English Premier League: Goal Difference to points correlation

So I was just looking down the English Premier League Table for the season, and I found that as I went down the list, the goal difference went lower. There’s nothing counterintuitive in this, but the degree of correlation seemed eerie.

So I downloaded the data and plotted a scatter-plot. And what do you have? A near-perfect regression. I even ran the regression and found a 96% R Square.

In other words, this EPL season has simply been all about scoring lots of goals and not letting in too many goals. It’s almost like the distribution of the goals itself doesn’t matter – apart from the relegation battle, that is!

PS: Look at the extent of Manchester City’s lead at the top. And what a scrap the relegation is!

Biases, statistics and luck

Tomorrow Liverpool plays Manchester City in the Premier League. As things stand now I don’t plan to watch this game. This entire season so far, I’ve only watched two games. First, I’d gone to a local pub to watch Liverpool’s visit to Manchester City, back in September. Liverpool got thrashed 5-0.

Then in October, I went to Wembley to watch Tottenham Hotspur play Liverpool. The Spurs won 4-1. These two remain Liverpool’s only defeats of the season.

I might consider myself to be a mostly rational person but I sometimes do fall for the correlation-implies-causation bias, and think that my watching those games had something to do with Liverpool’s losses in them. Never mind that these were away games played against other top sides which attack aggressively. And so I have this irrational “fear” that if I watch tomorrow’s game (even if it’s from a pub), it might lead to a heavy Liverpool defeat.

And so I told Baada, a Manchester City fan, that I’m not planning to watch tomorrow’s game. And he got back to me with some statistics, which he’d heard from a podcast. Apparently it’s been 80 years since Manchester City did the league “double” (winning both home and away games) over Liverpool. And that it’s been 15 years since they’ve won at Anfield. So, he suggested, there’s a good chance that tomorrow’s game won’t result in a mauling for Liverpool, even if I were to watch it.

With the easy availability of statistics, it has become a thing among football commentators to supply them during the commentary. And from first hearing, things like “never done this in 80 years” or “never done that for last 15 years” sounds compelling, and you’re inclined to believe that there is something to these numbers.

I don’t remember if it was Navjot Sidhu who said that statistics are like a bikini (“what they reveal is significant but what they hide is crucial” or something). That Manchester City hasn’t done a double over Liverpool in 80 years doesn’t mean a thing, nor does it say anything that they haven’t won at Anfield in 15 years.

Basically, until the mid 2000s, City were a middling team. I remember telling Baada after the 2007 season (when Stuart Pearce got fired as City manager) that they’d be surely relegated next season. And then came the investment from Thaksin Shinawatra. And the appointment of Sven-Goran Eriksson as manager. And then the youtube signings. And later the investment from the Abu Dhabi investment group. And in 2016 the appointment of Pep Guardiola as manager. And the significant investment in players after that.

In other words, Manchester City of today is a completely different team from what they were even 2-3 years back. And they’re surely a vastly improved team compared to a decade ago. I know Baada has been following them for over 15 years now, but they’re unrecognisable from the time he started following them!

Yes, even with City being a much improved team, Liverpool have never lost to them at home in the last few years – but then Liverpool have generally been a strong team playing at home in these years! On the other hand, City’s 18-game winning streak (which included wins at Chelsea and Manchester United) only came to an end (with a draw against Crystal Palace) rather recently.

So anyways, here are the takeaways:

  1. Whether I watch the game or not has no bearing on how well Liverpool will play. The instances from this season so far are based on 1. small samples and 2. biased samples (since I’ve chosen to watch Liverpool’s two toughest games of the season)
  2. 80-year history of a fixture has no bearing since teams have evolved significantly in these 80 years. So saying a record stands so long has no meaning or predictive power for tomorrow’s game.
  3. City have been in tremendous form this season, and Liverpool have just lost their key player (by selling Philippe Coutinho to Barcelona), so City can fancy their chances. That said, Anfield has been a fortress this season, so Liverpool might just hold (or even win it).

All of this points to a good game tomorrow! Maybe I should just watch it!



Football transfer markets

So the 2017 “summer transfer window” is going to close in three days’ time. It’s been an unusual market, with oddly inflated valuations – such as Neymar going for ~ €200 million from Barcelona to PSG, and Manchester City paying in excess of £50 million each for a pair of full backs (Kyle Walker and Benjamin Mendy).

Meanwhile, transfers are on in the NBA as well. Given that American sporting leagues have a rather socialist structure, there is no money exchanged. Instead, you have complicated structures such as this one between the Cleveland Cavaliers and Boston Celtics:

 by trading Kyrie Irving (pictured, left), their star point guard, to the Boston Celtics. In exchange, Mr Altman received a package of three players headlined by Isaiah Thomas (right), plus a pick in the 2018 entry draft

A week back, renowned blogger Amit Varma interviewed me for his The Seen and the unseen podcast. The topic was football transfers, something that I talk about in the first chapter of my soon-to-be-published book. In that, he asked me what the football transfer market might look like in the absence of price. And I mentioned that PSG might have had to give up their entire team in order to buy Neymar in that situation.

