conceding, and struggle to revive themselves. Indeed, so shocking are they once behind, that they actually have a negative proper GD, at -2!

They are also spending 10% longer at level this year, than last (they were at state ‘Goal diff’ 38% in 18/19, 42% now). Worse still, they spend just 4% of their entire season behind last year, seeing a 400% increase so far this term at 17%.

To summarise, City are still a powerful, capable team. They have been quite unlucky too, both the Spurs fixtures a good example – City should have won each by three or four goals, but took just a point across the matches.

There is little doubt in my mind, they remain a strong Premier League team, and their numbers and tally of 51 points right now seems quite fitting. They are on course for a high 70s points finish, and with an upturn in form over the last 13 games, could easily get 85. This would always represent a decent return in the Premier League.

In short – they are where they are and deserve to be.

All this primes our understanding well for what we are about to uncover about Liverpool. The standout stat in this piece, the one in ten million chance of us having won 33 and drawn 1 of our last 34, is the over-riding narrative of the season so far.

Of course pundits are giving us our dues, it would be stupid not to, but there is still a general feeling that we are lucky to be 22 points ahead, and City unlucky to be 22 behind. The VAR narrative, the ‘LiVARpool’ one, whilst not a big media angle, is certainly a rival fan favourite.

If I had to put a number on it, I’d say the general consensus is that we are a great team, and City are too, and we’ve been a bit fortunate with VAR, kind bounce of the ball etc, whilst City have had the opposite. If we were 8 points ahead of them, it would be about right.

Furthermore, the xG numbers on the face of it, bear this out, with City’s expected 57 points at this stage vs our 52.

The bald-faced fact though, the ones we shall see shortly, point to a Liverpool team of such incredible domination, both in its ‘environment’ and at its ‘ends’ that, if all the information is available to us, would show a team perfectly capable of winning 30+ games from every 34, without needing 1 in 10 000 000 odds.

In other words, I don’t think we have been incredibly lucky, I think we’ve been unimaginably brilliant. I don’t think this Liverpool team are a great team – I think it’s the best club team ever to play football.

Have a look:

Liverpool State Mins at State xG at State % Time at State GD at State Goal diff < -1 0 0 0% Goal diff -1 158 1.64 7% 4 Goal diff 0 892 1.35 38% 23 Goal diff +1 719 1.31 31% 14 Goal diff > +1 573 1.08 24% 4

Under Jürgen Klopp, Liverpool have morphed from an exciting attacking, but erratic, team, into one that can easily shift through the gears, both up or down, depending on the game state. Yes the goals flow, but the first stand out figure is that our performance when we are more than one goal to the good is only half as good as City’s. We have an xG of 1.08 at this state, City 1.81. They’ve scored 14 times, we have only 4.

But this might be the single clearest difference in the two team’s mentality. City have an ability to drill teams into the ground, once the team is beaten already. Liverpool on the other hand, possess a much greater ability to make sure the team is beaten, but to then conserve energy that is not required.

To digress slightly, I believe the rule change effected this season to decide the title on head to head rather than goal difference when teams are level must have been a godsend to Klopp. He would have automatically realised that goals for goals sake were no longer important, and the need to have a better GD than City had been largely negated. What would matter is only the results between the two teams if we would have ended level.

Even though I believe this to be a horrific rule, awful for the league and its excitement, it did allow for Klopp to switch his system to one of calm dominance when the game is ‘won’. There is no great need to expend energies at this game state.

If you want to see, at a micro-level, the sheer, unfettered brilliance of Klopp’s systems, look at game state Goal diff > +1, as it shows how capable his team are at switching gears from all out aggressive pressing and dominance to energy conservation.

People often mention that we’ve been luckier than City with injuries (though where City have lost Sane and Laporte for substantial lengths of time and others for shorter periods, Liverpool have lost Alisson, Lovren, Matip, Fabinho, Milner, Keita, Lallana, Shaqiri and Mane for varying periods and nay simultaneously – Ed).

I don’t believe in luck when it comes to Klopp. Part of that edge has been that we have been able to drop our intensity during games, lowering the risk of players to injury.

Of course, being able to relax when you are up is only useful if you can get up, and quickly.

Cast your greedy eyes now to ‘Goal diff 0’. At this state, Liverpool are so dominant at the ends that it’s practically game over. Whilst City create a higher xG, 1.81 to 1.35, a sizeable difference, we need to understand that in terms of the actual goals scored and conceded – they are at 23-10 for this period, whereas we are at 27-4, nearly double them.

