What is analysis?

Many people analyse football matches. They do that for many different reasons. If you write a football analysis for entertainment than anything you write goes. But if you write to explain football or even better yet, a pro football club is using your analyses for match preparation or training programs to improve players, then it matters what you write. For one your analysis need to be correct. An incorrect analysis can’t explain how football works. Even worse an incorrect analysis can lead to the unnecessary loss of matches. An incorrect analysis can mean that the training staff give players the wrong suggestions for improvement. Another point is that a description is not an analysis. For that reason it is good to discriminate between match reports like the Guardian has, tactical match reports like Between The Post has and match analyses like Spielverlagerung has.

A good analysis also explains why it is unlikely that the outcome is due to happenstance. For every draw and every match with a goal difference of 1, it is hard to explain why the match ended in this result rather than another.

Here is an example of how to argue beyond happenstance:

“As isolated incidents, these can be forgiven as no team is 100% perfect defensively and all the defensive organisation in the world cannot always negate the attacking side. But for Borussia Dortmund these aren’t isolated incidents. Of their five goals conceded so far this season, three now have come via corners. Last season BVB conceded 19 goals from set-pieces- six from corners and six from free-kicks.”

Source

That means that it pays to understand what an analysis entails. Now a philosophical analysis isn’t the same as a football analysis. Yet, the lessons philosophers learned about analysis equally apply to football. For instance, most people would think that analysis means that you break something down into its components. This is how analysis is used within football. Football analysis breaks a match down into components like formation, half spaces, tactics etcetera. This is what is called decompositional analysis within philosophy. Besides this form of analysis there are two other forms of analysis. So in total there are three forms of analysis:

1. Decompositional analysis where you break things down into components.
2. Regressive analysis where you work back to first principles.
3. Transformative or interpretive analysis where you translate what you analyse first into something else, preferably logic.

Let me give you my regressive and transformative analysis of the football game itself as I published in my boek “Voetbalstatistiek: filosofie voor voetballers”. Football has rules. Philosophers love rules as they provide a syntax. A syntax makes it easy to find the first principles. Here are the first principles of football as an example of regressive analysis:

• Principle 1: the purpose of football is to win.
• Principle 2: you win football by scoring more goals than your opponent.
• Principle 3: the closer you get to the opponents goal the easier the bigger the chance becomes to score a goal.

From these three basic principles you can then derive rules like these:

• Rule 1: scoring goals is good.
• Rule 2: if scoring is good, then assisting is good.
• Rule 3: if assisting is good then increasing the chance for an assist is also good.
• Rule 4: if assisting is good then decreasing the chance for an assist is bad.
• Rule 5: if scoring is good, then failing to score is bad.
• Rule 6: conceding a goal is bad.
• Rule 7: if conceding a goal is bad, then preventing a goal is good.
• Rule 8: if conceding a goal is bad, then increasing the chance that the opponent scores is bad.

Now these principles and rules might come across as very obvious statements. But that is exactly the point. You want to build your analysis on such simplicity that nobody would argue against it. Furthermore, through the process of synthesis which is the opposite of analysis, you can combine these basic building blocks into more complex statements. Or with transformative or interpretive analysis you can translate these rules to actually football analysis.

So let’s look at an example:

What is the better strategy for football: having a lot of small chances to score or only a few big chances? In the end the only thing that matters is whether a team scored more goals than the opposite teams. If the team managed to do that by shooting a lot on the goal, then that turns out to be the best strategy for them at that time. Here you can see the reasoning behind: the winning manager is always right. Nevertheless, you can also look at multiple matches and then you see that if you fail to score a lot (rule 5) even though you win now and then, over the long run you are worse of. That is the reason why teams are using crosspasses less and less. Statistics shows that crosspasses lower the chances to score (rule 4). So in general it is better to have a few big chances than more small chances as rule 4 and 5 bite less in that case.

Of course you don’t have to agree with my line of reasoning. That is not the point. The point is to show how analysis is done. This is important because many times an analysis consists of nothing more than describing what has happened on the pitch. A description is not an analysis. Stating “Team A played in a 4-3-3 formation” is not an analysis. It is a description. It would turn into an analysis when one would state: “Team A played in a 4-3-3 formation because they played with 4 defenders, 3 midfielders and 3 strikers”. Then you are breaking the 4-3-3 formation into its components. Yet, most people would not feel that this would be a very good description as it is too obvious. So an even better analysis would be where you would use data, for instance heat maps, to proof that indeed the team played with three lines of players and the line closest to their own goal had four players and the other two lines had three players.

If you use your analysis to identify causes, then it is important to know which criticisms can be leveraged against talking about cause and effect. The safer option is to talk about the probability of a certain pattern in a match or a certain sequence of actions of a player repeating in the future.

Patterns of weak or empty analysis

Thanks to the writing guide for analyses of the University of Michigan, we have a nice list of seven patterns of weak or empty analysis:

