Category: sport

The team around you

Back in 2016, footballer Oscar, then of Chelsea, was bought by Shanghai SIPT for a (then whopping) GBP 60M, with a salary of about GBP 20M a year.

Around the time the deal got announced, we were having our 10th year reunion at IIMB. During that a professor told us that one reason Shanghai had to pay Oscar so heavily was the quality (or lack thereof) of teammates he would have to deal with in Shanghai. He was then playing for Chelsea, who had won the Premier League in 2015, and would win it again that season (2016-17). And he was leaving that quality of teammates to join unknown teammates in China, and that meant he would have to be compensated heavily.

During and after last nights’ Manchester Derby, a friend and I were talking about Andre Onana, now the Manchester United goalie. Onana has been an extremely promising goalkeeper, excelling for Ajax and Inter (apart from one doping ban). He is a brilliant sweeper keeper (one reason he got chucked out of the Cameroon national team during last year’s World Cup), adept at playing with his feet and with great positioning sense.

And who does he have in front of him at ManYoo? The former Leicester defensive pair of Harry Maguire and Jonny Evans! They absolutely lack pace which means they can’t play a high line. That means Onana’s sweeping skills are grossly underutilised, and he ends up getting judged based on his shot-stopping skills, where he is nowhere in the same league as his predecessor David De Gea.

When we get into organisations, things we evaluate are the kind of work we do and what we are getting compensated for it. The thing we tend to overlook is who we need to work with, and whether they will elevate us or drag us down. Sometimes, the organisation (like Shanghai SIPT) recognises that you have to put up with suboptimal colleagues, and thus pay you a premium for your services.

Often, though, the organisation will be more like ManYoo, which doesn’t really recognise that the team around you may not be optimal for your playing style. And not everyone is willing to accept a premium in exchange for suboptimal colleagues. So, if you end up like Onana, you are not only frustrated because of the quality (or lack thereof) of your colleagues and peers, but you also end up getting judged on axes that are not your strengths (and what you have NOT been hired for).

Over the last decade, hiring at Manchester United has been curious, to say the least. There have been half-hearted attempts at changing the playing style, and almost everyone brought in to play the new style (I assume Erik Ten Haag wanted to play a more high-press style when he bought Onana) has been frustrated and unable to perform to potential.

Related to this, going back to something I’d written earlier this year, every company has an optimal rate of attrition, which is non-zero. If you end up paying too much of a premium to loyalty, you risk stagnation. If your Onana has to put up with Maguire and Evans, he won’t perform to potential. And then you go back to setting up the way it is optimal for Maguire and Evans.

Big and fast

In football, normally we see two kinds of strikers – small and quick or big and slow. About twenty years ago, when 4-4-2 was the dominant formation, it was common for teams to deploy a strike partnership with one of each. Liverpool, for example, played with Michael Owen (small and quick) and Emile Heskey (bit and slow).

While strike partnerships have gone out of fashion, you still see these two kinds of strikers in modern football. The small and quick striker usually “plays on the shoulder of the last defender”, looking to beat the offside trap and score. The big and slow striker holds up the ball in an advanced position, waiting for teammates to go past, so that the team can then attack in numbers. The big and slow striker is also usually good in the air and can convert crosses.

For a long time, I was wondering why there were no “big and fast” strikers in football. It isn’t as if bulk / size is negatively correlated with speed – there surely must exist big guys who are also quick, and I was wondering why there weren’t so many strikers like this.

That, of course changed last year, with the arrival of Erling Haaland, a striker who is both incredibly quick and incredibly big, and who has dominated the Premier League like nobody’s business. Similarly, there is also Darwin Nuñez, who can both play off the last defender, and head crosses towards goal, and hold up the ball. Then again, I can’t think of too many others in contemporary football.

This morning, I got a hypothesis on why this is so – the big and fast guys are all in rugby! I was watching highlights of the quarter finals (England beating Fiji and South Africa beating France), and what I noticed was that the rugby guys are all both big and fast.