Anyway, listen to the entire podcast episode here.

Oh, and I don’t know if I mentioned it here before, but my book is ready now and will be released on the 8th of September. It’s being published by the Takshashila Institution.

You can pre-order the book on Amazon. For some reason, the Kindle India store doesn’t have a facility to pre-order, so if you live in India and want to read the book on Kindle, you’ll have to wait until the 8th of September. Kindle stores elsewhere already allow you to pre-order. Follow the link above.

More football structuring

I’ve commented earlier on innovative structuring of football player contracts, with call options and put options and all other exotic options being involved. Now I see another interesting transfer structure, this time in the contract of Juventus (and Spain) striker Alvaro Morata.

In 2014, Real Madrid sold Morata to Juventus for a transfer fee of €20 million, but the sale had a “buy back clause”. Embedded in the sale was an option for Real Madrid to buy back Morata at any time for €30 million, and now it seems like they’re exercising it!

While this might be based on Morata’s performances (both for Juventus and Spain) in the last couple of years, the interesting thing about the buyback is that Real Madrid are unlikely to keep hold of Morata. Instead, talk is that they plan to sell him on, with PSG and Manchester United being interested in the forward.

Effectively the deal is something like “as long as Morata’s perceived market value is  < €30M, Juventus can keep him, but once his perceived market value goes up, all the upside goes to Real Madrid”. The downside (in case Morata regressed as a player and his market value went below €20M), of course, remained with Juventus. To put it simply, Madrid is exercising its call option on the player.

While loan agreements have earlier had clauses such as “right but obligation to make deal permanent” or “obligation but not right to make deal permanent”, this is the first time I’m seeing an actual transfer deal with this kind of a clause, which is being exercised. So why did Juventus and Real Madrid hammer out such a complicated-looking structure?

For Juventus, the simple answer is that the option they wrote reduced the cost of buying the player. While they have given up on significant upside in writing this call option, this is what perhaps made the purchase possible for them, and in some ways, it’s worked out by giving them two more Scudetti.

The answer is less clear from Real Madrid’s perspective. Clearly, the fact that they got a call option meant that they believed there was a significant chance of Morata improving significantly. At the point of time of sale (2014), however, he was surplus to their requirements and they believed sending him elsewhere would help in this significant improvement.

It is possible that the market in 2014 wasn’t willing to bear the price implied by Real Madrid’s expectation of Morata’s improvement, but was only willing to pay based on his then abilities and form. In other words, while Morata’s current abilities were fairly valued, his future abilities were grossly undervalued.

And Madrid did the smart thing by unbundling the current and future values, by structuring a deal that included a call option!

Again, this is only my speculation of how it would have turned out, but it’s indeed fascinating. Given how global financial markets are performing nowadays, it seems like structuring of football deals is now far more interesting than structuring financial derivatives! But then the market is illiquid!

Pricing season tickets

One observation about the crowd when I attended my first game at the Camp Nou (in October 2014, against Ajax in the 2014-15 Champions League) was how people around me all seemed to know each other. There were friendly nods and handshakes, and it was evident that these men and women were familiar with each other. They all arrived and departed independently, though, and there wasn’t much conversation during the game, suggesting they were acquaintances rather than friends.

On my second visit to the Camp Nou (ten days ago, for the 2015-16 Champions League game against Arsenal), I noticed hordes of empty seats. I was in a stand two tiers higher than where I had sat for the Ajax game, and despite that stand being priced at a princely €150, there were plenty of empty seats (my wife sat next to me for the duration of the game despite her assigned seat being one rank and a few files away). It was a cold and rainy day, but not so rainy that €150 be treated as “sunk cost”!

The common feature that explains both these phenomena is the “season ticket”. As the official club website explains,

The complete season ticket gives members the right to attend, always from the same seat, games played at the Camp Nou in official competitions: Spanish League, Champions League, Copa de Rey and UEFA Cup (emphasis added)

The reason people seated around me at the Ajax game were acquainted with each other was because they were season ticket holders, and would watch every game seated in close proximity to one another. And the empty seats for the Arsenal game were a result of season ticket holders, for whom the marginal cost of not attending the game was far less than €150, not attending the game (there is a “free seat” program that lets season ticket holders sell their ticket through official channels, but considering that the decision to not go would have been made in the last minute (given the rain) many season ticket holders may not have exercised this option.