1. Offers a new fact or piece of evidence in place of analysis. This is done a lot in football analyses. They tend to be a long list of more and more data being presented with very little analysis of the previous presented data. As the University of Michigan writes: “Telling the reader what happens next or another new fact is not analysis.”
2. Analysis is biased. There are a lot of implicit biases. For one statistics is counterintuitive. People draw conclusions from statistics that are wrong. Then there is confirmation bias. Information that supports your point of view reaches your conscious mind much easier than information that disproves your point. Finally we have survivor bias. Although there is a lot of confirmation bias in football. Survivor bias is even more rampant. With survivor bias you only look at the data of the football players who made it, without checking how many failed football players had the same data but did not make it.
3. Analysis restates claim. This happens a lot in Twitter discussion where someone does not agree with what is being said. Then the original author gives arguments why he is right or why the opposing view is wrong. Finally, rather than engaging the arguments, the critic simply restates his point of view. Also don’t use a tautology in an analysis.
4. Dismiss the relevance of the evidence. Here is an example from an actual dismissal of the relevance of the evidence: “The Union have quickly become the team in MLS that other teams should emulate. They’ve got the second best expected goal difference (xGD) per game. Though, in fairness,, the gap between them and LAFC in first is the same as the gap between them and the Columbus Crew, who currently sit 17th in MLS. But, in further fairness,their budget isn’t in the same stratosphere as LAFC, to say nothing of the teams they rank above likeAtlanta, Toronto, NYCFC, and the LA Galaxy.” Source.
5. Strains logic. People often mistake their logical error with a disagreement of opinion. Such is not the case. While there is no absolute truth in our empirical world where there is only probability, there is absolute truth in logic and mathematics. If an analysts for instance prefers to use xG because even if the correlation of xG with future goals is low (say 27%), it is the best correlation we have, he violates the laws of mathematics that show how little information there is in a 27% correlation. That is not a difference of opinion, but a logical error. The same goes with faulty statistics. Although our empirical world is ruled by probability, probability itself is ruled by the logic of uncertainty. In the same way as mathematics is ruled by the logic of certainty.
6. Generalization to arrive at the argument. There are many unfounded generalizations in football that are used to arrive at a certain conclusion. That is why a good analysis goes into great detail of the relevant data without adding more data to it as that would weaken the analysis as per our first point. So an analysis of team data without delving into the underlying player data for instance uses generalization to arrive at a conclusion. For example: In a player report I read, the consultancy firm was praising a central defender for being in the top 5% of the best defenders to support the attack because his goals per minute was very high. Then I looked in the underlying data. What was the case? This defender playing in the Premier League scored twice in the 16/17 season playing little more than 3000 minutes. Then in the 17/18 season he scored three times! And in just 2000 minutes played! That was a big boost for his goals per minute, but of course the underlying data demonstrated (a) that the difference between scoring two times or three times is pretty much a matter of happenstance and (b) that he played only 2000 minutes instead of 3000 minutes indicated that the manager did not appreciate him the way the consultancy firm concluded. This report was used to try and get this defender to play at a bigger club for a better salary and hefty transfer fee. But the generalizations were only used to reach a conclusion rather than support an analysis. The transfer did not happen and in the 18/19 season this defender only played 1000 minutes and did not score at all.
7. Offers advice or a solution without first providing analysis. It is not to criticize StatsBomb as they do many wonderful things, it just happened that their analysis was the first that I saw in my Twitter feed. Nevertheless, there opening sentence of the piece quoted earlier is an excellent example of offering advice with first providing the analysis: “The Union have quickly become the team in MLS that other teams should emulate.”

Associative learning is one of the three ways the brain learns. The other two ways are: imprinting and instrumental learning. Associative learning has been discovered and made famous by Pavlov. For that reason it is also called Pavlovian learning. With associative learning the brain creates a probabilistic relationship between two sense impressions.

Associative learning is very important in football as it is the underlying learning principle of game intelligence. Players with a lot of game intelligence have learned many associations between certain position of their teammates and opposing players. A lot of training a team involves building up the right set of associations. Associations steer our behavior unconsciously. That’s why most players play at their best when they are in the flow. When they don’t think about it and just act. That’s why you see players make the wrong decisions when they suddenly have more time to act than usually. Instead of relying on the associations build in the unconsciousness, they overthink the situation and make mistakes.

Youth development works best when they are trained to build as many correct associations as possible. Associative learning explains why it is so important to have the right trainers and develop in the right team. Because they brain learns as easily negative associations that hinder the achievement of your goals as they learn positive associations. So for youth development it is good to think really hard about which trainer and which team will build the best associations and hence improve the game intelligence of the player the most. One reason why the football academy of Ajax is producing so many great football players has to do with that their programme teaches the brain to build up associations that proof to be very valuable in their career.  

Of course, the scouts of Ajax also has a great eye for talent.  Yet, associative learning also explains why some scouts are better than other scouts. And why different scouts see different things when they watch the same player. The reason why top scouts are also very valuable is that their network of associations has been proven to have a high correlation with future success.

Associative learning is also the reason why it is best to have multiple scouts watch a player and why besides watching a video of a player it is also important to go and a live match. Watching videos triggers different associations than watching a player live. Top video scouts and top live scouts both have a network of valuable association. But because these are different networks and different associations both inputs are especially valuable as they are also independent. A player that is liked by both the video scout and the live scout has a bigger probability of future success as a player where the live scout and the video scout differ in their opinion.

Drills with and without context

Due to associative learning drills with context are much better than drills without context. Football is a thinking sport. That means that pattern recognition by the unconscious mind is crucial for success. Especially as this builds game intelligence. Game intelligence and pattern recognition are created mostly through associative learning. So if you do a drill without context, for instance indiscriminate dribbles or passing for passing’s sake, the brain will build dribbling associations without the correct patterns to recognize. So that means that the player will learn the dribble technique, but his brain won’t know when to dribble and when not to dribble because he lacks the game intelligence to recognize the correct pattern.

When you do drills with context, that enables the brain to learn to right patterns. Learning how to pass so to exploit space at the same time, not only teaches the passing technique, but also teaches how and when to pass according to patterns as they develop on the pitch. So drilling with context builds the right associations, while drilling without context teaches incorrect associations. To be clear: it is not that without context the brain doesn’t learn new associations. All sense impressions lead to new or updated associations. That is the reason why drilling without context actually teaches players the wrong associations and thus decreases their game intelligence.

NOTE: Please don’t drill players to dribble indiscriminately or to pass for passing’s sake. Ask players to exploit space choosing the best option to do so (dribble, receive, pass, shoot). In this way you will nurture intelligent, skillful AND courageous athletes. #TOVO pic.twitter.com/szDv7kjHkr

— Todd Beane (@_ToddBeane) September 28, 2019

Changing associations

Fortunately, associations can easily be changed. All sense impressions build up associations. So the more new experiences you have, the faster your associations change. Repetition is key here. Creating the right associations is one of the reasons, besides fitness and technique, why players train as much as they do. A team with a lot of new players often performs less well than a team that has played together for a long time. Again, the reason is that the new players haven’t yet build up the network of associations that are required for the strategy and tactics that the manager wants to deploy. A no look pass only works when the right associations are in the brains of both players involved in that pass. 