You need to be fast (and agile) to skip past the opponents to do a touchdown. And then you need tremendous upper body strength to be able to take down an opponent, or resist when an opponent tries to take you down. From that perspective, being big and being fast are both non negotiable for you to be a top rugby player.

I know there is a class difference in places like England between those who take up football and those who take up rugby (football is working class, rugby is upper class), but could it be that most people who are big and fast, and want to take up professional sport, choose rugby rather than football? And is this why you find few big and fast players from countries traditionally good at both games – such as England and France (and maybe Argentina)?

Haaland is from Norway, which doesn’t really play rugby (again, his father was a footballer). Nuñez is from Uruguay, which is a massive football nation, but not much in rugby (they made their rugby debut at this world cup, i think). And so despite their physique and speed, they chose football.

Had they been from England or France, it’s likely they would’ve played rugby instead!

SHAP and WAR

A few months back, at work, a couple of kids in my team taught me this concept called “SHAP“. I won’t go into the technical details here (or maybe I will later on in this post), but it is basically an algo that helps us explain a machine learning model.

It was one of those concepts that I found absolutely mind-blowing, to the extent that after these guys taught this concept to me, it became the proverbial hammer, and I started looking for “nails” all around the company. I’m pretty sure I’ve abused it (SHAP I mean).

Most of the documentation of SHAP is not very good, as you might expect about something that is very deeply technical. So maybe I’ll give a brief intro here. Or maybe not – it’s been a few months since I started using and abusing it, and so I’ve forgotten the maths.

In any case, this is one of those concepts that made me incredibly happy on the day I learnt about it. Basically, to put it “in brief”, what you essentially do is to zero out an explanatory variable, and see what the model predicts with the rest of the variables. The difference between this and the actual model output, approximately speaking, is the contribution of this explanatory variable to this particular prediction.

The beauty of SHAP is that you can calculate the value for hundreds of explanatory variables and millions of observations in fairly quick time. And that’s what’s led me to use and abuse it.

In any case, I was reading something about American sport recently, and I realised that SHAP is almost exactly identical (in concept, though not in maths) to Wins Above Replacement.

WAR works the same way – a player is replaced by a hypothetical “average similar player” (the replacement), and the model calculates how much the team would have won in that case. A player’s WAR is thus the difference between the “actuals” (what the team has actually won) and the hypothetical if this particular player had been replaced by the average replacement.

This, if you think about it, is exactly similar to zeroing out the idiosyncrasies of a particular player. So – let’s say you had a machine learning model where you had to predict wins based on certain sets of features of each player (think of the features they put on those otherwise horrible spider charts when comparing footballers).

You build this model. And then to find out the contribution of a particular player, you get rid of all of this person’s features (or replace it with “average” for all data points). And then look at the prediction and how different it is from the “actual prediction”. Depending on how you look at it, it can either be SHAP or WAR.

In other words, the two concepts are pretty much exactly the same!

4-2-4 and Huns

Last night, in the game at Stamford Bridge, Liverpool started with a formation that could have been described as a 4-2-4. While Cody Gakpo ultimately played in midfield, to make it a more conventional 4-3-3, he is ultimately a forward who was playing there, and made Liverpool vulnerable down the left side for the duration of the first half.

This wasn’t the first time Liverpool lined up in a 4-2-4 without an obvious holding midfielder. For a while during the title chase of 2013-14, Liverpool lined up broadly similarly, with Gerrard and Henderson in central midfield, and Sterling, Sturridge, Suarez and Coutinho forming a front four.

And the thing that characterised a lot of games in that title chase was Liverpool’s fast starts. I remember this game against Arsenal (I wasn’t watching) when Liverpool went 4-0 or something up very very quickly. That was emblematic of that half season – very very quick starts, lots of goals up front, and then quickly tiring and  having to hold on for dear life in the end of the game.

When Liverpool failed to score early, like they did in the game against Chelsea (when Gerrard famously slipped, and when Salah started for Chelsea), they would get immensely frustrated and look short of ideas. It was very different to recent years when Liverpool have been able to conjure up last minute equalisers and winnres.

