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.

The first heart attack

Gerard Houllier is no more. The man who led Liverpool to the “cup treble” in 2001 passed away following a heart operation. Supporters of the club might remember that he had had yet another heart operation when he was managing Liverpool, and the impact of that heart attack on the club was serious.

I’m reusing a graph that I’d put here a couple of years back. This shows Liverpool’s Elo Rating (as per clubelo.com) over the years, with managers’s reigns being overlaid on top.

Notice the green region towards the right – it says “Houllier”, and it has one massive up and one massive down. Actually I’m going to re-upload this graph to blow up the Premier League period.

Liverpool’s Elo Rating in the Premier League period

Now you can see that there are two separate regions marked “Gerard Houllier”, with a small gap that says “Phil Thompson”. This gap represented Houllier’s first heart operation. Notice how, before his heart operation, Liverpool had been on a massive upswing, on their way back nearly to the levels where they had started off in the Premier League (they had last won  the league in 1990; compare to the first graph here).

And then the heart attack, and heart operation happened. Houllier’s assistant Phil Thompson took over and held things (here is Thompson’s tribute to Houllier). And then Houllier came back and he and Thompson became joint managers (the “orange” region here). And Liverpool’s rally was gone. The 2001-2 season was gone.

Looking at this graph, with the full benefit of hindsight, Houllier’s sacking in 2004 (to be replaced by Rafa Benitez) seems fully justified. And then notice the club’s steep fall under Benitez after Xabi Alonso got sold in 2009.

I’ve said here before – these Elo graphs can be used to tell a lot of footballing stories.

Yet another initiation

I’m still reeling from the Merseyside derby. It had been a long time since a game of football so emotionally drained me. In fact, the last time I remember getting a fever (literally) while watching a game of football was in the exact same fixture in 2013, which had ended 3-3 thanks to a Daniel Sturridge equaliser towards the end.

In any case, my fever (which I’ve now recovered from) and emotional exhaustion is not the reason today’s match will be memorable. It also happens to be a sort of initiation of my daughter as a bonafide Liverpool fan.

 

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Initiating @abherikarthik to the Merseyside derby. #ynwa #lfc

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It’s been a sort of trend in recent times (at least since the lockdown) that Liverpool games have been scheduled for late evenings or late night India times.  That has meant that I haven’t been able to involve the daughter, who on most days goes to bed at seven, in the football.

She has seen me watch highlights of Liverpool games. She admires the “Liverpool. We are Champions” poster that I had ordered after last season’s Premier League victory, and have since stuck on the walls of our study. She knows I’ve been a fan of Liverpool for a long time now (it dates to more than eleven years before she was born).

However, till date, after she had truly started understand stuff (she is four now), we had never watched a game together. And so when it was announced that the Everton-Liverpool game would be held at 5pm IST, I decided it was time for initiation.

I had casually slipped it to her on Tuesday (or so) that “on Saturday, we will be watching football together. And we will have drinks and snacks along with it”. And then on Wednesday she asked me what day of the week it was. “So how many days to Saturday”, she asked. When I asked her what was special about the coming Saturday, she let out a happy scream saying “football party!!”. On the same day she had informed her mother that we both were “going to have a football party on Saturday”, and that her mother was not welcome.

She’s spent the last three days looking forward to today. At four o’clock today, as I was “busy” watching the IPL game, she expressed her disappointment that I had not yet started preparing for the party. I finally swung into action around 4:30 (though a shopping trip in the morning had taken care of most of the prep).

A popcorn packet was put into the microwave. The potato chips packet (from a local “Sai hot chips” store) was opened, and part of its contents poured into a bowl. I showed her the bottles of fresh fruit juice that I had got, that had been pushed to me by a promoter at the local Namdhari’s store. Initially opting for the orange juice, she later said she wanted the “berry smoothie”. I poured it into a small wine glass that she likes. A can of diet coke and some Haldiram salted peanuts for me, and we were set.

I was pleasantly surprised that she sat still on the couch with me pretty much for the length of the match (she’s generally the restless types, like me). She tied the Liverpool scarf around her in many different ways. She gorged on the snacks (popcorn, potato chips and pomegranate in the first half; nachos with ketchup in the second). She kept asking who is winning. She kept asking me “where Liverpool was from” after I told her that “Everton are from Liverpool”.

I explained to her the concept of football, and goals. Once in the second half she was curious to see Adrian in the Liverpool goal, and that she “hadn’t seen the Liverpool goal in a long time”. Presently, Dominic Calvert-Lewin equalised to make it 2-2, giving her the glimpse of the goal she had so desired.

