The Numbers Game is a challenge. This is a book about football, surely “the beautiful game” – the antithesis of the numbers game. The essential proposition of this book is that the best way to understand winning football is analytically, using the science of numbers. I’m an economist, and co-author of Soccernomics, so this book could almost have been written for me. I couldn’t wait to get hold of a copy (I wonder if this might not appear on the publisher’s blurb at some point – I don’t mind if it does) and skim read it on the afternoon it arrived.
I like watching football, mostly good football, but I’m fascinated by what it is about the game that can be understood systematically, and how much of it is purely random. Some purists would like the game to remain forever a random event, unanalyzable. I certainly wouldn’t ever want to see randomness reduced to zero, but there is excitement in the idea that randomness can be attenuated (at least there is, if like me, you like numbers).
I think of this book as a link in a chain. I think the chain starts with Fever Pitch, which is the first book to seriously deal with what it means to be fan (reading this was when I realized I would never be a true fan). The next step is Football Against the Enemy, which dealt with the fan as an anthropological phenomenon. Then comes Inverting the Pyramid, the first book to properly dissect football tactics. I’d like to think that Soccernomics is the next link, in that we showed how data and economic theory can be used to understand what we see.
Whereas Simon and I ranged far and wide Chris Anderson and David Sally have focused narrowly on winning strategy. What is the link between Fever Pitch and The Numbers Game? Football is both a participation and spectator sport. Many of us interact at both levels, but almost all of us are only spectators when it comes to the highest levels. What these books do is peel layers from the onion, to enable us to imagine more fully what it is like to be part of the event. To turn us from spectators into participants.
[I don’t mean to say that there have not been other great football books in the last two decades, obviously there have, and one might find a place for some of these in the progression, but I don’t think that would detract from my basic point].
The following is a review of the book chapter by chapter. To be honest I wanted to decide what I thought their message is and what I thought- so I’m really just sharing these thoughts (which is the great thing about writing a blog, I don’t have to have a bigger point). There’s more to the book than is described in the review, lots of interesting stuff, so this review is in no way meant to substitute for the full experience.
Football statistics have been around since the 1950s, but unlike sports like baseball, team managers have proved remarkably resistant to using stats to develop winning strategies. Like we did in Soccernomics, Anderson and Sally rely heavily on Moneyball to make the case for the use of statistical analysis. But the truth is that baseball has always been a very stats oriented sport – a more obvious question is why cricket, which ought to yield just as easily to the ardour of the statistician, has only started to do so in recent years. The authors here point out that big data is now available to analyse the minutiae of football, but it’s time to get smart about how to analyze that data. Right now football clubs do not hire professors from Cornell or Michigan to help them- surely this anomaly has got to end?
This chapter explains that randomness is more important in football than almost any other sport. The reason is that it is such a low scoring game. Given that single goal so often decides a game, a weak team only needs to get lucky for a few seconds in ninety minutes to pull off an upset. The question then is “how random is football?”- the authors conclude it is 50-50. The claim follows from the finding that teams which shoot more often win roughly 50% of the time. I’m not sure I grasp this entirely (after all, maybe the team that shot less was better prepared when it did shoot, and therefore not lucky if it happened to win), but I see the general idea.
The previous chapter introduced the statistical model which best fits goalscoring (Poisson), this chapter shows that however different leagues might be, they are all subject to common trends. Notably, that goalscoring is becoming rarer over time (there’s an excellent book from a few years back by Loek Groot on this subject). The simple explanation is that defence have improved faster than attack. I’m not sure why this is presented as surprising –anyone watching old videos notices how much space was left to attackers, who are closed down far more quickly nowadays. Some comparative perspective might be useful here. For example, baseball scores have a similar trend over time, but American football and basketball score, I think, haven’t. Underlying this is an interesting question about the distribution of talent. There are more teams and more players over time, so according to the talent compression hypothesis (attributable to Stephen Jay Gould who talked about its effect on baseball records) talent is being drawn from a larger and larger population (what kid doesn’t want to be a professional footballer nowadays?), and so the difference in talent at the top end is being compressed, making it harder to achieve exceptional feats (like scoring a goal).
This is a rather short chapter but makes a very neat point. Goals are very valuable, but the goal that wins the game is the most valuable of all. The authors calculate the most valuable goals by order in which they are scored. It turns out that the second goal on average produces the biggest addition to points, on average. They then produce a league table of goals scored, when each goal scored is valued according to its rank, and therefore the extra points it contributed to the team’s season. Cute.
