Premier League Points Efficiency

It would be tautological to say that you win in football by scoring more goals than your opponent. What is interesting is that scoring more goals and letting in fewer works across games in a season as well, as data from the English Premier League shows.

We had seen an inkling of this last year, when I had showed that points in the Premier League were highly correlated with goal difference (96% R square for those that are interested). A little past the midway point of the current season and the correlation holds – 96% again.

In other words, a team’s goal difference (number of goals scored minus goals let in) can explain 96% of the variance in the number of points gained by the team in the season so far. The point of this post is to focus on the rest.

In the above image, the blue line is the line of best fit (or regression line). This line predicts the number of points scored by a team given their goal difference. Teams located above this line have been more efficient or lucky – they have got more points than their goal different would suggest. Teams below this line have been less efficient or unlucky – their goal difference has been distributed badly across games, leading to fewer points than the team should have got.

Manchester City seem to be extremely unlucky this season, in that they have scored about five fewer points than what their goal difference suggests. The other teams close to the top of the league are all above the line – showing they’ve been more efficient in the way their goals have been distributed (Spurs and Arsenal have been luckier than ManYoo, Chelski and Liverpool).

At the other end of the table, Huddersfield Town have been unlucky – their goal difference suggests they should have had four more points – a big difference for a relegation threatened team. Southampton, Newcastle and Crystal Palace are also in the same boat.

Finally, the use of goal difference is used to break ties in league tables is an attempt to undo the luck (or lack of it) that would have resulted in teams under- or over-performing in terms of points given the number of goals they’ve scored and let in. Some teams would have gotten much more (or less) points than deserved by sheer dint of their goals having been distributed better across matches (big losses and narrow wins). The use of goal difference is a small attempt to set that right.

Football Elo Application

This morning, I discovered the Club Elo Ratings, and promptly proceeded to analyse Liverpool FC’s performance over the years based on these ratings, and then correlated the performance by manager.

Then, playing around with the data of different clubs, I realised that there are plenty more stories to be told using this data, and they are best told by people who are passionate about their respective clubs. So the best thing I could do is to put the data out there (in a form similar to what I did for Liverpool), so that people can analyse how their clubs have performed over the years, and under different managers.

Sitting beside me as I was doing this analysis, my wife popped in with a pertinent observation. Now, she doesn’t watch football. She hates it that I watch so much football. Nevertheless, she has a strong eye for metrics. And watching me analyse club performance by manager, she asked me if I can analyse manager performance by club!

And so I’ve added that as well to the Shiny app that I’ve built. It might look a bit clunky, with two unrelate graphs, one on top of the other, but since the two are strongly related, it makes sense to have both in the same app. The managers listed in the bottom dropdown are those who have managed at least two clubs in the Premier League.

If you’re interested in Premier League football, you should definitely check out the app. I think there are some interesting insights to be gleaned (such as what I presented in this morning’s post).

Built by Shanks

This morning, I found this tweet by John Burn-Murdoch, a statistician at the Financial Times, about a graphic he had made for a Simon Kuper (of Soccernomics fame) piece on Jose Mourinho.

Burn-Murdoch also helpfully shared the code he had written to produce this graphic, through which I discovered ClubElo, a website that produces chess-style Elo ratings for football clubs. They have a free and open API, through which Burn-Murdoch got the data for the above graphic, and which I used to download all-time Elo ratings for all clubs available (I can be greedy that way).

So the first order of business was to see how Liverpool’s rating has moved over time. The initial graph looked interesting, but not very interesting, so I decided to overlay it with periods of managerial regimes (the latter data I got through wikipedia). And this is what the all-time Elo rating of Liverpool looks like.

It is easy to see that the biggest improvement in the club’s performance came under the long reign of Bill Shankly (no surprises there), who took them from the Second Division to winning the old First Division. There was  brief dip when Shankly retired and his assistant Bob Paisley took over (might this be the time when Paisley got intimidated by Shankly’s frequent visits to the club, and then asked him not to come any more?), but Paisley consolidated on Shankly’s improvement to lead the club to its first three European Cups.

Around 2010, when the club was owned by Americans Tom Hicks and George Gillett and on a decline in terms of performance, this banner became popular at Anfield.

The Yanks were subsequently yanked following a protracted court battle, to be replaced by another Yank (John W Henry), under whose ownership the club has done much better. What is also interesting from the above graph is the managerial change decisions.

