Review: The Numbers Game: Why Everything You Know About Football Is Wrong

By now, you’ve probably all seen the video; Harry Redknapp is forced to defend himself against an angry fan over his supposed favouritism of 17-year-old Frank Lampard – his nephew – over other, supposedly more talented graduates of the academy system. When Redknapp argues that Lampard is better than those players, the angry fan disagrees, to which Redknapp replies that football “is a game of opinions. You’ve got a right to your opinion and I’ve got a right to my opinion.”

For a long time, this is how football operated – and still does – largely based on instinct and intuition. Over time, this has created accepted truths in the game, truths that only now we find out aren’t entirely correct. For example, that a team is most vulnerable after scoring (in fact, this is the moment they are less likely to concede); that more shots on target means better a chance of winning (actually it’s true only 50-58% of the time) and that the manager has a big influence on where their team will finish in the league (only 15%).

The revelations are probably not groundbreaking, although that’s what Chris Anderson and David Sally promise in The Numbers Game: Why Everything You Know About Football Is Wrong. But they are certainly thought-provoking and highlight the edge, should you use it properly, that data can give teams.

The book is littered with some great examples. Such as how Manchester City adjusted the way they took corner-kicks to win the Premier League in 2011/12, and appropriately, it was a header by Vincent Kompany which confirmed the title. The next season, Manchester United did the same thing, profiting from Robin van Persie’s in-swinging deliveries to score the most goals from set-pieces in the way to the championship. And how Roberto Martinez went against the grain to miraculously keep Wigan Athletic in the Premier League. But these are contradicted later in the book, which only goes to show why the interpretation data is an art rather than a science. Football is a fluid game and as such, actions cannot be isolated and for teams to get an edge, they will have to learn to master it. Wigan went down the next season because they didn’t have the quality to win games, often passing for passing sakes, while relying massively on Shaun Maloney’s free-kicks. And that actually, corner-kicks are largely wasteful as only 0.02 of the total corners taken resulting in goals. (Actually, the numbers are similar to the research I did on open play crosses, and later by Jan Vecer, which would have been a better topic).

The best managers and teams realise that data is one tool among many which can back up the way you think about the game. That’s what Arsène  Wenger does and actually, many of the revelations in The Numbers Game make you wonder if the Frenchman actually ghost-wrote the book himself!

Of course, Wenger was one of the first to embrace statistics. As coach of Monaco in the late 1980’s, he would use a program developed by a friend, called Top Score, to judge players (the program would assign points to players depending on the actions they performed to give a final score). Nowadays, Wenger uses data to validate the way he thinks about the game. “Technical superiority can be measured,” he said in 2008 for Total Youth Football Magazine. “If I know that the passing ability of a player is averaging 3.2 seconds to receive the ball and pass it, and suddenly he goes up to 4.5, I can say to him, ‘Listen, you keep the ball too much, we need you to pass it quicker.’ If he says ‘no’, I can say look at the last three games – 2.9 seconds, 3.1, 3.2, 4.5. He’ll say, ‘People around me don’t move so much!’ But you have the statistics there to back you up too.”

One can envisage a similar scenario from last season where those numbers might have been of use. It concerned Aaron Ramsey and his form in the middle of the season which was so poor; it was hard to find a place for him in the team. But an injury to Mikel Arteta transformed his season, giving him a chance in a new defensive-midfield position. This was a great risk by Wenger because Arsenal don’t usually win without Arteta (their success rate is 23% when he doesn’t play) and Ramsey’s confidence was so low he couldn’t surely replicate Arteta’s smooth passing. But Wenger realised the psychological effect that getting more touches of the ball could have on Ramsey and sure enough, his confidence increased. From losing the ball through hesitation, miscontrol or dispossession 4.8 times a game, it decreased to 2.7 times per match after the 5-1 win over West Ham United in January. If the passing speed figures were readily available to us, surely they’d show an improvement. Nevertheless, Ramsey indicates that that was the case: “I’m feeling good. My confidence is coming back and I’m getting stuck in more, winning more balls back and doing more with the ball as well, moving it around quickly,” he said after the West Ham win.

In the last season too, Arsenal began to learn mastering their own luck.In The Numbers Game, Anderson and Sally reveal that 50% of a match is down to luck. The other 50% means that Arsenal already have won half of the match through their superiority but random variation can swing it the other way or towards their favour. Certainly for the first-half of the season, Arsenal’s’ play was riddled with so many mistakes that it undermined their their ability to win matches, and it wasn’t until they rectified their defensive shape that they saved their season. Indeed, the extra focus on the defence concurs with what was said at the end ofThe Numbers Game: that keeping a clean sheet helps a team more than scoring lots of goals does. “That’s where we’ve improved the most,” Wenger told Arsenal Player. “It’s very important for the confidence of the team that we have such a [defensive] stability. As I said many times, we are an offensive team, but you are only a good offensive team if you have a good defensive stability. In the last two months that was much better.”