Anyway, yesterday seemed like 2013-14 again. Liverpool was clearly the better team in the first half hour, only a very tight offside prevented the game from going 2-0. The profusion of forwards, and Alexis Mac Allister pinging balls to all parts of the frontline, meant that Liverpool dominated.

Then the inevitable happened – Chelsea settled. Their midfield three got working and soon Liverpool were massively overrun in midfield. Chelsea quickly got one back, almost got one more, and dominated most of the rest of the game (until Liverpool took of Salah and Diaz for a pair of kids).

The thing with the 4-2-4 is that it is an unusual and incredibly attacking formation. The opposition will inevitably take time to settle down against it and figure out how to deal with it. And in that time, the attacking team needs to make merry and score as much as they can (Liverpool only got one).

Once the opposition settles down, the shortage of personnel in midfield can be quickly exploited and the opposition starts dominating the game.

As I was watching, I was reminded of the Age of Empires (2; the conquerors expansion) which I used to play back in college. There, you can select the civilisation you want to play as (sometimes it’s “random”). A few people used to prefer to play as Huns.

The thing with Huns is that they don’t need to build houses (they are nomadic), and so can grow very quickly very fast. And in an AoE game, if you are playing as the Huns, the only strategy is to attack quickly and cause enough damage to the opposition in the opening stages of the game that they can’t recover after that. Because once the opposition has settled down, the Huns’ speed advantage has lost its bite.

And so, playing a 4-2-4 in football is similar to playing as the Huns in AoE. You better make a good start and inflict enough damage on the opposition in the early stages so that they aren’t able to sufficiently damage you back after they’ve inevitably settled down.

Connecting these two topics – I heard on commentary last night that Liverpool has never won a game where a Hungarian has represented them. That trend continues after last night. Hopefully Dominik Szoboszlai can make amends soon.

New blood joins this team

I intended to write this a year ago, when Sadio Mane left Liverpool after six brilliant years at the club. There was much heartbreak among the club fan base about Mane leaving, and a lot of people saw it as a failure on the part of the management and ownership in terms of not being able to keep him.

Now, a year on, I admit that Darwin Nunez hasn’t quite set the club on fire (though I personally quite like him), but as a general principle, this kind of “freshening up” is a highly necessary process in a team, if you need to avoid stagnation.

A month or two back, I was watching some YouTube video on “Liverpool’s greatest Premier League goals against Manchester City” (this was just before the 4-1 hammering at the Etihad). As the goals were shown one by one, I kept trying to guess which season and game it was in.

There were important clues – whether Firmino wore 9 or 11, whether Mane wore 19 or 10, the identity of some players, the length of Trent Alexander Arnold’s hair, my memory of the scoreline from that game, etc. (Liverpool always wear the home Red at the Etihad, so the colour of the away kit wasn’t a clue).

However, for one goal I simply wasn’t able to figure out which season it was. There was TAA wearing 66, Fabinho, Henderson, the fab front three (Firmino-Mane-Salah, wearing 9-10-11 respectively) and Robertson. That’s when it hit me that for a fairly long time, a large part of Liverpool’s team had stayed constant! There was very little change at the club.

Now, there are benefits to having a consistently settled team (as the fabulous 2021-22 season showed), but there is also the danger of stasis. In something like football where careers are short, you don’t want the whole team “getting old together”. In the corporate world, people can get into too much of a comfort zone. And cynicism can set in.

Good new employees are always buzzing with ideas, fearless about what has been rejected before and who thinks how. As people spend longer in the organisation, though, colleagues become predictable and certain ways of doing things become institutionalised. Sooner than you know it, you would have become a “company man”, (figuratively) wearing the same white shirt and blue suits as your fellow company men, and socialising with your colleagues at the (figurative) company club.

There can be different kinds of companies here – some companies allow people to retain a lot of their individuality; and there the “decay” into company-manhood is slower. In this kind of a place, the same set of people can stay together for longer and still continue to innovate and add significant value to one another.

Other companies are less forgiving, and you very quickly assimilate, and lose part of your idiosyncrasy. Insofar as innovation comes out of fresh ideas and thinking and unusual connections, these companies are not very good at it. And in such companies, pretty much the only way to keep the innovative wheel going and continue to add value is by bringing in fresh blood well-at-a-faster-rate.