At the end of the game, she couldn’t grasp the concept of a draw. “But who won?”, she kept asking. She didn’t grasp the concept of offside either, though it possibly didn’t help that Liverpool seemed to play a far deeper line today than they have this season.

I’m glad that she had such an interesting game to make her “football watching debut”. Not technically, of course, since I remember cradling her on my lap when Jose Mourinho parked two Manchester United buses at Anfield (she was a month old then), and that had been a dreadful game.

A friend told me that I should “let her make her own choices” and not foist my club affiliations on her. Let’s see where this goes.

 

Front Five, Back Five

I recently realised that there are two ways in which you can describe a team’s formation in football. The traditional way is to describe it in terms of the number of defenders, midfielders and attackers. 4-4-2 and all that (speaking of which, I don’t think I’ve mentioned here at all about The Paper, a new venture I’ve started with Suprio Guha Thakurta, where we dissect one piece of India business news every day. Subscribe here if you aren’t yet a subscriber. In yesterday’s edition, we used Inverting The Pyramid to describe India’s National Education Policy).

Back to football, so you can describe teams as 2-3-5, or 4-4-2, or 4-2-3-1, or whatever. However, in the last few months, maybe since Jose Mourinho took over at Spurs, I’ve discovered another way of describing a football team. It’s not that elegant, I must admit, and it takes more effort to describe it. This is what I call the “back five, front five” method.

In his early days at Spurs, Jose sort of surprised us by the way he set up the team. We all expected a 4-3-3 (or even a 4-2-3-1) given his history. It was still a nominal 4-2-3-1, but it was highly asymmetrical. Right back Serge Aurier was given license to attack, while left back Ben Davies stayed back. So the “front five” (players responsible for attack) were centre forward Harry Kane, wide left forward Heung Min Son, the attacking midfielders Dele Alli and Lucas Moura, and Aurier.

In other words, it was the 3-1 of the 4-2-3-1 and the right back that constituted the front five for Spurs under Jose. The remaining two defenders and two defensive midfielders were the “back five”, responsible for holding the position when the front five went on attack.

Now, Jose has tweaked his formation several times after this, but once I had seen this front five back five description, I couldn’t “unsee” it. Every team’s formation fit nicely into a front five and a back five.

Liverpool and Manchester City both play with nominal 4-3-3s, but that doesn’t tell you how different these teams are in the way they attack. Well, for both, the front line of three are all attackers, but the interesting thing is who joins them.

For Liverpool, it is the full backs Trent Alexander Arnold and Andy Robertson. The job of the entire midfield is to be part of the back five (though they do join attacks in turns), which makes their job very different from similar midfielders at other clubs. Check out this statistic, for example:

Manchester City (and Guardiola’s Bayern Munich before them) do it differently. For them, all the back four are part of the back five, assisted by one of the midfielders. The other two midfielders (most commonly, Kevin De Bruyne and David Silva in the last two seasons) are part of the attack (Pep  calls them “twin eights”).

Manchester United struggled for most of the season, trying out different formations and not being particularly good at it until they landed Bruno Fernandes in the winter break. That, along with the emergence of “wide striker” Mason Greenwood meant that they’ve since adopted a front-back policy similar to their City rivals. The resurgence after the pandemic break was spectacular.

So think about it – the reason nominally similar formations might play very differently, or why nominally different formations produce similar styles of play, is that they interpret the front five and back five differently. Maybe it doesn’t work for all teams, but this is a good framework to describe teams.

Night trains

In anticipation of tonight’s Merseyside Derby, I was thinking of previous instances of this fixture at Goodison Park. My mind first went back to the game in the 2013-14 season, which was a see-saw 3-3 draw, with the Liverpool backline being incredibly troubled by Romelu Lukaku, and Daniel Sturridge scoring with a header immediately after coming on to make it 3-3 (and Joe Allen had missed a sitter earlier when Liverpool were 2-1 up).

I remember my wife coming back home from work in the middle of that game, and I didn’t pay attention to her until it was over. She wasn’t particularly happy about that, but the intense nature of the game gave me a fever (that used to happen often in the 2013-14 and 2008-9 seasons).

Then I remember Everton winning 3-0 once, though I don’t remember when that was (googling tells me that was in the 2006-7 season, when I was already a Liverpool fan, but not watching regularly).