Football clubs (and other performance venues) sell season tickets in order to create a “base load” of demand for their tickets. While these season tickets are sold at a deep discount (relative to what it costs to buy a ticket for each game), the fact that they are sold at once and at the beginning of the season means that the club can be sure of a certain amount of revenue from ticket sales, and can be assured to fill a certain proportion of seats at the stadium in every round.

Season tickets are also important because they help create a sense of loyalty among the fans, and the same fans sitting in the same spaces week after week can bond and help create a better viewing atmosphere at the club. In other words, season tickets seems like a no-brainer. Except that Hull City, which plays in the English Championship, has decided to do away with season tickets starting next season.

The official statements related to this move seem like sanitised PR (refer link above), but the linked article gives away an important piece of information that suggests why this new ticket scheme might have been brought into play:

The club said the Upper Stand would be closed, meaning 1,800 fans must be relocated, but would be opened for high-profile matches

While the club doesn’t want to admit it, the reason it is doing away with season tickets is that attendance at the KC Stadium has been falling, and it appears that there have been lots of empty seats in the stadium.

As I had noted in my earlier piece on pricing Liverpool FC tickets, there are network effects to watching a football game in the stadium. You gain value not only from what happens on the pitch, but also from the atmosphere that fans at the stadium (including you) build up. And while there are many ways in which fans can affect the watching experience of co-fans, it shouldn’t be hard to understand that empty seats do not add to the stadium atmosphere in any way.

The problem with season tickets is that even with programs such as “free seat” (where the season ticket holder can get paid for giving up their seat), the cost for a season ticket holder to not attend a game is extremely low. And when several season ticket holders decide to not attend certain games, it can lead to rather low attendances, and diminished stadium experience for the fans who do end up attending.

This network effect – of fans helping shape experience of fellow fans – makes the sale of football season tickets different from that of long term cargo contracts, for example. You not only seek to assure yourself of revenues by selling season tickets, but also seek to fill a certain portion of the seats for every game through such a program, and help create the experience.

And when your fans are being delinquent (by purchasing season tickets but not attending), your first action would be to increase the price of such season tickets so that only “serious fans” will buy it and the (sunk) cost of not attending a game is higher. It seems Hull City has already gone through one such exercise, and raised its season ticket prices, which hasn’t helped drive overall attendances.

Hence, the club has decided to do away with season tickets altogether. With the new rolling monthly ticket program, fans will purchase if and only if they are confident of attending a certain number of games. On the one hand, this pushes up the cost of not going for a game, and on the other, allows the club to manage its revenues on a larger portion of the tickets.

From a revenue point of view, this is a risky strategy, as the club foregoes assured revenues from season tickets in favour of more volatile monthly ticket revenues, and greater tickets to sell in the open market before every game. However, considering the network effects of watching football in a stadium, what the club is banking on is that this measure will help them fill up their stadium more than before, and that the improved atmosphere that comes out of that can be monetised in the long run.

It’s a bold move by Hull City to improve football attendances. If it works out, it offers a way out for other clubs that are currently unable to fill their stadiums. But you must remember that optimisation here takes place on two axes – revenues and crowds!

Revenue management at Liverpool Football Club

Liverpool Football Club, of which I’ve been a fan for nearly eleven years now, is in the midst of a storm with fans protesting against high ticket prices. The butt of the fans’ ire has been the new £77 ticket that will be introduced next season. Though there will be few tickets that will be sold at that price, the existence of the price point has been enough to provoke the fans, many of whom walked out in the 77th minute of the home draw against Sunderland last weekend.

For a stadium that routinely sells out its tickets, an increase in ticket prices should be a no-brainer – it is poor revenue management if either people are scrambling for tickets or if there are empty seats. The problem here has been the way the price increase has been handled and communicated to the fans, and also what the club is optimising for.

At the outset, it must be understood that from a pure watching point of view, being in a stadium is inferior to being in front of a television. In the latter case, you not only have the best view of the action at all points in time, but also replays of important events and (occasionally) expert commentary to help you understand the game. From this point of view, the reason people want to watch a game at the ground is for reasons other than just watching – to put it simply, they go for “the experience”.

Now the thing with stadium experience is that it is a function of the other people at the stadium. In other words, it displays network effects – your experience at the stadium is a function of who else is in the stadium along with you.

This can be complex to model – for this could involve modelling every possible interaction between every pair of spectators at the ground. For example, if your sworn nemesis is at the ground a few seats away from you, you are unlikely to enjoy the game much.

However, given the rather large number of spectators, these individual interactions can be ignored, and only aggregate interactions considered. In other words, we can look at the interaction term between each spectator (who wants to watch the game at the ground) and the “rest of the crowd” (we assume idiosyncrasies like your sworn enemy’s presence as getting averaged out).