At the time, Kenny Dalglish’s sacking at the end of the 2011-12 season (which ended with Liverpool losing the FA Cup final to Chelsea) seemed unfair, but the Elo rating shows that the club’s rating had fallen below the level when Dalglish took over (initially as caretaker). Then there was a steep ascent under Brendan Rodgers (leading to second in 2013-14), when Suarez bit and got sold and the team went into deep decline.

Again, we can see that Rodgers got sacked when the team had reverted to the rating that he had started off with. That’s when Jurgen Klopp came in, and thankfully so far there has been a much longer period of ascendance (which will hopefully continue). It is interesting to see, though, that the club’s current rating is still nowhere near the peak reached under Rafa Benitez (in the 2008-9 title challenge).

Impressed by the story that Elo Ratings could tell, I got data on all Premier League managers, and decided to repeat the analysis for all clubs. Here is what the analysis for the so-called “top 6” clubs returns:

We see, for example, that Chelsea’s ascendancy started not with Mourinho’s first term as manager, but towards the end of Ranieri’s term – when Roman Abramovich had made his investment. We find that Jose Mourinho actually made up for the decline under David Moyes and Louis van Gaal, and then started losing it. In that sense, Manchester United have got their sacking timing right (though they were already in decline by the time they finished last season in second place).

Manchester City also seem to have done pretty well in terms of the timing of managerial changes. And Spurs’s belief in Mauricio Pochettino, who started off badly, seems to have paid off.

I wonder why Elo Ratings haven’t made more impact in sports other than chess!

AlphaZero Revisited

It’s been over a year since Google’s DeepMind first made its splash with the reinforcement-learning based chess playing engine AlphaZero. The first anniversary of the story of AlphaZero being released also coincided with the publication of the peer-reviewed paper.

To go with the peer-reviewed paper, DeepMind has released a further 200 games played between AlphaZero and the conventional chess engine StockFish, which is again heavily loaded in favour of wins for AlphaZero, but also contains 6 game where AlphaZero lost. I’ve been following these games on GM Daniel King’s excellent Powerplaychess channel, and want to revise my opinion on AlphaZero.

Back then, I had looked at AlphaZero’s play from my favourite studs and fighter framework, which in hindsight doesn’t do full justice to AlphaZero. From the games that I’ve seen from the set released this season, AlphaZero’s play hasn’t exactly been “stud”. It’s just that it’s much more “human”. And the reason why AlphaZero’s play possibly seems more human is because of the way it “learns”.

Conventional chess engines evaluate a position by considering all possible paths (ok not really, they use an intelligent method called Alpha-Beta Pruning to limit their search size), and then play the move that leads to the best position at the end of the search. These engines use “pre-learnt human concepts” such as point count for different pieces, which are used to evaluate positions. And this leads to a certain kind of play.

AlphaZero’s learning, process, however, involves playing zillions of games against itself (since I wrote that previous post, I’ve come back up to speed with reinforcement learning). And then based on the results of these games, it evaluates positions it reached in the course of play (in hindsight). On top of this, it builds a deep learning model to identify the goodness of positions.

Given my limited knowledge of how deep learning works, this process involves AlphaZero learning about “features” of games that have more often than not enabled it to win. So somewhere in the network there will be a node that represents “control of centre”. Another node deep in the network might represent “safety of king”. Yet another might perhaps involve “open A file”.

Of course, none of these features have been pre-specified to AlphaZero. It has simply learnt it by training its neural network on zillions of games it has played against itself. And while deep learning is hard to “explain”, it is likely to have so happened that the features of the game that AlphaZero has learnt are remarkably similar to the “features” of the game that human players have learnt over the centuries. And it is because of the commonality in these features that we find AlphaZero’s play so “human”.

Another way to look at is from the concept of “10000 hours” that Malcolm Gladwell spoke about in his book Outliers. As I had written in my review of the book, the concept of 10000 hours can be thought of as “putting fight until you get enough intuition to become stud”. AlphaZero, thanks to its large number of processors, has effectively spent much more than “10000 hours” playing against itself, with its neural network constantly “learning” from the positions faced and the outcomes of the game reached. And this way, it has “gained intuition” over features of the game that lead to wins, giving it an air of “studness”.