Data might help Wenger make informed decisions on whom to purchase in the transfer window. But as The Numbers Game suggests, it’s often better to improve your worst player than to buy a superstar.” In that case, the fans have always been right in regards to their belligerent stance on players which they perceive as being “deadwood.” However, it’s not as if Wenger is in disagreement with them. He was quick to discard Andre Santos, while Sebastian Squillaci, Marouane Chamakh, Andriy Arshavin and Denilson found that they were quickly cast aside (but harder to sell) when performances deteriorated or they didn’t fit the system. And he’s always maintained, rightly so, that he would not simply buy just to make up the numbers – often to the chagrin of supporters paradoxically – but only once a player proves he has the “super-quality” to improve the squad.

One such player who fits the bill is Gonzalo Higuain, and his arrival is notable because it’ll change the way Arsenal play. Firstly, it means they have the goalscorer they’ve desperately been looking for since Robin van Persie left the club. Last season, they tried to compensate by getting goals all over the pitch. It worked – to a degree but the team fell desperately short when looking for a game-changer. Last season for Real Madrid, Higuain goals won more points than any other Arsenal player. On it’s own that doesn’t mean he’s the right choice. In The Numbers Game, they suggest Chelsea should have signed Darren Bent instead of Fernando Torres. That’s only half-correct; Torres has blundered but Bent has shown he hasn’t got the attributes that Chelsea required. Higuain, though, improves Arsenal because his style (through his ability to stretch defences thus creating more space for the team) is one that could make Arsenal’s system. However, that’s an area that can’t easily be quantified by stats. We just have to trust Arsène Wenger’s judgement on it.

NB: There are a couple more interesting points that I could have added. For example, how Wenger is correct in rigidly sticking to his belief that the best time to make a substitution is on the 70th minute mark to try and win a game (although as The Numbers Game points out, if Arsenal are losing, he should consider making changes as early as the 58th minute). And more so when he removes certain players after a certain period all the time because their returns start diminishing rapidly (as he did for Dennis Bergkamp later in his career).

Also another interesting stat: Olivier Giroud has the worst pass accuracy of any outfield player in the Arsenal side (64%) and even lower than the goalkeeper, Wojciech Szczeszny (66%). As Sally and Anderson ascertain, football is game of turnovers and the ball changes sides 380 times per match (or 190 times per side). Arsenal’s average is 175 times but if Olivier Giroud fails to make them stick, then it’s preventing further attacking plays from developing. Perhaps, with the signing of Higuain, Wenger doesn’t really feel the need to have a striker in the build-up. Which is very much unlike Wenger sides in the past.


Exploring the Chance Quality Index: Why more chances doesn’t necessarily mean more goals

Karthik (KV) seeks to establish why more chances don’t necessarily mean more goals.

How do you win a football game? The simplest answer would be to score more goals than the other team. So, how do you score more goals than the other team? Create more chances than the other team and you are likely to score more than them. How accurate is that statement? Not very accurate, in fact. What we can conclude with certainty is that, the team that creates chances of higher quality is likely to score more compared to the other team.

At every press conference that Arsene Wenger has had to attend in the past few years, he would respond to the customary question on possible transfers by stating that he always opts for ‘quality over quantity.’ Signing a player of top quality is more important than signing 3-4 players just to fill the void. We can apply the same principle to chances created. The probability of scoring from a chance of very high quality is more compared to scoring from three chances of mediocre quality. For better clarity, OPTA describes a chance as ‘assists plus key passes.’ Is it possible to measure the quality of a chance? Yes, that is what I have tried to do in the following lines.

The factors affecting the quality of a chance are:

  1. Distance from the goal
  2. The angle by which the goal is visible.
  3. The number of opponent players surrounding the player with the ball.

Based on this, we can say that Chance Quality is:

  1. Inversely proportional to the distance from goal.
  2. Inversely proportional to the number of opponent players surrounding the player taking the shot.
  3. Inversely proportional to angle A as shown.


C.Q.I = cos(A)/D*P

Where, A is the angle between the line joining the centres of the two goals and the line joining the centre of the goal to the point from where the shot is taken. D is the distance between the centre of the goal and the point from where the shot is taken. P is the number of opposition players close to the player when the shot was taken. It is to be noted that Cos of the angle A is taken because, due to the property of the Cos function, as A increases, Cos(A) decreases and that is exactly what we need.