Now we have different ways in which a particular spectator can influence the rest of the crowd – in the most trivial case, he just quietly takes his seat, watches the game and leaves without uttering a word, in which case he adds zero value. In another case, he could be a hooligan and be a pain to everyone around him, adding negative value. A third spectator could be a possible cheerleader getting people around him to contribute positively, organising Mexican waves and generally keeping everyone entertained. There can be several other such categories.

The question is what the stadium is aiming to optimise for – the trivial case would be to optimise for revenue from a particular game, but that might come at the cost of stadium “atmosphere”. Stadium atmosphere is important not only to galvanise the team but also to enthuse spectators and get them to want to come for the next game, too. These two objectives (revenue and atmosphere) are never perfectly correlated (in fact their correlation might be negative), and the challenge for the club is to price in a way that the chosen linear combination of these objectives is maximised.

Fundamental principles of pricing in two-sided markets (here it’s a multisided market) say that the price to be charged to a participant should be a negative function of the value he adds to the rest of the event (to the “rest of the crowd” in this case).

A spectator who adds value to the crowd by this metric should be given a discount, while one who subtracts value (by either being a hooligan or a prude) should be charged a premium. The challenge here is that it may not be possible to discriminate at the spectator level – other proxies might have to be used for price discrimination.

One way to do this could be to model the value added by a spectator class as a function of the historic revenues from that class – with some clever modelling it might be possible to come up with credible values for this one, and then taking this value into account while adjusting the prices.

Coming back to Liverpool, the problem seems to be that the ticket price increase (no doubt given by an intention to further maximise revenue takings) has badly hit fans who were otherwise adding positive value to the stadium atmosphere. With such fans potentially getting priced out (in favour of fans who are willing to pay more, but not necessarily adding as much value to the ground), they are trying to send a message to the club that their value (toward the stadium atmosphere) is being underestimated, and thus they need greater discounts. The stadium walkouts are a vehicle to get across this point.

Maximising for per-game revenue need not be sustainable in the long term – an element of “atmosphere” has to be added, too. It seems like the current worthies at Liverpool Football Club have failed to take this into account, resulting in the current unsavoury negotiations.

Now that I’ve moved to Barcelona, Liverpool FC need not look too far – I’ve done a fair bit of work on pricing and revenue management, and on two-sided markets, and can help them understand and analyse the kind of value added by different kinds of spectators, and how this can translate to actual revenues and atmosphere. So go ahead and hire me!

Rodgers and the Ranatunga Principle

It was a wonderful display of the “Ranatunga Principle” by Brendan Rodgers last night, when he fielded what was effectively a second string Liverpool team at Real Madrid. That they lost only 1-0 shows that it wasn’t that bad a ploy, especially given the more important features coming up ahead.

Firstly, Liverpool have not given up on the Champions League. They have simply prioritised. The group they are is a rather weird one – where one team is significantly superior to the others which are approximately at the same level. It is not inconceivable at all that Real Madrid will win all their six games and get 18 points.

Before the game at Anfield two weeks back the degree of Real Madrid’s superiority over Liverpool wasn’t yet fully established and Rodgers smelt the chances of handing out an upset at home and fielded his strongest team. It backfired spectacularly as Real Madrid hammered Liverpool. The more important result of the night, though, was the unfancied but promising Ludogorets beating Basel at home. It was that result that allowed Rodgers to do what he did yesterday.

Real Madrid’s dominance means that Liverpool, Basel and Ludogorets are effectively playing a 3-team mini league the winner of which will go through to the knockouts (of course the extents of their respective thrashings by Real Madrid will matter if it comes down to goal difference). So far, in this mini group, all games have gone to the “home team”.

Liverpool’s last two games of the season see them take on Basel at home and Ludogorets away, and if they win both of them, they are through to the knockouts. Even if Liverpool had come away with a point in last night’s game, this equation would not have changed significantly (three points last night would have helped but the game at Anfield showed how impossible that was).

Liverpool have had a rather busy fixture list in the last 3 weeks. In the space of three weeks they’ve had to play QPR, Real Madrid, Hull, Swansea, Newcastle, Real Madrid and Chelsea – not an easy fixture list at all, and Liverpool’s poor form in the league has made them take even the Capital One Cup seriously, meaning not too many players could be rotated for the game against Swansea. In the loss to Newcastle on Saturday, the fatigue was evident as Liverpool’s attackers were all anonymous. A rest day was thus in order.

This, combined with the weird nature of the Champions League group that Liverpool are in meant that last night’s game was the “least important” for Liverpool in the current run of fixtures, which permitted them to rest key players and give a run out to the perennial subs. And on the evidence of the 1-0 defeat, it seems it didn’t go too badly. Now if only Liverpool can make use of this rest and beat Chelsea on the weekend!


Gerrard came on around three-quarters into last night’s game. I have come to believe that is his best position for the team now. Come on as an “impact substitute” in the second half and play in the “old Gerrard role”.