Putting it another way, if you are a cohesive kind of company, some attrition may not actually be a bad thing (unless you are growing rapidly enough to expand your team rapidly). To grow and innovate, you need people to think different.

And you get there either by having the sort of superior culture where existing employees continue to think different long after they’ve been exposed to one another’s thoughts; or by continuing to bring in fresh employees.

There is no other way.

Darwin Nunez and missed chances

There is one “fact” I’m rather proud of – it is highly likely (there is absolutely no way to verify) that in CAT 2003-4 (scheduled for 2003; then paper got leaked and it was held in Feb 2004), among all those who actually joined IIMs that year, I had the most number of wrong answers.

By my calculations after the exam (yeah I remember these things) I had got 20 answers wrong (in a 150 question paper). Most of my friends had their wrong counts in the single digits. That I did rather well in the exam despite getting so many answers wrong was down to one thing – I got a very large number of answers right.

Most readers of this blog will know that I can be a bit narcissist. So when I see or read something, I immediately correlate it to my own life. Recently I was watching this video on striker Darwin Nunez, and his struggles to settle into the English Premier League.

“Nobody has missed more clear chances this season than Darwin Nunez”, begins JJ Bull in this otherwise nice analysis. Somewhere in the middle of this video, he slips in that Nunez has missed so many chances because he has created so many more of them in the first place – by being in the right place at the right time.

Long ago when I used to be a regular quizzer (nowadays I’m rather irregular), in finals I wouldn’t get stressed if our team missed a lot of questions (either with other teams answering before us, or getting something narrowly wrong). That we came so close to getting the points, I would reason, meant that we had our processes right in the first place, and sooner or later we would start getting those points.

In general I like Nunez. Maybe because he’s rather unpredictable (“Chaos” as JJ Bull calls him in the above video), I identify with him more than some of the more predictable characters in the team (it’s another matter that this whole season has been a disaster for Liverpool -I knew it on the opening day when Virgil Van Dijk gave away a clumsy penalty to Fulham). He is clumsy, misses seemingly easy chances, but creates some impossible stuff out of nothing (in that sense, he is very similar to Mo Salah, so I don’t know how they together work out as a portfolio for Liverpool. That said, I love watching them play together).

In the world of finance, losing money is seen as a positive bullet point. If you have lost more money, it is a bigger status symbol. In most cases, that you lost so much money means that your bank had trusted you with that much money in the first place, and so there must be something right about you.

You see this in the startup world. Someone’s startup folds. Some get acquihired. And then a few months later, you find that they are back in the market and investors are showering them with funds. One thing is that investors trust that other investors had trusted these founders with much more money in the past. The other, of course, is the hope that this time they would have learnt from the mistakes.

Fundamentally, though, the connecting thread running across all this is about how to evaluate risk, and luck. Conditional on your bank trusting you with a large trading account, one bad trading loss is more likely to be bad luck than your incompetence. And so other banks quickly hire you and trust you with their money.

That you have missed 15 big chances in half a season means that you have managed to create so many more chances (as part of a struggling team). And that actually makes you a good footballer (though vanilla pundits don’t see it that way).

So trust the process. And keep at it. As long as you are in the right place at the right time a lot of times, you will cash on average.

Dhoni and Japan

Back in MS Dhoni’s heyday, CSK fans would rave about his strategy that they called as “taking it deep”. The idea was that while chasing  a target, Dhoni would initially bat steadily, getting sort of close but increasing the required run rate. And then when it seemed to be getting out of hand, he would start belting, taking the bowlers by surprise and his team to victory.

This happened many times to be recognised by fans as a consistent strategy. Initially it didn’t make sense to me – why was it that he would purposely decrease the average chances of his team’s victory so that he could take them to a heroic chase?

But then, thinking about it, the strategy seems fair – he would never do this in a comfortable chase (where the chase was “in the money”). This would happen only in steep (out of the money) chases. And his idea of “taking it deep” was in terms of increasing the volatility.