The interesting thing to me about AlphaZero’s play is that thanks to its “independent development” (in a way like the Finches of Galapagos), it has not been burdened by human intuition on what is good or bad, and learnt its own heuristics. And along the way, it has come up with a bunch of heuristics that have not commonly be used by human players.

Keeping bishops on the back rank (once the rooks have been connected), for example. A stronger preference for bishops to knights than humans. Suddenly simplifying from a terrifying-looking attack into a winning endgame (machines are generally good at endgames, so this is not that surprising). Temporary pawn and piece sacrifices. And all that.

Thanks to engines such as LeelaZero, we can soon see the results of these learnings being applied to human chess as well. And human chess can only become better!

What Ails Liverpool

So Liverpool FC has had a mixed season so far. They’re second in the Premier League with 36 points from 14 games (only points dropped being draws against ManCity, Chelsea and Arsenal), but are on the verge of going out of the Champions League, having lost all three away games.

Yesterday’s win over Everton was damn lucky, down to a 96th minute freak goal scored by Divock Origi (I’d forgotten he’s still at the club). Last weekend’s 3-0 against Watford wasn’t as comfortable as the scoreline suggested, the scoreline having been opened only midway through the second half. The 2-0 against Fulham before that was similarly a close-fought game.

Of concern to most Liverpool fans has been the form of the starting front three – Mo Salah, Roberto Firmino and Sadio Mane. The trio has missed a host of chances this season, and the team has looked incredibly ineffective in the away losses in the Champions League (the only shot on target in the 2-1 loss against PSG being the penalty that was scored by Milner).

There are positives, of course. The defence has been tightened considerably compared to last season. Liverpool aren’t leaking goals the way they did last season. There have been quite a few clean sheets so far this season. So far there has been no repeat of last season’s situation where they went 4-1 up against ManCity, only to quickly let in two goals and then set up a tense finish.

So my theory is this – each of the front three of Liverpool has an incredibly low strike rate. I don’t know if the xG stat captures this, but the number of chances required by each of Mane, Salah and Firmino before they can convert is rather low. If the average striker converts one in two chances, all of these guys convert one in four (these numbers are pulled out of thin air. I haven’t looked at the statistics).

And even during the “glory days” of last season when Liverpool was scoring like crazy, this low strike rate remained. Instead, what helped then was a massive increase in the number of chances created. The one game I watched live (against Spurs at Wembley), what struck me was the number of chances Salah kept missing. But as the chances kept getting created, he ultimately scored one (Liverpool lost 4-1).

What I suspect is that as Klopp decided to tighten things up at the back this season, the number of chances being created has dropped. And with the low strike rate of each of the front three, this lower number of chances translates into much lower number of goals being scored. If we want last season’s scoring rate, we might also have to accept last season’s concession rate (though this season’s goalie is much much better).

There ain’t no such thing as a free lunch.

Magnus Carlsen’s Endowment

Game 12 of the ongoing Chess World Championship match between Magnus Carlsen and Fabiano Caruana ended in an unexpected draw after only 31 moves, when Carlsen, in a clearly better position and clearly ahead on time, made an unexpected draw offer.

The match will now go into a series of tie-breaks, played with ever-shortening time controls, as the world looks for a winner. Given the players’ historical record, Carlsen is the favourite for the rapid playoffs. And he knows it, since starting in game 11, he seemed to play towards taking it into the playoffs.

Yesterday’s Game 12 was a strange one. It started off with a sharp Sicilian Pelikan like games 8 and 10, and then between moves 15 and 20, players repeated the position twice. Now, the rules of chess state that if the same position appears three times on the board, the game is declared a draw. And there was this move where Caruana had the chance to repeat a position for the third time, thus drawing the game.

He spent nearly half an hour on the move, and at the end of it, he decided to deviate. In other words, no quick draw. My suspicion is that this unnerved Carlsen, who decided to then take a draw at the earliest available opportunity available to him (the rules of the match state that a draw cannot be agreed before move 30. Carlsen made his offer on move 31).

In behavioural economics, Endowment Effect refers to the bias where you place a higher value on something you own than on something you don’t own. This has several implications, all of which can lead to potentially irrational behaviour. The best example is “throwing good money after bad” – if you have made an investment that has lost money, rather than cutting your losses, you double down on the investment in the hope that you’ll recoup your losses.