Pavlov has made an interesting observation that besides new experiences hypnosis might also be a great way of changing negative associations. More and more sports teams are working with hypnotists to improve their play. Hypnosis sound really out of the ordinary. But that is because most people think of hypnosis in a very narrow sense. The famous hypnotist Derren Brown has defined hypnosis as the ability to get people to play along with your story. Influential talk always consists of hypnotic language patterns. So actually talking to players in the right way, as great coaches and managers do, also change the associations players have.

Unfortunately, associations also explain why a manager sometimes can’t seem to reach his players anymore. Associations build an expectation. And what we experience is much more influenced by what we expect to experience than by the data that actually reaches our brain through our senses. Over the years if players have the same manager each and every year, their associated expectation of that manager becomes stronger and stronger by the day. That is perfectly fine as long as everything works out great, because then the players only need to hear half a word the manager says to understand what he wants them to do on the pitch. But as soon as the old way of playing starts to fail and the manager decides to change his tack, then suddenly the old association block the players from understanding, and even literally hearing, what the manager has to say. Bringing in a new manager can then in fact work, for the reason that the players don’t have an associated expectation of the new manager. It then becomes easier for their brain to actually listen to what the new manager has to say, instead of filling in his words based on previous associations.

Averages are used a lot in football. Yet, an average lacks a lot of context. A player who scores an average of one goal per match, could have gotten that average by scoring ten goals in the first match (against an easy opponent) and then not scored at all for the next nine matches. So a weighted average might already be better than a simple average, although some people feel that you then introduce more subjectivity. This is not the case. An average is as subjective as a weighted average. The only difference is that often there is less convergence of opinion on a weighted average than on a simple average. By introducing weights you introduce more elements where people can disagree.

Most often average are take over many data points. That also makes an average insensitive. That means that if a player suddenly starts to do better or worse, it takes a lot of time before you see that change in the averages. Especially when preparing for the upcoming match, it is often much better to look at measures that are more sensitive to change than an average.

For player recruitment scouts are looking for players who are above average. But here there are pitfalls too. If your club is above average, it doesn’t tell you much if you learn that player A is above average for the league. That player is probably better than a player who is below the league average, but he still might weaken the team given that the team itself is also above average. 

In fact even if your club is below the league average and you can hire a player whose is above the league average, then you still don’t know whether he is going to strengthen the team. For you have to also look at the player he is going to replace in the team. If that player is one of your star players and even better than the above average player, hiring this above average player is still going to weaken your team. Of course, if the only other option is a below league average player, then hiring the above league average player is the least bad option. But simply stating that a player is above the league average is not enough to conclude that he will strengthen the team.

The same goes for stating that a player is in the top 5% percentile, or even the top 1% percentile. If data shows that a player is above the league average, that only means that he is in the top 50% percentile. So placing the player in the top 5% percentile already gives you much more information. Nevertheless, if the player he needs to replace or the team itself is in the top 1% percentile, then even a top 5% player can weaken the team.

The average of multiple variables

In reality most clubs don’t work with a single variable to determine whether a player is above or below the league average. Although it can be done. You can summarize many data points or averages in an average of averages. But in most cases clubs are looking at a lot of different variables. Players can be above average for a couple of those and below average for other variables.

With multiple variables it becomes even harder to use averages to see whether a player is going to strengthen or weaken the team. Looking at playing style helps a bit, but it remains uncertain whether a player can replicate his stats in a different team. Here is where the eye of human scout works wonders. In one case we were looking for a winger and a striker for an average club in the Dutch Eredivisie. I had found a striker that had nice stats in the FBM statistics I have developed. The very seasoned scout I work with told me he was no good as a striker, but that he was an interesting option for that club as a winger.

When the head scout at the club saw that we proposed this striker as an option, he also expressed a dislike for this player. Yet, when I explained that we weren’t proposing him as the center forward, but as a winger his face lit up. “Yes” he said, “I can see him excel as a winger indeed.” That is one of the many reasons why you always combine data scouting with video and live scouting. The human brain is still a wonderful biocomputer to find solutions where digital computers have a hard time coming up with the right solution.

When looking at multiple variables, it is important to be very skeptical of reports telling you that player X is above average or in the top 5% percentile in regard to skill Y. For instance In a player report I read, the consultancy firm was praising a central defender for being in the top 5% of the best defenders to support the attack because his goals per minute was very high. Then I looked in the underlying data. What was the case? This defender playing in the Premier League scored twice in the 16/17 season playing little more than 3000 minutes. Then in the 17/18 season he scored three times! And in just 2000 minutes played! That was a big boost for his goals per minute, but of course the underlying data demonstrated (a) that the difference between scoring two times or three times is pretty much a matter of happenstance and (b) that he played only 2000 minutes instead of 3000 minutes indicated that the manager did not appreciate him the way the consultancy firm concluded. This report was used to try and get this defender to play at a bigger club for a better salary and hefty transfer fee. The transfer did not happen and in the 18/19 season this defender only played 1000 minutes and did not score at all.

Such a presentation are not only misleading, but even if the underlying data is solid, then it is still risky. Our mind tends to focus and remember outstanding stats and overlook and forget all other stats. This is part of how confirmation bias works. Our unconscious mind then only processes the highlights of a player. Through associative learning our brain then connects good feelings to this player. Feelings that our conscious mind interprets as a good intuition. For that reason it is important to really delve deep into the underlying data of an average or risk making mistakes. Fortunately, in my experience that people working for clubs really do delve deep and often get very annoyed and distrustful (which is a good thing) when data providers can’t explain how they arrived at a certain value of a variable or an average.