Everyone knows that when your option is out of the money, volatility is good for you. Which means an increase in volatility will increase the value of the option.

And that is exactly what Dhoni would do. Keep wickets and let the required rate increase, which would basically increase volatility. And then rely on “mental strength” and “functioning under pressure” to win. It didn’t always succeed, of course (and that it didn’t always fail meant Dhoni wouldn’t come off badly when it failed). However, it was a very good gamble.

We see this kind of a gamble often in chess as well. When a player has a slightly inferior position, he/she decides to increase chances by “mixing it up a bit”. Usually that involves a piece or an exchange sacrifice, in the hope of complicating the position, or creating an imbalance. This, once again, increases volatility, which means increases the chances for the player with the slightly inferior position.

And in the ongoing World Cup, we have seen Japan follow this kind of strategy in football as well. It worked well in games against Germany and Spain, which were a priori better teams than Japan.

In both games, Japan started with a conservative lineup, hoping to keep it tight in the first half and go into half time either level or only one goal behind. And then at half time, they would bring on a couple of fast and tricky players – Ritsu Doan and Kaoru Mitoma. Basically increasing the volatility against an already tired opposition.

And then these high volatility players would do their bit, and as it happened in both games, Japan came back from 0-1 at half time to win 2-1. Basically, having “taken the game deep”, they would go helter skelter (I was conscious to not say “hara kiri” here, since it wasn’t really suicidal). And hit the opposition quickly, and on the break.

Surprisingly, they didn’t follow the same strategy against Croatia, in the pre-quarterfinal, where Doan started the game, and Mitoma came on only in the 64th minute. Maybe they reasoned that Croatia weren’t that much better than them, and so the option wasn’t out of the money enough to increase volatility through the game. As it happened, the game went to penalties (basically deeper than Japan’s usual strategy) where Croatia prevailed.

The difference between Dhoni and Japan is that in Japan’s case, the players who increase the volatility and those who then take advantage are different. In Dhoni’s case, he performs both functions – he first bats steadily to increase vol, and then goes bonkers himself!

Luxury and frugal managers

You remember very random things from business school, nearly two decades on. Usually none of this is academic – the lessons are only “internalised”, not “learnt”. A lot of it is from outside the classroom, silly things someone said or did or posted on the internal bulletin board. Most of the stuff you remember are rather arbitrary things that professors said, and made it seem like something profound.

“Management is like making music”, one professor lectured to us in the first week of classes at IIMB, back in 2004. “First you make music with what you have, and when you don’t have that, you make music with what you have left”. It was rather random, but random enough to stick in my head 18 years on.

It has been another disappointing season beginning for Liverpool. I didn’t watch the Crystal Palace game last night, but I clearly remember feeling at multiple points during the draw at Fulham that this was “like 2020-21 all over again”. The sort of mistakes that Virgil Van Dijk made. The length of the injury list. More players (Thiago) going off injured midway through the game. Nat Phillips starting. And add some new issues – like having your shiny new striker getting himself sent off and suspended for 3 games for a stupid show of anger.

I see the list of substitutes.

  • 2
    Joe Gomez (s 63′)
  • 8
    Naby Keita
  • 13
    del Castillo Adrian
  • 14
    Jordan Henderson (s 63′)
  • 21
    Konstantinos Tsimikas (s 63′)
  • 28
    Fabio Carvalho (s 79′)
  • 43
    Stefan Bajcetic
  • 72
    Sepp van den Berg
  • 42
    Bobby Clark

Yes, there are youngsters (unlike 2021-22) but that is fully understandable. What I don’t understand is seeing youngsters I’ve never heard of. Two games in, I’m already getting the feeling that this will be a really hard league campaign.

I wonder if Klopp is more of a “luxury manager” than a “frugal manager”. These are two very different management styles, requiring very different skillsets. The names are fairly descriptive.

Luxury managers need luxury. They need resources for “option value”. In the corporate context, they need large budgets and space and little control over how they operate. And given all of this, a lot of the time, they deliver big. Yes – there are cases where they spectacularly fail (in which case they don’t stay on in their management jobs), but when they do deliver they deliver big.