And then I started thinking about what happened to this game last season, and then remembered that it was a 0-0 draw. Incidentally, it was on the same day that I travelled to Liverpool – I had a ticket for an Anfield Tour the next morning.

I now see that I had written about getting to Liverpool after I got to my hotel that night. However, I haven’t written about what happened before that. My train from Euston was around 8:00 pm. I remember leaving home (which was in Ealing) at around 6 or so, and then taking two tubes (Central changing to Victoria at Oxford Circus) to get to Euston. And then buying chewing gum and a bottle of water at Marks and Spencer while waiting for my train.

I also remember that while leaving home that evening, I was scared. I was psyched out. It wasn’t supposed to be that way. This was a trip to Liverpool I had been wanting to make for the best part of 14 years. I had kept putting it off during my stay in London until I knew that I was going to move out of London in two weeks’ time. Liverpool were having a great season (they would go on to win the Champions League, and only narrowly lose the Premiser League title).

I was supposed to be excited. Instead I was nervous. My nerve possibly settled only after I was seated in the train that evening.

Thinking about it, I basically hate night trains (well, this wasn’t an overnight train, but it started late in the evening). I hate night buses as well. And this only applies to night trains and buses that take me away from my normal place of residence – starting towards “home” late in the night never worries me.

This anxiety possibly started when I was in IIT Madras. I remember clearly then that I used to sleep comfortably without fail while travelling from Madras to Bangalore, but almost always never slept or only slept fitfully when travelling in the opposite direction. While in hindsight it all appears fine, I never felt particularly settled when I was at IITM.

And consequently, anything that reminds me of travelling to IITM psyches me out. I always took the night train while travelling there, and the anxiety would start on the drive to the railway station. Even now, sometimes, I get anxious while taking that road late in the evening.

Then, taking night trains has been indelibly linked to travelling to Madras, and something that I’ve come to fear as well. While I haven’t taken a train in India since 2012, my experience with the trip to Liverpool last year tells me that even non-overnight night trains have that effect on me.

And then, of course, there is the city of Chennai as well. The smells of the city after the train crosses Basin Bridge trigger the first wave of anxiety. Stepping out of the railway station and the thought of finding an autorickshaw trigger the next wave (things might be different now with Uber/Ola, but I haven’t experienced that).

The last time I went to Chennai was for a close friend’s wedding in 2012. I remember waking up early on the day of the wedding and then having a massive panic attack. I spent long enough time staring at the ceiling of my hotel room that I ended up missing the muhurtham.

I’ve made up my mind that the next time I have to go to Chennai, I’ll just drive there. And for sure, I’m not going to take a train leaving Bangalore in the night.

Studs and Fighters and Attack and Defence

The general impression in sport is that attack is “stud” and defence is “Fighter“. This is mainly because defence (in any game, pretty much) is primarily about not making errors, and being disciplined. Flamboyance can pay off in attack, when you only need to strike occasionally, but not in defence, where the real payoff comes from being consistent and excellent.

However, attack need not always be stud, and defence need not always be fighter. This is especially true in team sports such as football, where there can be a fair degree of organisation and coaching to get players to coordinate.

This piece in The Athletic (paywalled) gives an interesting instance of how attacking can be fighter, and how modern football is all about fighter attacking. It takes the instance of this weekend’s game between Tottenham Hotspur and Liverpool F.C., which the latter won.

Jack Pitt-Brooke, the author, talks about how Liverpool is fighter in attack because the players are well-drilled in attacking, and practice combination play, or what are known in football as “automisations”.

But in modern football, the opposite is true. The best football, the type played by Pep Guardiola’s Manchester City or Jurgen Klopp’s Liverpool, is the most rigorously planned, drilled and co-ordinated. Those two managers have spent years teaching their players the complex attacking patterns and synchronised movements that allow them to cut through every team in the country. That is why they can never be frustrated by opponents who just sit in and defend, why they are racking up points totals beyond the reach of anyone else.

Jose Mourinho, on the other hand, might be fighter in the way he sets up his defence, but not so when it comes to attacking. He steadfastly refuses to have his teams train attacking automisations. While defences are extremely well drilled, and know exactly how to coordinate, attackers are left to their own forces and creativity. What Mourinho does is to identify a handful of attackers (usually the centre forward and the guy just behind him) who are given “free roles” and are expected to use their own creativity in leading their team’s attacks.

As Pitt-Brooke went on to write in his article,

That, more than anything else, explains the difference between Klopp and Mourinho. Klopp wants to plan his way out of the randomness of football. Mourinho is more willing to accept it as a fact and work around it. So while the modern manager — Klopp, Guardiola, Antonio Conte — coaches players in ‘automisations’, pre-planned moves and patterns, Mourinho does not.