Let’s look at ten basic principles of football and see how they connect with complexity. Here I use the term complexity as it is used in information theory and cybernetics. A cybernetic system has a higher complexity when there is more variation. With less variation there is less complexity. Variation is a measure for the number of options there are.

In terms of football: the more options you have, the more complex the situation becomes because it becomes harder to make decisions. That does not mean that it becomes more difficult to play. In fact, most of the time, having more options makes it easier to execute the decision you make. Because you have more options, it becomes more difficult for your opponent to anticipate your actions. You and your team become less predictable. So the more options you have, the less your opponent is able to resist you. Thus play becomes easier for you. To conclude with more complexity of the decision making process becomes harder and the decision executing process becomes easier.

Width

Width is an attacking principle. With more lateral options, your opponent needs to stretch their defenders to close all avenues of attack. That means less defenders in the space of your attackers. Less defenders means more options. So width is a good principle of attack because it increases complexity. With more width your attackers get more options. The attack becomes less predictable and it becomes more difficult for your opponent to defend against you.

Support

Players without the ball need to support the player with the ball. If the supporting players create opportunities for the player with the ball to pass, then options increase again and so does the complexity. If supporting players get close to the player with the ball but not too close, passing opportunities increase, but also the ratio between attackers and defenders in the same space tilts to favor the attack. The more options, the more complexity, the less predictability and the better your chance to score. If supporting players get too close to the player with the ball, then they start to limit the space available to that player and they start to limit the options he has. On the other hand if a supporting player runs into an open space and pulls a defender with him, he is creating more options for the player with the ball because there are less defenders to limit his options.

Penetration

Support and width are attacking principles that a team can always employ independent of your opponent . Penetration is more of a goal that the team tries to achieve. Yet, your opponent can prevent you from penetrating their defensive lines. The reason why penetration is desirable, is that when you penetrate the opposing defense you are able to get the ball under your control in a space that has less or no defenders. That in turn increases your options, increases complexity and increases your chances to score.

Mobility

If your players are staying at the same spot on the pitch, it becomes a lot easier for your opponent to limit the options of those players. Your opponent can block pass lines or limit the space your player is. Resulting in a decreasing number of options static players have. When your players keep moving around, it becomes more difficult to block pass lines and limit the space your players have. Preventing the decrease of options and thusly maintaining the number of options your currently has, make sure that your team is not forced to play in more and more predictable patterns. Of course, when mobility is used to support the player with the ball or penetrate the defensive lines, options increases.

Creativity

A creative player has more variation in his behaviors. His play becomes less predictable because he has a larger palette to choose from. Besides having more options, a creative player also needs to have flexibility to actually use all available options to him. Finally, a creative player also must have the technique to execute the decision correctly. So adding creative players to your team automatically increases the options your team has. Nevertheless, as most of the additional options are often quite difficult to execute correctly, the risk of losing the ball also increases.

Yet, there is another source of creativity that is not linked to individual players and that is the team itself. As long as the team plays in a way that creates more options, creativity will follow automatically. We have already seen that more options, leads to more unpredictability. And creativity is defined in football as doing something unpredictable. So even without creative players, the team can still play in a way that is less predictable.

Compactness

The less space between defending and attacking lines, the more compact a team is. Compactness is a defensive principle, because the aim of compactness is to try to have as many defending players as possible in the smallest possible space in order to prevent the opponent getting significantly closer to the goal with the ball. The more defending players there are in a small space, preferably the space where the ball is, the less options the attacking team has. With less options, the level of complexity decreases, so the game becomes easier. Thus it also becomes easier to defend. With less complexity there is also less risk. So the game becomes less risky. Less complexity also means that the opponent is easier to predict, again making it easier to capture the ball. 

It really doesn’t matter whether the compact block is close by the keeper or high up on the pitch. Playing high up the pitch with a compact block, makes it easier for the opponent to try to penetrate the defending block by passing in the space behind it. But that is also predictable and the defenders can be trained to anticipate that move to counter it.

Interruption

Although it is of course best to regain control over the ball, interrupting the attack of the opponent is also good to do. Football is not only limited in space, it is also limited in time. The more time there is, the more options there are for the attacking team to score. The less time, the less options. So interrupting the effective use of time also limits the options for the opposing team. Of course, this is especially handy if you are actual ahead in the match. Time is a sword that cuts both ways. As you are limiting the amount of time the opponent has, you are also limiting the amount of time your team has as soon as it regains possession.

If time is running out, you see the team that is about to lose or who doesn’t want to draw, play more and more predictable. That doesn’t automatically mean that the team that is winning, will definitely win in the end. That also has to do with the game intelligence and technique of the players on the pitch. But it does indicate how important it is to score more goals than your opponent. The moment you do, not only do the number of ways they can win decrease (for instance they can’t win 0-1 anymore), but interrupting their attack costs them time. Which limits the options they have.

Less space and time

Pressure doesn’t really exist in football. There is only the amount of space and time an individual player gets to make and execute decisions. The less space and time, the harder football becomes. Unless, there is too much time and space and players start to overthink the situation. In that case that particular player can’t handle the highly increased level of complexity of his situation and he blunders. But in most cases, the less space and time, the harder it becomes.

The reason why less space and time, make it harder to play, is because as a player you get less options. So because you have less options and your actions will become more predictable, it becomes harder to beat your opponent. Of course, when you are a defender and you want to capture the ball, it is great when the attacker has less options. The more predictable the attacker is, the easier it is to win the ball.

Patience

Patience is a virtue. Patience itself won’t decrease or increase complexity. Yet, patience is needed to wait for the moment complexity has dropped so much that the behavior of the attackers has become so predictable that there is a high chance of capturing the ball. If you act too quickly as a defender, before you have shut down as many options as possible, then there are still options open for the attacker. The more options the attacker has, the smaller the chance you have to predict the behavior of the attacker and capture the ball. So patiently abiding your time till the level of complexity has dropped enough, is often the best defending strategy.