Frugal managers don’t need any of this luxury. They are experts at making the most of whatever they have been given. In Ramnath’s words, they are adept at “making music with what they have left”. Any kind of luxury, any kind of optionality, seems like a waste to them. Why pay the option premium when you can get the same payoff through a complicated basket of one deltas?

And just like any other dichotomies (think of studs vs fighters, for example), luxury and frugal managers struggle in the opposite settings. Without the luxury, luxury managers are simply out of their depth. They are necessarily wasteful (a bit like Salah) and cannot produce if they are not able to waste some. However, they win big when they do.

Frugal managers are good at eking out solutions in terms of adversity, but abundant resources can overwhelm them. They won’t know what to do with it. More importantly, they are unable to deal with the expectations of delivering big (which come with the luxury) – they have been experts at delivering small against nonexistent expectations.

What about teams though? If you’ve been used to working for a luxury manager, what happens when you get a frugal manager? And the other way round? I don’t have immediate answers for this but I suppose you will struggle as well?

Mo Salah and Machine Learning

First of all, I’m damn happy that Mo Salah has renewed his Liverpool contract. With Sadio Mane also leaving, the attack was looking a bit thin (I was distinctly unhappy with the Jota-Mane-Diaz forward line we used in the Champions League final. Lacked cohesion). Nunez is still untested in terms of “leadership”, and without Salah that would’ve left Firmino as the only “attacking leader”.

(non-technical readers can skip the section in italics and still make sense of this post)

Now that this is out of the way, I’m interested in seeing one statistic (for which I’m pretty sure I don’t have the data). For each of the chances that Salah has created, I want to look at the xG (expected goals) and whether he scored or not. And then look at a density plot of xG for both categories (scored or not). 

For most players, this is likely to result in two very distinct curves – they are likely to score from a large % of high xG chances, and almost not score at all from low xG chances. For Salah, though, the two density curves are likely to be a lot closer.

What I’m saying is – most strikers score well from easy chances, and fail to score from difficult chances. Salah is not like that. On the one hand, he creates and scores some extraordinary goals out of nothing (low xG). On the other, he tends to miss a lot of seemingly easy chances (high xG).

In fact, it is quite possible to look at a player like Salah, see a few sitters that he has missed (he misses quite a few of them), and think he is a poor forward. And if you look at a small sample of data (or short periods of time) you are likely to come to the same conclusion. Look at the last 3-4 months of the 2021-22 season. The consensus among pundits then was that Salah had become poor (and on Reddit, you could see Liverpool fans arguing that we shouldn’t give him a lucrative contract extension since ‘he has lost it’).

It is well possible that this is exactly the conclusion Jose Mourinho came to back in 2013-14 when he managed Salah at Chelsea (and gave him very few opportunities). The thing with a player like Salah is that he is so unpredictable that it is very possible to see samples and think he is useless.

Of late, I’ve been doing (rather, supervising (and there is no pun intended) ) a lot of machine learning work. A lot of this has to do with binary classification – classifying something as either a 0 or a 1. Data scientists build models, which give out a probability score that the thing is a 1, and then use some (sometimes arbitrary) cutoff to determine whether the thing is a 0 or a 1.

There are a bunch of metrics in data science on how good a model is, and it all comes down to what the model predicted and what “really” happened. And I’ve seen data scientists work super hard to improve on these accuracy measures. What can be done to predict a little bit better? Why is this model only giving me 77% ROC-AUC when for the other problem I was able to get 90%?

The thing is – if the variable you are trying to predict is something like whether Salah will score from a particular chance, your accuracy metric will be really low indeed. Because he is fundamentally unpredictable. It is the same with some of the machine learning stuff – a lot of models are trying to predict something that is fundamentally unpredictable, so there is a limit on how accurate the model will get.

The problem is that you would have come across several problem statements that are much more predictable that you think it is a problem with you (or your model) that you can’t predict better. Pundits (or Jose) would have seen so many strikers who predictably score from good chances that they think Salah is not good.