Another implication is that even when it is rational to sell something you own, you hold on because of the irrationally high value you place on it. The endowment effect also has an impact in pricing and negotiations – you don’t mind that “convenience charge” that the travel aggregator adds on just before you enter your credit card details, for you have already mentally “bought” the ticket, and this convenience charge is only a minor inconvenience. Once you are convinced that you need to do a business deal, you don’t mind if the price moves away from you in small marginal steps – once you’ve made the decision that you have to do the deal, these moves away are only minor, and well within the higher value you’ve placed on the deal.

So where does this fit in to Carlsen’s draw offer yesterday? It was clear from the outset that Carlsen was playing for a draw. When the position was repeated twice, it raised Carlsen’s hope that the game would be a draw, and he assumed that he was getting the draw he wanted. When Caruana refused to repeat position, and did so after a really long think, Carlsen suddenly realised that he wasn’t getting the draw he thought he was getting.

It was as if the draw was Carlsen’s and it had now been taken away from him, so now he needed to somehow get it. Carlsen played well after that, and Caruana played badly, and the engines clearly showed that Carlsen had an advantage when the game crossed move 30.

However, having “accepted” a draw earlier in the game (by repeating moves twice), Carlsen wanted to lock in the draw, rather than play on in an inferior mental state and risk a loss (which would also result in the loss of the Championship). And hence, despite the significantly superior position, he made the draw offer, which Caruana was only happy to accept (given his worse situation).

 

 

Hypothesis Testing in Monte Carlo

I find it incredible, and not in a good way, that I took fourteen years to make the connection between two concepts I learnt barely a year apart.

In August-September 2003, I was auditing an advanced (graduate) course on Advanced Algorithms, where we learnt about randomised algorithms (I soon stopped auditing since the maths got heavy). And one important class of randomised algorithms is what is known as “Monte Carlo Algorithms”. Not to be confused with Monte Carlo Simulations, these are randomised algorithms that give a one way result. So, using the most prominent example of such an algorithm, you can ask “is this number prime?” and the answer to that can be either “maybe” or “no”.

The randomised algorithm can never conclusively answer “yes” to the primality question. If the algorithm can find a prime factor of the number, it answers “no” (this is conclusive). Otherwise it returns “maybe”. So the way you “conclude” that a number is prime is by running the test a large number of times. Each run reduces the probability that it is a “no” (since they’re all independent evaluations of “maybe”), and when the probability of “no” is low enough, you “think” it’s a “yes”. You might like this old post of mine regarding Monte Carlo algorithms in the context of romantic relationships.

Less than a year later, in July 2004, as part of a basic course in statistics, I learnt about hypothesis testing. Now (I’m kicking myself for failing to see the similarity then), the main principle of hypothesis testing is that you can never “accept a hypothesis”. You either reject a hypothesis or “fail to reject” it.  And if you fail to reject a hypothesis with a certain high probability (basically with more data, which implies more independent evaluations that don’t say “reject”), you will start thinking about “accept”.

Basically hypothesis testing is a one-sided  test, where you are trying to reject a hypothesis. And not being able to reject a hypothesis doesn’t mean we necessarily accept it – there is still the chance of going wrong if we were to accept it (this is where we get into messy territory such as p-values). And this is exactly like Monte Carlo algorithms – one-sided algorithms where we can only conclusively take a decision one way.

So I was thinking of these concepts when I came across this headline in ESPNCricinfo yesterday that said “Rahul Johri not found guilty” (not linking since Cricinfo has since changed the headline). The choice, or rather ordering, of words was interesting. “Not found guilty”, it said, rather than the usual “found not guilty”.

This is again a concept of one-sided testing. An investigation can either find someone guilty or it fails to do so, and the heading in this case suggested that the latter had happened. And as a deliberate choice, it became apparent why the headline was constructed this way – later it emerged that the decision to clear Rahul Johri of sexual harassment charges was a contentious one.

In most cases, when someone is “found not guilty” following an investigation, it usually suggests that the evidence on hand was enough to say that the chance of the person being guilty was rather low. The phrase “not found guilty”, on the other hand, says that one test failed to reject the hypothesis, but it didn’t have sufficient confidence to clear the person of guilt.

So due credit to the Cricinfo copywriters, and due debit to the product managers for later changing the headline rather than putting a fresh follow-up piece.

PS: The discussion following my tweet on the topic threw up one very interesting insight – such as Scotland having had a “not proven” verdict in the past for such cases (you can trust DD for coming up with such gems).