The Ade”Can’t hit a barn door”bayor problem:

If you rewind a few seasons back to the 2008-09 season, you would realize that Arsenal lost 6 games, drew 12 and finished fourth. Teams that we lost to included Fulham, Hull City, Aston Villa and Manchester City. All of them won by a one goal margin (except for Man City) and all the games were dominated by Arsenal, in regards to possession. The number of shots taken by Arsenal also outnumbered the other teams, but the other teams just sat deep and chose the right moment to counter attack and create chances which had a high C.Q.I rating (statistics have shown that 43% of the chances created from transitions get converted to goals). At that time, everyone were busy criticizing the finishing of the Arsenal strikers like Emmanuel Adebayor and the inability of our defensive midfielders to stop perform better and not concede(Alex Song and Denilson), when the actual problem was that Arsenal lacked the creative firepower to breakdown teams and create high quality chances. A study on the recently concluded Barca-Milan game showed that, while Barca dominated possession(65%) and had 18 shots on target compared to Milan’s six, Milan had the best opportunity to score in the game, with a shot that had a C.Q.I rating of 0.08(which looks like a small number, but is actually higher than other shots).

The only shot off target by Milan proved pivotal – it was the best chance of the game, missed by Robinho with no defenders in front.

How can the C.Q.I be of help?

A higher C.Q.I pass means a better chance of scoring. So, players who create more number of C.Q.I passes are extremely valuable to the team. For example, in the Barca-Milan game, Xavi, Messi and Dani Alves created chances with high C.Q.I rating and they were also the best players on the pitch. It can also be used to analyse games and bring about changes. Iniesta wasn’t creating much, so Rodrigo Tello came on and immediately created a chance with a fairly high C.Q.I rating. It can even help develop tactics. For instance, we know that counter attacks tend to result in goals 43% of the time, so it makes sense to leave a player that creates high C.Q.I chances high up the pitch (like Messi). ‘The Invincibles’ Arsenal team had great players like Dennis Bergkamp, Thierry Henry and Robert Pires who created chances with high C.Q.I and won games playing counter attacking football.


So often coaches have bemoaned the loss of a game which they felt they had deserved but succumbed because the other team just purely finished their chances. It happened last night with Barcelona claiming they should have won when in fact, they failed to create a better chance than Milan which was fired over by Robinho early on. Indeed, one article after the game questioned why Robinho regularly gets picked even though he hits the target with 44% of his shots and misses some great chances to boot (Ibrahimovic has 60%;  El Shaarawy’s, Pato 52%). (As it turned out, the author concluded that goals are not everything as Robinho causes trouble with his movement – and that’s what creates chances for Milan).

While in it’s infancy (give us the funding!), Chance Quality Index has it’s merits if anything to challenge the established conceptions of chances and the likelihood of winning a game. Indeed, it was Wenger who once remarked, “the measure of football is the ratio of chances created to chances conceded” and that he concluded means Arsenal deserve to win the game as they have dominated. This is surely dependent on the quality of chances you create, is it not?

If that is true, however, then Arsenal should follow the route of Barcelona who believe possession is “nine-tenths” of the game. That should ensure Arsenal keep down the number of shots they concede which is currently at 10 per game in the league (and consequently, help them press better) – Barcelona’s is 7 despite both teams creating on average 17 shots per game. But that is patently not Arséne Wenger’s style as he says he’d rather a player who takes in a risk in their passing in the final third than play it safe – for Barcelona, it’s all about the quality of the chance. Wenger prefers urgency and while we are seeing a better drilled Arsenal this part of the season, the fact that they have gone down in half of the games recently, shows there’s gaps in the system.

It’s unfortunate Milan-Barcelona yielded no goals; it seemed the perfect encounter to experiment CQI because it carried with it, the old adage that possession (for Barcelona) should equal chances and consequently, a win – but that’s not necessarily the case. In fact, good chances are harder to come by when defences defend deep as Milan did because the attacking team is hindered by a lack of time and space. Milan on the other hand, had less chances but the best one on the night as Robinho fired over. Had the chance fell to Ibrahimovic, it might have gone in. That’s one of the issues with C.Q.I; it’s still subjective as much as it tries to quantify the art of the chance. Because some players are much more composed in front of goal. Take for instance, Thierry Henry’s goal against Leeds in the FA Cup; for some players, the chance may be harder due to the angle, the defender haring down on Henry’s back and not to mention the technique. But such was the familiarity of him in that position, it was almost a 10 out of 10 chance. It’s notable that in the game against Milan, coincidentally enough, Wenger altered the system so Henry could get into such situations. But it’s probably not the varying expertise of the player taking the shot that’s most important with the Henry chance; sometimes the angled shot IS the optimal way to score.