Predictability

Due to the close reverse connection between complexity and predictability, I have already explained everywhere how defending is a matter of decreasing complexity in order to increase predictability, whereas the aim of attacking is to increase complexity in order to increase unpredictability. Besides everything I described so far, the defending team can also specific strategies to increase predictability. For instance, a manager can use data analysis to find out which attacker of the opponent most often loses the ball. Or is the least creative and the most predictable. Then the team can employ a strategy where the opponents options are limited when it comes to passing to other attackers, so the ball gets passed to the attacker most likely to lose the ball.

Our brain is a Bayesian biocomputer that foresees the future. Or to put it more precisely: the workings of our brain can best be described with Bayesian statistics. That is why philosophers, psychiatrists and neuroscientists now talk about the Bayesian brain. At the lowest level the workings of brain cells can best be described with Bayesian statistics. (Doya 2007, Bayesian Brain) Brain cells are triggered to fire a signal depending on a jolt of electricity. Pathways that are triggered easily and often require very little electricity. Pathways that are rare and difficult to trigger require much more energy. Yet, the energy levels don’t rise and fall lineair, but they use a certain quantum, i.e. discrete jumps or drops in energy. These quanta pretty much follow Bayes Theorem. The same goes for the neurotransmitters brain cells send the next cell. This is a kind of morse code that again doesn’t rise or fall lineair, but also uses quanta that pretty much follow Bayes Theorem.

At a bigger level the brain can be divided into two parts: (a) a bottom up part that processes sense data and (b) a top down part that processes our expectations. What makes our brain Bayesian is that our brain tries to make a prevision of what it is about to experience and then checks the incoming sense data to see whether the sense data matches what was expected. Our expectations are created through associative learning and instrumental learning. Or to put it in terms of football: game intelligence and technique.

What is interesting is that when there is discord between our expectations and our sense data, the brain tries to reason the difference away. This is mainly done by the brain to see if it can ignore the incoming sense data and stick with its expectation. This leads to inattentional blindness, fallacy and biases. This process is the main reason why players with game intelligent are often the better players. Players who lack game intelligence are literally blind to unexpected patterns. Players who lack game intelligence can literally not see opposite defenders and attackers if they do something unexpected. On the pitch this looks as if the player is blundering, but in reality his model of the game inside his Bayesian brain that produces his expectation is too poor to deal with the complexity of the game.

The Bayesian brain also explains why the influence of the manager on his players can decrease over time. Over time players don’t hear what the manager is actually saying, but literally hear what they expect him to say. For more details on this phenomenon, see: bias.

What is better live, video or data scouting?

The Bayesian brain explains why you need all three forms of scouting: live, video and data scouting. The reason is that the brain of the decision maker works through Bayesian principles. That means that the decision maker takes into account all the recommendations from different sources and comes up with the final decision. The more trustworthy sources the decision maker has the less risky his decision will be. A decision maker that only uses one form of scouting will make more risky decisions because he has less data to work with.

Yet, acknowledging this also brings additional responsibilities for all scouts, no matter whether they scout live or through video or data. Scouts have to make their probability estimations explicit! A live scout can’t simply give a player an A and an advice of getting the player as soon as possible. No, the live scout also has to give a concrete number for the probability that the player is going to be a success. That is a number between 0 and 100. The same goes for the video scout. The same goes even for the data scout. Because almost all data scouts come up with a player report with lots of numbers, but almost never with a number for the probability that the player will be a success.

When all the scouts actually make their unconscious probability estimation explicit, then the decision making process can be made more rational. By building a Bayesian network that uses all the inputs from the scouts, the club can rank the players as to who would have the highest probability of success. 

More importantly, one can then track how good the probability estimations of the scouts were by giving penalty points for the gap between prediction and reality. It will take up some time to build up enough reference points. Yet, once that has been done, one immediately sees which scout is most trustworthy. That enables you to enhance your Bayesian model by giving more weight to the opinion of the most trustworthy scouts, independent on whether they are live, video or data scouts.

In football it is very important to pay attention to actual behavior rather than cognitivist constructs. Behavior can be distinguished between internal and external behavior. To check to see whether something is external behavior there is the MARCO acronym:

• M stands for measurable. External behavior can be counted. Passing is external behavior as it can be measured.
• A stands for active. Someone needs to be doing the external behavior. There is a dead man’s test here: if a corpse can do it, it ain’t behavior. Lying on the pitch ain’t behavior as a corpse can do it as well. Tackling is external behavior as a corpse can’t tackle someone.
• R stands for reliable. External behavior can not only be measured, but most people will reliably come to the same conclusions when counting external behavior.
• C stands for control. External behavior has to be under the control of the agent. “Go and win this match” is a bad suggestion for a manager to make as it suggests something that is not under the control of the agent. “Go and score a goal” is a good suggestion as scoring is under the control of the player.
• O stands for observable. External behavior can be observed by third parties.

Here is a great example of external behavior:

🎬 Breakdown: Douglas Costa 'akka'

1️⃣ Read the defender his bodypositioning.

2️⃣ Make an outside-foot contact to switch his center of gravity to his other knee

3️⃣ Make an inside-foot contact at tho moment of the switch to change direction. Look away to hide your intention 👀 pic.twitter.com/9OAkNnzDfO

— Zeb Jacobs (@ZebJacobs) October 1, 2019

Our subjective experience is internal behavior. We all understand that in order for our body to produce external behavior, our brain has to do a lot of processing. The same goes for our subjective experience. Subjective experience is not a mental state, but the end product of a lot of unconscious processing in the same way that our external behavior is not a state, but the end product of a lot of brain processing. 

Internal behaviors basically boil down to:

• Feelings and emotions.
• Visualizing by remembering what the past looked like.
• Visualizing by making a memory like fantasy about the future.
• Inner self talk.
• Remembering what other people said or how music sounded.
• To be complete: memories of taste and smell are also internal behaviors. But for most people these are so unconscious that they have very little subjective experiences of these and therefore we can ignore them most of the time.