Jurgen Klopp the fighter, and Jose Mourinho the stud. That actually makes sense when you think of how their teams attack. It may not be intuitive, but upon some thought it makes sense.

Yes, attack is also being fighterised in modern sport.

Liverpool FC: Mid Season Review

After 20 games played, Liverpool are sitting pretty on top of the Premier League with 58 points (out of a possible 60). The only jitter in the campaign so far came in a draw away at Manchester United.

I made what I think is a cool graph to put this performance in perspective. I looked at Liverpool’s points tally at the end of the first 19 match days through the length of the Premier League, and looked at “progress” (the data for last night’s win against Sheffield isn’t yet up on my dataset, which also doesn’t include data for the 1992-93 season, so those are left out).

Given the strength of this season’s performance, I don’t think there’s that much information in the graph, but here it goes in any case:

I’ve coloured all the seasons where Liverpool were the title contenders. A few things stand out:

  1. This season, while great, isn’t that much better than the last one. Last season, Liverpool had three draws in the first half of the league (Man City at home, Chelsea away and Arsenal away). It was the first month of the second half where the campaign faltered (starting with the loss to Man City).
  2. This possibly went under the radar, but Liverpool had a fantastic start to the 2016-17 season as well, with 43 points at the halfway stage. To put that in perspective, this was one more than the points total at that stage in the title-chasing 2008-9 season.
  3. Liverpool went close in 2013-14, but in terms of points, the halfway performance wasn’t anything to write home about. That was also back in the time when teams didn’t dominate like nowadays, and eighty odd points was enough to win the league.

This is what Liverpool’s full season looked like (note that I’ve used a different kind of graph here. Not sure which one is better).

 

Finally, what’s the relationship between points at the end of the first half of the season (19 games) and the full season? Let’s run a regression across all teams, across all 38 game EPL seasons.

The regression doesn’t turn out to be THAT significant, with an R Squared of 41%. In other words, a team’s points tally at the halfway point in the season explains less than 50% of the variation in the points tally that the team will get in the second half of the season.

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  9.42967    0.97671   9.655   <2e-16 ***
Midway       0.64126    0.03549  18.070   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.992 on 478 degrees of freedom
  (20 observations deleted due to missingness)
Multiple R-squared:  0.4059,    Adjusted R-squared:  0.4046 
F-statistic: 326.5 on 1 and 478 DF,  p-value: < 2.2e-16

The interesting thing is that the coefficient of the midway score is less than 1, which implies that teams’ performances at the end of the season (literally) regress to the mean.

55 points at the end of the first 19 games is projected to translate to 100 at the end of the season. In fact, based on this regression model run on the first 19 games of the season, Liverpool should win the title by a canter.

PS: Look at the bottom of this projections table. It seems like for the first time in a very long time, the “magical” 40 points might be necessary to stave off relegation. Then again, it’s regression (pun intended).

EPL: Mid-Season Review

Going into the November international break, Liverpool are eight points ahead at the top of the Premier League. Defending champions Manchester City have slipped to fourth place following their loss to Liverpool. The question most commentators are asking is if Liverpool can hold on to this lead.

We are two-thirds of the way through the first round robin of the premier league. The thing with evaluating league standings midway through the round robin is that it doesn’t account for the fixture list. For example, Liverpool have finished playing the rest of the “big six” (or seven, if you include Leicester), but Manchester City have many games to go among the top teams.

So my practice over the years has been to compare team performance to corresponding fixtures in the previous season, and to look at the points difference. Then, assuming the rest of the season goes just like last year, we can project who is likely to end up where.

Now, relegation and promotion introduces a source of complication, but we can “solve” that by replacing last season’s relegated teams with this season’s promoted teams (18th by Championship winners, 19th by Championship runners-up, and 20th by Championship playoff winners).

It’s not the first time I’m doing this analysis. I’d done it once in 2013-14, and once in 2014-15. You will notice that the graphs look similar as well – that’s how lazy I am.

Anyways, this is the points differential thus far compared to corresponding fixtures of last season. 

 

 

 

Leicester are the most improved team from last season, having scored 8 points more than in corresponding fixtures from last season. Sheffield United, albeit starting from a low base, have done extremely well as well. And last season’s runners-up Liverpool are on a plus 6.