Back to the goalless draw at the San Siro, Pep Guardiola might have argued that his side deserved to win but Milan might have been the most aggrieved as a shot in the third minute flew over. It proved pivotal.

Denilson has risen from the shadows to take centre stage

Denilson’s performances in the centre of midfield have largely gone unnoticed with the stats showing the Brazilian as the Gunners’ top performer.

At 16th place, he’s Arsenal’s best player this season according to the Actim Index stats which ranks players according their contribution to the team’s success. The more direct forward play one is involved in, the higher he ranks. Not just that, he’s the best interceptor in the the Premier League, the most accurate passer, fifth best tackler and the fourth most fouled player (OPTA stats). But while he’s a great number cruncher, Denilson has yet to get the recognition he deserves because his style is less crowd pleasing than his other teammate in the same position, Alex Song.

The Actim Index and Opta stats only includes actions that can be measured objectively therefore positioning, marking and balance cannot be quantified. Which is just as well as Denilson would surely have been placed much higher. An invisible wall in every sense, the Brazilian combines sound positional play with efficiency, linking up play whether sideways, forwards or backwards and covers as high a distance as any other Arsenal player.

Of course his job was made more difficult after the Gunners made an inconsistent start to the season. It could be described as a season of two halves; the first of which saw Arsenal looking to strike the right balance in their play after key personnel went missing, primarily playing in a 4-4-2. As a result Denilson was often left exposed to do most of the sweeping up and as Arsenal were not as strong in possession as last season, the ball was likely to come back more.

The second half was played in a 4-2-3-1 as Arsene Wenger looked to make up for the deficiencies of the first half, now trying to get the balance between attack and defence and focusing on getting the ball forward quicker. Denilson’s stats were just as impressive and even with an extra midfielder still assumed the main holding role.

Overall, he has managed on average 59 accurate passes a game this season and Song just 38 while Flamini last year made 47. Interceptions are counted as 146 (on average 4 a game) for the full season, 51 for Song (average 2.5 a game) and just 57 for Flamini (average 2 a game). On average Song made more tackles than the other two and the Cameroon midfielder showed why Wenger prefers him in central defence. Song had performed better against the more direct clubs such as Wigan and Liverpool as he is a player who is more comfortable at reading the play in front of him rather than around. Against the ‘weaker’ clubs (those who Arsenal played during their unbeaten run), Song played just as decently but has always assumed a supporting role to Denilson and Fabregas/Nasri.

The two players can be used where the situation best suits them; Wenger deployed Song in the second leg against Villarreal as he wanted the side to pressure higher up the pitch and win the ball back quicker. At Chelsea however, Song failed to impress. Although the tracking back in front of him wasn’t great, Denilson made nearly as much passes as him and twice as many interceptions in the 25 minutes he was on the pitch. The Brazilian has excelled in more technical games, preferring to use his his intelligence to nip the ball away and ensure the ball is always moving.

Matthieu Flamini’s statistics paint a bigger picture of the differences between this season’s Arsenal and last season’s. That season the link up play, movement and balance was better with the ball likely to stay in the opposition’s half more. With Hleb and Rosicky available for much of the season Arsenal were able to play their passing game with greater effect. Also just by a bit, Fabregas’ discipline was better as he went about picking the ball up deeper while Flamini’s role was about keeping the shape if the Gunners did lose the ball. This season, Denilson has had to contend with an inconsistent side hampered by injuries, the lack of team cohesion in defending and without such creative midfielders who owe much to the Arsenal style.

Arsene Wenger’s main priority next season must be about getting his side to become the expansive, ball-hogging side they were in previous years and the role of the defensive midfielder cannot be crucial enough. Denilson has come on leaps and bounds and although he still has much to learn, has shown with his performances that the position is in safe hands.

2008/9 Denilson (3,074 minutes)

Tackles won (includes aerial): 148 (average 4 per game)
Tackles lost: 81 (average 2 per game)
Pass interceptions: 146 (average 4 per game)
Accurate passes: 2,009 (average 59 per game)
Bad passes: 238 (average 7 per game)
Assists: 7
Goals: 3

2008/9 Song  (1,741 minutes in midfield)
Tackles won: 104 (average 5 per game)
Tackles lost: 50 (average 2.5 per game)
Pass interceptions: 51 (average 2.5 per game)
Accurate passes: 742 (average 38.4 per game)
Bad passes: 90 (average 5 per game)
Assists: 0
Goals: 1

2007/8 Flamini (2,665 minutes)

Tackles won: 102 (average 3.4 per game)
Tackles lost: 56 (average 1.9 per game)
Pass interceptions: 57 (average 1.9 per game)
Accurate passes: 1,321 (average 44.6 per game)
Bad passes: 100 (average 3.4 per game)
Assists 2
Goals 1