The solution in these cases is to look at aggregates. Looking for each single prediction will not take us anywhere. Instead, can we predict over a large set of data whether we broadly got it right? In my “research” for this blogpost, I found this.

Last season, on average, Salah scored precisely as many goals as the model would’ve predicted! You might remember stunners like the one against Manchester City at Anfield. So you know where things got averaged out.

Compensation at the right tail

Yesterday I was reading this article ($) about how Liverpool FC is going about (not) retaining its star forwards Sadio Mane and Mo Salah, who have been key parts of the team that has (almost) “cracked it” in the last 5 seasons.

One of the key ideas in the (paywalled) piece is that Liverpool is more careful about spending on its players than other top contemporary clubs. As Oliver Kay writes:

[…] the Spanish club have the financial strength to operate differently — retaining their superstars well into their 30s and paying them accordingly until they are perceived to have served their purpose, at which point either another A-list star or one of the most coveted youngsters in world football (an Eder Militao, an Eduardo Camavinga, a Vinicius Junior, a Rodrygo and perhaps imminently, an Aurelien Tchouameni) will usually emerge to replace them.

In an ideal world, Liverpool would do something similar with Salah and Mane, just as Manchester City did with Vincent Kompany, Fernandinho, Yaya Toure, David Silva and Sergio Aguero — and as they will surely do with De Bruyne.

But the reality is that the Merseyside club are more restricted. Not dramatically so, but restricted enough for Salah, Mane and their agents to know there is more to be earned elsewhere, and that presents a problem not just when it comes to retaining talent but also when it comes to competing for the signings that might fill the footsteps of today’s heroes.

To go back to fundamentals, earnings in sport follow a power law distribution – a small number of elite players make a large portion of the money. And the deal with the power law is that it is self-similar – you can cut off the distribution at any arbitrary amount, and what remains to the right is still a power law.

So income in football follows a power law. Income in elite football also follows the same power law. The English Premier League is at the far right end of this, but wages there again follow a power law. If you look at really elite players in the league, again it is a (sort of – since number of data points would have become small by now) power law.

What this means is that if you can define “marginal returns to additional skill”, at this far right end of the distribution it can be massive. For example, the article talks about how Salah has been offered a 50% hike (to make him the best paid Liverpool player ever), but that is still short of what some other (perceptibly less skilled) footballers earn.

So how do you go about getting value while operating in this kind of a market? One approach, that Liverpool seems to be playing, is to go Moneyball. “The marginal cost of getting a slightly superior player is massive, so we will operate not so far out at the right tail”, seems to be their strategy.

This means not breaking the bank for any particular player. It means ruthlessly assessing each player’s costs and benefits and acting accordingly (though sometimes it comes across as acting without emotion). For example, James Milner has just got an extension in his contract, but at lower wages to reflect his marginally decreased efficiency as he gets older.

Some of the other elite clubs (Real Madrid, PSG, Manchester City, etc.), on the other hand, believe that the premium for marginal quality is worth it, and so splurge on the elite players (including keeping them till fairly late in their careers even if it costs a lot). The rationale here is that the differences (to the “next level”) might be small, but these differences are sufficient to outperform compared to their peers (for example, Manchester City has won the league by one point over Liverpool twice in the last four seasons).

(Liverpool’s moneyball approach, of course, means that they try to get these “marginal advantages” in other (cheaper) ways, like employing a throw in coach or neuroscience consultants).

This approach is not without risk, of course. At the far right end of the tail, the variance in output can be rather high. Because the marginal cost of small increases in competence is so high, even if a player slightly underperforms, the effective monetary value of this underperformance is massive – you have paid for insanely elite players to win you everything, but they win you nothing.

And the consequences can be disastrous, as FC Barcelona found out last year.

In any case, the story doing the rounds now is that Barcelona want to hire Salah, but given their financial situation, they can’t afford to buy out his contract at Liverpool. So, they are hoping that he will run down his contract and join them on a free transfer next year. Then again, that’s what they had hoped from Gini Wijnaldum two years ago as well. And he’s ended up at PSG, where (to the best of my knowledge) he doesn’t play much.