The team that has done worst relative to last season is Tottenham Hotspur, at minus 13. Key players entering the final years of their contract and not signing extensions, and scanty recruitment over the last 2-3 years, haven’t helped. And then there is Manchester City at minus 9!

So assuming the rest of the season’s fixtures go according to last season’s corresponding fixtures, what will the final table look  like at the end of the season?
We see that if Liverpool replicate their results from last season for the rest of the fixtures, they should win the league comfortably.

What is more interesting is the gaps between 1-2, 2-3 and 3-4. Each of the top three positions is likely to be decided “comfortably”, with a fairly congested mid-table.

As mentioned earlier, this kind of analysis is unfair to the promoted teams. It is highly unlikely that Sheffield will get relegated based on the start they’ve had.

We’ll repeat this analysis after a couple of months to see where the league stands!

Liverpool FC: 2014 vs 2019

Last night I watched the first half of the Champions League semifinal between FC Barcelona and Liverpool FC, going off to bed when the score was 1-0 in favour of Barcelona. I woke up this morning to much dismay to see that Liverpool lost 3-0, but I’d constructed this post in my head when Liverpool was trailing 1-0, and so executing now.

It’s about the difference between the title-challenging Liverpool of 2014 and the title-challenging Liverpool of this season. Luis Suarez, in a brilliant interview with Sid Lowe, had mentioned that the current team is much better than the 2014 team, but last night’s Champions League game suggests that the two teams five years apart are simply two very different teams.

Last night Barcelona went ahead with a goal from Suarez in the 25th minute. It wasn’t an easy goal. There was a cross from the left by Jordi Alba, and Suarez got ahead, and managed to get the precise touch required to put it past Alisson into Liverpool’s goal. Liverpool had dominated the game until then, but with that one little half chance Suarez had converted.

Ten minutes later Sadio Mane got a chance to equalise, from a broadly similar chance. It was another ball above the defence from Mo Salah, but Mane hit it to the sky. And that was representative of Liverpool this season – both Mane and Salah have required lots of chances to score.

In that sense, Liverpool’s defence and midfield this season is far superior to the title-challenging side of 2014, when Suarez led the line. Back then few chances were created, but Suarez and an in-form Daniel Sturridge would take most of them, meaning that even with the midfield creating few chances and the defence leaking lots of goals, Liverpool could mount a challenge.

One could only imagine how this season’s team would have performed with someone of Suarez’s finishing ability leading the line. Salah, Mane and Firmino are no doubt a brilliant front three, but their conversion rate is low. If only one of them had a higher conversion rate, we wouldn’t have been struggling in both the League and the Champions League this season.

 

Liverpool

While I absolutely remain a fan of Liverpool Football Club, and had a fascinating tour of their facilities this morning, I’m not such a big fan of the city itself. Somehow overall the experience there (barring some taxi rides and the Anfield experience itself) was not particularly great.

For starters, it doesn’t help that the city has lousy weather. Being up north, in England and on the coast means there are strong winds, and it can be pretty bad when it rains. Then, when I got off the train station last night, the city seemed dead and the roads that I walked on until I found a taxi were deserted.

And this afternoon, after I had finished my stadium tour and went to the renowned Albert Docks, the experience there was similar as well. Rather dull and without too many people around. And once again the weather didn’t help matters.

And then there is the hotel I stayed in last night. The check in and check out were rather pleasant and I mostly got a good night’s sleep as well, but a former office building converted to a hotel can be a bit depressing. The room was rather small, with the bed stuck to two walls. And a part of it had been earmarked for the bathroom anyway. Even this morning when I got out of the hotel the area wasn’t really bustling (this was in central Liverpool).

And while I found the breakfast to be pretty good (I got a a “large English breakfast”), the service and decor of the restaurant wasn’t particularly appealing. And as I got out of the restaurant, I saw a “up for sale” board on the door!

Anyway, it’s just a few data points. However, in hindsight I feel less bad now about not booking my ticket to York yesterday itself, which would’ve cut my journey cost by 50%. Without a booked ticket, not finding the place particularly interesting meant I could quickly get to the station and take the next train onward.

So here I am, nearing York (I’m finishing this post now in a hurry since I should reach any time now, and I don’t want to scramble). The views on the journey have been rather stunning. The big breakfast meant that I didn’t need to have lunch today. And I had some beer and peanuts and cake on the train and am feeling happy about it now!

The only sore point is that soon after I had bought beer from the cart on the train, the conductor announced that the toilets on train aren’t working. In any case, York isn’t far away!

Cheers