The numbers game is a book about the use of statistics in analyzing football (soccer). The book sits in an uncomfortable middle ground between Moneyball and a technical manual. There is no story thread as in Moneyball, but it is not detailed enough to be used as a manual for performing your own analysis. The book examines different aspects of the game in each chapter. Chapters loosely build on ideas presented in previous sections. I would say that this book has helped me understand football better, but what I found most interesting are the lessons that can be directly applied to performance analysis of any organization. I will divide this review into two sections: what I learned about football and lessons for managers.
There are many persistent myths in football and a tendency to do things the way things have always been done.
There has been an explosion in football analytics since the 1990s. There is detailed data available on all top league matches. Data includes everything from final scores, ball possession, the number of passes each team made, the number of successive passes before losing possession, distance covered by each player, and so on.
Data analysis can be tricky. You can confound cause with effect. Does attempting many goal shots make a team good, or is it that good teams create more opportunities to attempt goal shots?
Football is more random than other team sports. The favorite team only wins slightly over 50% of the time. In basketball, for example, the percentage is over 65%.
Goals scored and goals avoided are nearly as important to match results. It is easy to assess the value of strikers because their output (goals scored) is easy to measure. Goals avoided by a good defender, on the other hand, have to be inferred from statistical data, and are not as obvious. This means that defenders on average may be undervalued. It may be more cost-effective for a team that wants to increase its performance to hire better defenders. However, it is not easy to identify the best defenders. The best defenders are not the ones that tackle more, but the ones that through anticipation and good placement on the field do not need to tackle. Counterintuitively, the defenders that seem to do less may be the ones that are most effective.
The tiki-taka style is common in modern football. Despite this, the number of successfully completed passes tends to be very low. A team most often loses the ball after the first pass. The probability of succcessfully completing a string of passes goes down with each additional pass.
There is no best tactic overall. A specific tactic works best against a specific opponent. The authors conclude that, in order to be successful, teams have to either be very effective or be innovative.
The chance of scoring after a corner is not higher than scoring in normal play. Corners have no special value and it may be more effective to take a short corner than to try a long pass.
Player budget explains 81-89% of a team's performance in a 10-year league average. There is a strong correlation between better players (read more expensive) and results, but it is the worst player on a team that holds the whole team down, rather than the best player lifting the team up. A football team is only as good as its weakest link. A team composed of consistently good players, with little difference in skill between the best and the worst, will perform better than a team composed of a few super-stars and some mediocre players. Related to this, data shows that decentralized playing networks yield better results than passing to the same players all the time. In other words, it is better to have many passing options than to target the same striker repeatedly.
A professional player runs on average 12km every match, but only has the ball for fewer than five minutes.
A football team is just a particular kind of organization. If football teams can benefit from analyzing game data, so can other kinds of organizations. The insight that what you cannot see is important (goals avoided) is relevant for companies and other organizations as well. For example, a police force that prevents crime may be more effective than one that makes many arrests. But arrests are easy to measure, while crimes not committed are not.
Managers may make decisions based on gut instinct or do things a certain way because that is how they always have been done, just as football teams sometimes do, but collecting and analyzing data may provide a better path to improveing performance.
The final chapters of the book handle about teamwork and management, which can be applied directly.
The authors discuss a paper by Hamilton, Nickerson, and Owan on the introduction of teamwork at a garment factory operated by the Koret Company. The company changed worker compensation between 1995-1997. Before the change, each worker sewed a part of a garment and was paid per piece. After the change, workers formed teams and teams were paid per completed garment. What the authors found is that teams were 14% more productive than the sum of each member working individually. They speculate that more skilled workers helped improve the ability of less skilled ones.
Something similar has been observed in football teams. A superstar player can improve the rest of the team by setting an example. Excellent players with high standards and a strong work ethic serve as an inspiration for younger or less talented players on the team and do improve team performance. The effect disappears when superstars behave like prima donnas that demand special treatment and privileges.
The same may be true in companies. If a very productive employee is a jerk, rarely does his extra output compensate for the damage he does to the team. On the other hand, exceptional employees who are willing to share their knowledge and mentor others help create strong teams.
Another cool piece of research discussed in the book is the Köhler effect. Köhler asked subjects to pull a rope with a weight for as long as they could. He repeated the experiment, doubling the weight and asking pairs of subjects to hold it for as long as they could. What he observed was that when people worked in pairs, they held on longer than when they did the experiment alone. Not letting others down is a powerful motivation to perform better. If your contribution to the team is visible, and player contribution very much is, you will strive to do your absolute best not to disappoint your colleagues.
To assess whether managers matter at all, the authors turned to a Danish study on the impact of CEOs on performance. Bennedsen, Pérez-González, and Wolfenzon used data on over 1,000 companies. They found that CEO death reduces company profits by 28% and death in the CEO's family, which presumably keeps the CEO distracted, reduces profits by 16%.
Managers who have been good players themselves are statistically better. The difference is larger when leading lower-paid and less talented players. Managers help their players perform better and aid in their development.
In the corporate world, there is sometimes a belief that management is independent of the industry, that management performance is portable. Data from football managers do not seem to support this belief. The solution for companies is to promote from within or at least have a plan to see how outsiders fit in.
Given the random nature of football results, it is expected that good teams will have losing streaks just by chance. Over time, the losing streak will give way to a more typical series of results. This is a statistical phenomenon called reversion to the mean. Extreme observations tend to be followed by observations closer to the average. Remember that the favorite team has a probability of about 55% of winning. A team may lose a few matches just by chance, but over time, it is increasingly likely to accumulate a victory average that reflects its true quality.
Football clubs tend to fire their managers if the team has a bad streak. When a new manager arrives, the team is very likely to have better performance, and the improvement will be credited to the new manager. In reality, the team may be reverting to the mean, and would have done so under the old manager as well.
Managers do matter, but football results (and company performance) have some randomness. If a new manager, brought in to end a bad spell, yells at the players, and performance subsequently improves, one may conclude that management by intimidation works, when really all that happened was reversion to the mean. Any other approach would have been just as effective. The authors provide the example of a flight instructor who said: "When a student does well and I praise him, he performs worse on the next lesson. On the other hand, when I chide a student who did poorly, he does better the next time. Therfore, be hard on your students if you want them to improve". This is obviously nonsense. What the instructor was seeing was reversion to the mean, and neither the praising nor the scolding had any effect.
The authors not only lay out a framework for understanding football, but were brave enough to write a full chapter with forecasts for the following decade. Since the book was published in 2014, we can check how well they did.
They forecast that there would be about 1,000 goals scored in the Premiership in both 2014 and 2024. In the 2013-14 season there were 1,052 goals across 380 matches. In the 2023-24 season there were 1,246 across the same number of matches.
They predicted that the salary gap between strikers and defenders would narrow. I found data on Premier League payrolls per position, and the trend is the opposite. During the 2013-14 season, all clubs combined spent £297 million on defense and £300 million on forward. In 2023-24, they spent £639 million and £723 million respectively. It is possible that these payroll figures reflect fewer defenders and more strikers, but I don't think so. The increase in the number of goals per season suggests that clubs are investing more in strikers and less in defenders.
Other forecasts were more vaguely worded, or difficult for me to verify. They hedged their bets when they forecast both that there would be an increase in analytics in football and that clubs could continue to be successful without analytics, just by outspending their rivals.
The book is interesting and thought provoking, but given how the predictions have fared, either football markets are not very efficient or the authors were wrong.
Last updated: 2025-09-01