For scouts it is crucial to make sure that when they report on a player they only report on external behaviors if they can’t actually interview a player to ask him about his internal behavior. For coaches and the manager internal behavior is very important. Each player has a distinct set of internal behaviors that help him achieve his best performance. This depends a lot on the biological hardware structure of his brain that most people think of as the player’s personality. For some players it is important that they feel good or that they feel relaxed. For other players, it is important that they feel tension and excitement. Knowing which player needs what kind of internal behavior makes a great manager.

Visual internal behavior works differently. When we create memory like fantasies about the future our conscious mind thinks we are contemplating that future. But our unconscious mind sees those memory like fantasies as instruction videos to be carried out in the future. Therefore it is important that players refrain from visualizing mistakes or setbacks that make them feel bad. It is much better to first visualize setbacks and see upfront that even though there is a setback, the player keeps on feeling whatever feeling helps him perform at his best. After having visualized these conditional negative scenarios that are less negative as the player sees himself reacting correctly to setbacks, it is time to visualize positively. It helps players to achieve their best performance to actually see them doing inside their mind’s eye before they actually go out and do it.

Inner self talk seldom helps players achieve their best performance. Players need to learn to trust their body and unconscious mind. All those training hours improve their technique and game intelligence. During the match for most players it is best to actually be in the moment and perform rather than overthink situations.

Avoid mental constructs

Behavioral analysis as described above was mainstream in the period of the late nineteenth century up until the mid sixties of the twentieth century. Around that time behavioral analysis was replaced by cognitivism. Cognitivism took the functional behavioral approach of cybernetics and started to create mental constructs inside our mind. Examples of mental constructs are:

• Motivation.
• Will power.
• Intuition.
• Respect.
• Trust.
• Confidence.

Current thinking in football is heavily influenced by cognitivism. Yet, cognitivism is failing because neuroscience is not finding brain cells that produce these mental constructs. So rather than using mental constructs and fooling yourself into believing that these mental constructs explain anything, it is much better to go and look at the actual external behaviors combined with internal behaviors if you are capable of interviewing the player.

Everyone is biased. There are explicit biases and implicit biases. Explicit biases are at least recognized by the people surrounding you and if you are honest with yourself also by you. Implicit biases are unconscious and, by definition, cannot be known. Though there are tests that will show you how your implicit biases influences your decisions and actions.

Biases are closely related with the expectations that form an important part of the brain. The brain has basically two systems: one to process sensory data and one our process our expectations. Knowledge and skills are stored in the brain through associative learning and instrumental learning. These learnings can best be described as a model of the world. In football terms: players learn technique (instrumental learning) and game intelligence (associative learning) and create a model of the beautiful game, of their team, their teammates and themselves. Based on this model the brain calculates what it expect to sense next.

The theory about how the brain works, is called Predictive Processing. The idea is that there is way too much information in the environment for the senses to take in. So rather than see everything, our senses only process relevant changes. What happens is that the brain creates an expectation of what it is going to sense next and compares that expectation with what the data the senses provide. As long as the sense data is in line with the expectations the brain is happy. Yet, if there is a conflict between what the brain expects to sense and the sense data, then things become interesting. In most cases the brain will reject the sense data and hang on to its expectations. Or to be more precise: the brain will reason the differences away. But if the sense data persistently and impactful differs from the expectation the brain created, then the brain is forced to update its model of the world.

This is the reason why players who have less game intelligence than average literally don’t see opposing players or the ball. The manager might ask himself: “How come that my defender didn’t see that attack coming?” The answer is: the ray if lights of the attack did reach the eyes of the defender and were processed by the brain of the defender, but because the defender did not expect the attack to happen the sense data was overruled because it conflicted with the expectations of the brain. As a result the sense data of the attack was deleted and the defender literally didn’t see the attack happen. That is the reason why an attack with little predictability has a better chance of success. If the unexpected happens, players with less game intelligence than average, will fail to see patterns developing. 

Another example of how expectations and implicit biases work, is when a manager after a few years of doing great things with the team, suddenly is unable to influence his players anymore. Most of the time this happens when he wants to change the system he is using because the results are less than satisfactory. But no matter how much he tries to explain his new ideas to his players, it seems as if they don’t listen to him. In fact, they literally don’t hear the new things he is saying. Instead they hear what they expect him to say. This is one of the reasons why Louis van Gaal has a reputation of doing weird stuff in the locker room. When he feels he can’t reach his players, he does something completely out of the ordinary to shock the players so they stop prioritizing their expectations and instead let their sense data through.

The most common biases

So now that we have seen the underlying structure of biases, we can look at the most common biases:

Confirmation bias

Confirmation bias is a bias where the brain embraces information that support the current beliefs of the person and at the same time dismisses information that contradict the person’s current beliefs. Confirmation bias can easily be explained with Predictive Processing. Information coming in through the sense that confirm to the expectation of the person are taken in by the brain, whereas information that contradicts the expectation is deleted. Even though confirmation bias is well known, many people who know about confirmation bias, still make mistakes due to confirmation bias. 

The reason is that confirmation bias is so much built in the way the brain works, that conscious understanding is simply not enough to get rid of it. It is an unconscious process. The best way to countermand confirmation bias is the use of statistics. But only statistics that shock you now and then. Because if you do not strongly disagree with your statistical data, chances are that you selected that data source because it confirmed your biases.

Survivor bias

We all love Messi. Let’s research how Messi learned to play football so well and apply those lessons to all other players. Sounds like a great idea, but the idea suffers from survivor bias. Maybe Messi’s development is a lesson for many, but as long as don’t know how many players tried to do the same and failed, we don’t know whether the path Messi took is any good. Theoretically it could be that only 1 in 100.000 players actually learns to play football at a professional level following Messi’s development plan. 

In football many people suffer from survivor bias because a lot of attention is paid to players who make it. We all love a positive story. But the negative stories of players who did not make it, are at least as interesting, if not more. Focussing only on the positive is called the Via Postiva, the positive road. Many people prefer to take that road. But the Via Negativa, the negative road, is in many cases more important.