It would be easy to put this down to luck, but it would be much better placed to understand that Liverpool don’t begin too many games at full tilt, even though lazy punditry would have you believe this.

Whereas Pep’s go-to strategy has always been to overwhelm his opponents with dazzling speed and quality from the first whistle, Klopp has evolved past that.

Our strategy is to ‘switch on’ the pressing at different points in the first half, usually on or around the 25th minute. This system has the psychological effect of allowing the opponents a bit of breathing room to almost lull them into a false sense of security. They are then swamped by a sudden and prolonged (usually till half-time) surge of energy against them which most teams don’t cope with.

It also allows us to have a go, then step off if it doesn’t work, conserve energy and regroup to go again later in the game.

Again this is quite at odds with City, this time from Gary Fulcher’s ever-excellent pre-match previews:

Liverpool from the 31st to 45th minute, have scored 16 times, conceding just 2. City in that same period have scored 10 and conceded 3, still excellent but again, half the GD. Liverpool have won many matches during this period. For further comparison, Leicester in third, are plus 7 too, but are at zero GD for the rest of the first half, whereas we are at plus 11 for the other periods.

Its important to remember that City and Liverpool represent the 90th and above percentiles in the league in terms of performance, so we should never find ourselves doubling them in such key metrics.

So we have a pattern emerging, and that is that a decently performing City team, doing well in most metrics, can’t come close to a Liverpool team at the top, and the primary reason appears to be a total domination by Liverpool of every type of game state.

For further evidence, let’s look at when Liverpool fall behind. Yes, a small sample, in itself a bellwether for total dominance, but what we see is that once chasing a game, we switch into an incredibly high gear, having not conceded again, nor looking like it. We’ve got a GD of 4-0 at this state, with xG matching.

Equally too, the fact that we show such a similar xG in states ‘Goal diff 0’ and ‘Goal diff +1’, suggest a superb coaching of mentality by Klopp. Keep on top, keep pushing, change nothing, go for the second, make the game safe.

If we go one behind – accelerate hard to get level, if we are at nil-nil, keep control, mentally fatigue opponents by dominance, and at a goal up – the same.

Fundamentally, systems like xG and market odds are way behind in terms of making sense of Liverpool’s amazing form. Yes, we could be beating or xG by 21 points, and a regression will occur, and yes, maybe ou are witnessing a 1 in 10 000 000 event before your eyes but don’t bet on it.

The incomplete information here is that not enough people have been able to quantify Liverpool’s game state dominance. It is here where we find the truth.

In other words, no matter the game state, Liverpool are mentally thrashing you. It’s not luck, it’s not the bounce of the ball and it’s not VAR.

To consider it from the angle of ‘ends’ domination paints a similarly pretty picture. When teams manage to get forward, into good areas, they are thwarted in the one-on-one situations by our superior goalkeeper and defenders, time and again. In attack, Mo Salah will finish from acute angles, whilst Mane will score all manner of technically brilliant goals, over and over. In those crucial moments, be they in attack or defence, Liverpool’s better players come to the fore, making the difference. This is the primary reason why you will see our actual GD battering our xG one – because our players have been better in the key moments.

Earlier I spoke of Klopp’s achievement of synthesising ‘ends’ domination with ‘environmental’ and I think we see this in the brilliance and variance of Liverpool’s goals. As Paul has been at pains to point out over the last few months, Liverpool are genius at the following types of goals;

Set-pieces (ends domination)

Intricate game play (ends & environmental domination)

Worldies (ends domination)

Speed of transition (counter-attack) Goals (environmental domination)

Goals due to defender fatigue and/or error (environmental domination)

Goals due to attacking system (environmental domination)

Long Ball Goals (ends & environmental domination)

You see, Liverpool are wizards at scoring any type of goal, from any type of situation in any game state. Whereas City perfected a certain type of goal, Liverpool have perfected the art of making sure the ball is in the back of the net, come what may.

Whereas City try and control you through their own highly skilled scoring, Liverpool push and pull you apart at both ends, saving or blocking your shots, lowering your morale, and then scoring when presented with a chance.

I’ve never seen a team so capable of so many different types of football, from swashbuckling, to calm and serene control, to emphatic dominance, to tight defence, all in 90 minutes.

Perhaps my statement of being the best ever could prove to be hyperbole as the season winds down – we might win the league with a few defeats, get knocked out of the CL, and life will go on.

Or perhaps we are not a team on a 1 in 10 000 000 run, maybe the lucky narrative is wrong, and maybe we will just win the lot.

I believe that in a hundred years’ time they will still be writing books about this team, its unimaginable numbers this year, and the unstoppable force Jürgen Klopp created.