This chapter argues that success is dependent on defence as well as offence (I suspect this American classification will become commonplace in soccer soon enough). However, cognitive biases (Wikipedia has a great page on these, well worth a read if you want to understand the many different ways your brain can fool you), lead us to focus more on offence than defence. This means that we can undervalue defenders. I think this might reflect the dichotomy between fan and practitioner; I’m sure this observation is true for fans, but less sure it’s true for managers and clubs.
Chapters 5 & 6
These two really could be merged to one. The authors focus on the issue of possession. Teams that have more possession tend to win more often. But passing along the back four for 90 minutes will not win you games. This leads to the idea that the right kind of possession will win you games. Charles Reep, the founder of football statistics, developed the idea that possession in the last third was what mattered, and so was born the long ball game. This works pretty well as most levels of the game but, as long suffering England fans know, not at the highest levels. However, the authors resurrect a version of Reep which is based on managing possession. The problem with the long ball game is that you allow the other team to retain the ball for too long. Stoke have found the answer to the problem; even if they are not able to do much with the possession they get, they get more points from the limited possession they have compared to similar teams. They achieve this by slowing down the game, reducing the number of minutes that the ball is in play, and so giving the opposition fewer opportunities to use their superior ball skills.
This brief chapter is really just a reprise of the book’s theme, relying on the example of American football: data analysis can improve performance- football (soccer) managers should try it.
Chapters 8 & 9
These chapters are best of the book, and unlike most of the rest of the book, which reports the research of others, they are based on the authors original research. They also make me feel a bit guilty. Andrew Scott is a brilliant economist at London Business School and an old friend (for years we used to kick each other on a grim 5-a-side court under London’s Westway). Three or four years ago we had lunch and I tried to interest him in some research ideas. He objected to some of my ideas, which tended to value the contribution of each player separately, rather than seeing it as a team game. “O-Ring Theory”, he said, that’s how you should think about it. I went back to the office and looked up the relevant paper and realized he was right: O-ring theory is simply the observation that in many situations you are no better than your weakest link. Had I taken him up on his observation we could have written a brilliant paper- now poor old Andrew will have to defend the position that he thought of it first.
This really is a great way to use data. Anderson and Sally show that not only are you vulnerable to your weakest link, but that this dictates the structure of football teams- the best tend to play with the best. What’s the point of having Messi on your team if your weakest link is a donkey? This raises a puzzle which still bothers me. Another implication is that player’s value is not independent of his team-mates- the whole is greater than the sum of the parts. So why don’t we see players sell themselves as (more valuable) teams, rather than always selling themselves as individuals?
Chapters 10 & 11
I think these chapters should have been reversed. Chapter 11 says that firing a manager doesn’t achieve anything even though results improve. This point has been made in the academic literature for a while now. The reason is that a bad run of results usually reflect bad luck – which will usually end whether you replace the manager or not. The authors want to argue that clubs should have more faith in their managers- but of course that all depends on whether you can tell the good from the bad.
That is the subject of chapter 10, which is a rebuttal of the argument in Soccernomics that generally managers don’t add very much. Since I have a personal stake in this I’m going to write a separate blog on the issue. All I’ll say here is that I don’t think the authors have especially good evidence that managers do make a difference, although they might right in thinking that they do. It’s a grey area.
The authors conclude with some predictions about what will happen in the world of football and data. I won’t go into these predictions here, so at least Chris and David won’t complain that I gave everything away.
What I liked about this book, and what makes it an important step in the development of the popular football literature, is that it the first book devoted exclusively to the proposition that statistical analysis can help us understand who wins football games. It is eclectic in its willingness to draw on different sources and different methods of analysis.
I think the main issue I have with the book, and with the growing field of sports analytics, is this eclecticism. Call me an old fashioned out-of-date economist (how much worse can it get?), but I like a good theory. Theory brings order to the data, and eclecticism risks a tendency toward the position that the only thing that matters is what works (which of course most sports managers would agree with). The problem with espousing what works without a theory is that the data has a nasty habit of changing its mind.
I think there is a theory that can explain what happens in football, and that is game theory. Game theory suggests that what your strategy in a match should be determined by what you believe your opponent will do. I think this is what the very best managers do. Thus the outcome of any game should really be considered as the combination of two sets of choices. I think Anderson and Sally know this, but too often it sounds as if they think strategy can be determined independently of your opponent.
There are very few examples of successfully using game theory to approach strategy in sports. The authors cite a famous example from American football (Romer on fourth downs) and in Soccernomics we deal extensively with Ignacio Palacios-Huerta’s powerful research on penalty taking. I think the next link in the chain will be the one that uses theory more rigorously to support the data analysis. Who knows, maybe this will be Anderson and Sally’s next book.