Another example of survivor bias happens in data scouting of players. If a player breaks through, data scouts start looking in the history of the player, to see whether there is a specific pattern that already signalled his greatness years earlier. The idea is that if this pattern is recognized it can be used to find future talent. But often, the data scout is uncareful with how many years he goes back. For player A he finds a pattern three years ago, and then he confirms his find for player B, even though he has to go five years back. So here you see both Survivor Bias and Confirmation Bias at work at the same time. Even worse, the data scout never looks at how many failed players had the same pattern.

Selection bias

Survivor bias is a form of selection bias. In the case of survivor bias the selection bias is selecting only survivors. But there are many more selection biases. For instance in the Eredivisie Dutch clubs have a strong selection bias to prefer players who have played in the Eredivisie. One can argue that for Dutch clubs to prefer to have Dutch players is okay. But the selection bias of Dutch clubs goes beyond that. They also have a strong preference for foreign players who have played in the Eredivisie. The Eredivisie is a relatively weak league. So it is strange to prefer foreign players who done (relatively) well in a weak league over foreign players who have done (relatively) well in a stronger league.

Belief in truth

Belief in truth in itself is a bias. If you would define bias as a systematic deviation from the truth, even though you are trying to recognize your own biases, you fall for the belief in truth bias. Truth can only be defined in formal logic and mathematics with the use of truth-tables. There is no truth outside of mathematics and logic. Everything empirical has some measure of uncertainty.

Habermas, one of the most stern supporters of truth outside of mathematics, defines true statements as statements that will hold up for everyone, everywhere and always. That means that if something is true, it is true for us and it is true for people living in Australia. It is true for everyone who will ever be born from this day forward. In fact it is even true for everyone who has ever lived so far. If aliens from outer space visit our planet, then they too will recognize a true statement as being true. While this holds for mathematical and logical statements, it fails for empirical statements. The bar for truth in the empirical world is too high.

Nor is truth needed in the empirical world. Probability gives you everything you ever wanted out of truth. Rather than saying that X is true, it suffices to say that X is highly likely. The self defeat tests of Bayesian statistics allow you to define bias much more elegantly. A bias is a probability estimation that leads people to systematically lose bets or gain unnecessary penalty points in a loss function.

Business Insider has a nice overview of 20 biases:

All of these are correct, except placebo. Placebo is the natural rate of healing in humans. Medicines need to be better than this natural rate of healing. Strengthening believes by talking to people is hypnosis or the use of hypnotic language patterns in communication.

If a team loses it is only natural to look for the cause of the defeat. But cause and effect do not really exist. They are abstract concepts that need a justification to be used. In football no such justification can be found. Instead in football we have to work with the probability of a certain sequence repeating in the future. That might sound quite a lot like cause and effect, but it isn’t.

As the following tweet attest, more and more people are becoming aware that cause and effect might not be very useful in football. So let me explain what philosophical issue there are with cause and effect.

This is a great thread for 2 reasons:

1. It’s a fabulous explanation of what Perception – action coupling actually is.

2. It’s a brilliant expose of the lack of understanding of ecological approaches by those blinkered by strict cause and effect notions of human development https://t.co/X21EsF2rkV

— The Talent Equation (@stu_arm) August 31, 2019

Criticism of cause and effect starts in the eighteen century with David Hume. He defines cause and effect as follows: if every time we experience an event B, there has been an event A just before it, the A is the cause of B and B is the effect of A. If Pepe tackles Messi and Messi is injured then Pepe is the cause of Messi’s injury.

At least that is what seems to follow from Hume’s definition. But Hume warns us against such a conclusion for he states that a cause if only a cause if the effect is always preceded by the cause. As not every time Pepe tackles Messi he is injured, we can doubt whether Pepe’s tackle is the real cause of Messi’s injury. Also, Pepe’s tackle is not the only thing that has preceded Messi’s injury. Maybe Messi has been tackled by other players earlier in the game. Or maybe he already started the match injured. The problem with causes is that we can always find more causes than we want and we can always go further back to look at the cause of the cause. Maybe Messi was injured by Pepe’s tackle because Pep Guardiola pushed him to take more risk attacking. But maybe Pep only did so because Barcelona was behind. And maybe Barcelona was behind because Messi missed a big opportunity. So maybe Messi is the cause of Messi’s injury.

In the nineteenth century cause and effect is criticized by Friedrich Nietzsche. Nietzsche shows that there is an inherent mistake in the concept of cause and effect. As the effect has to happen after the cause, cause and effect can’t be simultaneously. For if cause and effect would be simultaneously we would be unable to tell what the cause is and what the effect is. As Louis van Gaal liked to say: “Are we so good or are they so bad?”. Is Messi scoring so easy because Messi is very good or is Messi scoring so easy because the defense is so bad? But if cause and effect can’t be simultaneously, then there has to be time in between cause and effect. What happens in the time between cause and effect? If you don’t know how are you able to connect the cause to the effect. But if you do know what happens in between, then you are coming up with a new cause and effect pair. And then we ask the same question again: what happens in the time between the new pair of cause and effect. In football terms: Messi is able to score because he overtakes Pepe. But what happens in the time between overtaking Pepe and scoring? No matter the answer, we can zoom in to an even smaller time scale. Nowadays we register 2.500 actions during a match, but with more precise measurement we might be able to increase this to 25.000 actions. The smaller the time scale the more irrelevant the cause and effect pairs become. But at a larger time scale we run into Nietzsche’s argument about the time in between.

In the twentieth century Russell expands Nietzsche’s argument. Influenced by the newly discovered quantum mechanics and relativity theory, he states that even if take cause and effect to be connected in time, then both cause and effect as an event on it’s own take time. Messi’s overtaking Pepe take some time. Russell notices that the first half of the cause is ineffective in the same way as the second half of the effect. So we can subtract those ineffective halves of the cause and the effect. But we can keep doing this until there is nothing left of the cause and effect! 

Causation implies absolute truth. If we don’t know the cause absolutely, we cannot speak of cause and effect because the effect might not always be preceded by the cause if things are uncertain. But quantum mechanics show that everything has a measure of uncertainty. The same goes for football: there is so much uncertainty within football that it is overly simple to think in terms of cause and effect. Every time you indicate that you know the cause of something, you are actually proposing a theory. That theory is always uncertain due to the underdetermination of the theory by the data.

The probability of a sequence repeating in the future

It is very hard to live and work without cause and effect. Cause and effect talk is very much ingrained in our daily lives, inside and outside of football. In fact, our brain is hardwired to see cause and effect. Research has shown that whatever is the most salient detail at the same time as we experience the effect, is taken by the brain to be the cause of the effect. We see Pepe tackle Messi and we see Messi falling, so our brain concludes that Pepe’s tackle is the cause of Messi’s fall. But we have already seen that cause and effect can’t be simultaneously. So our brain assigns cause and effect incorrectly. Evolutionary this is a great strategy. To survive you don’t have to be correct, as long as you are safe when you are wrong. Our brain likes finding cause and effect so much that whenever you find a cause you are rewarded with a dopamine rush that is also used to reward you whenever you have achieved one of your goals. So cause and effect talk is ineffective because (a) the concept is incorrect and (b) our brain is biased to interpret the wrong things as if they were causes.

Nevertheless, almost everyone wants to talk in terms of cause and effect. Fortunately, that want can be satisfied by a healthy alternative for cause and effect talk. Instead of talking about how A causes B, one can talk about the probability of B following A. We experience sequences of events multiple times. The more we experience these sequences, and the more other people also talk about the same sequences happening even though you personally did not experience them, the more probable it becomes that these sequences repeat themselves in the future. This is actually how the brain learns game intelligence through associative learning.

So while people feel the need for cause and effect talk, it is much better to stop talking about cause and effect and replace all that talk with talking about the probability of a certain sequence repeating itself. In terms of football: stop talking about the causes of the loss if you lost a match, but instead look for patterns of events that preceded the loss and calculate how probable it is that those patterns repeat themselves in the future. 

Our brains are Bayesian brains. They are best described as biocomputers that use Bayesian statistics to calculate how probable patterns repeat themselves. The more we are able to train players to think in terms of the probability of a specific pattern repeating itself, the easier we make it for the player to increase his game intelligence. For example: the next time he looks at where the opposing players are currently in the match, the easier he can spot different scenarios of how the game will evolve and what probability each scenario has. That is much better than trying to find a single cause. First of all because causes don’t exist. Secondly because football is way too complex to be described in a simple cause and effect. And thirdly because our brain tends to pick up with wrong events as causes. 

There are two modes of communication (Skinner, Verbal Behavior 1957). Either you communicate to clarify or you communicate to influence. The basic principle of communicating to clarify is to be as specific as possible. To clarify, you need to make sure that you do not delete, distort or generalize relevant details. Because clarification entails a lot of details, people don’t like this mode of communication. Details are often antecedents for punishments. That is why people feel uncomfortable when you clarify matters. They fear that all these details either proof that they made mistakes or that they need to reproduce these details as if they were still in high school. Of course there are techniques like rapport building techniques that lessen this negative attitude towards details. Yet the need to use such techniques underlines the basic negative attitude to details. So as a coach you often want to clarify a lot to your players. So you need to take into account that your players are not too happy on details.

People love influence as a mode of communication. This is ironic, because communicating to clarify can be seen as a much more pure and honest mode of communication. Whereas communicating to influence people is much more manipulative. Nevertheless, people’s attitude towards communication to influence them is often very positive. The main reason for this is that when you communicate to influence people you communicate in a way that seems specific, but is not specific. By deleting, distorting and generalizing relevant details, you create a lot of room in the way the listener understands you to fill in the blanks based on their own experiences. That way it seems as if you really connect to their world and their world view, even if you don’t. Besides deleting, distorting and generalizing relevant details, there are also a number of hypnotic language patterns that increase the level of influence your communication have when you use them.

So as a coach you need to (a) clarify details so your players know what to do and (b) influence them so they go out and do it. Those two objectives require two different methods of communication. Often, people master only one of those two and think that the other one isn’t needed. Either a coach thinks that if his players understand in detail what he wants them to do, then that understanding will make his players do the correct thing. Unfortunately, that is not the case. These coaches often talk too much. The other case is where a coach is a great influencer, but forgets to actually clarify the relevant details to his players. Now his players are all pumped up, but don’t have a clue what to do.

In many clubs these two objectives are achieved by having an assistant communicate all the details and then have the manager influence the players to go out and do whatever the assistant has explained to them. Yet, ideally a coach is a master in both modes of communication. As talking is for a large part an unconscious activity, if a coach doesn’t use these two modes of communication naturally, he needs training to make sure that his unconsciousness is able to switch between these two modes of communication fluently.

Complexity is a measure of how much variation there is in a system. Variation is a measure of how many variables there are and how many different values these variables can have. The more variables you have, especially when many of these variables can have many different values, the more complex the system is. A different way to explain complexity, is noting that the longer it takes to describe all the different options a system has, the more complex the system is. (Source: An Introduction to Complex Systems Science and its Applications by Alexander F. Siegenfeld and Yaneer Bar-Yam 2019)

Given how much you need to write about football before you have said it all (if that is even possible), football is a game with a very high level of complexity!

Our interest in complexity lies in our desire to deal with complexity. Cybernetics is about communication and control in man and machine (which is actually also the subtitle of the first book on Cybernetics by professor Wiener). As said, football is a very complex game and the question is how do we control this complexity. The first step to take control is to define the system and the environment. We are completely free to define anything in football as a system. As we have very little control over the opposing team, it is best to define our own team as the system and let the opposing team be part of the environment. The question then becomes how can the manager regulate the way the team (or the system) deals with complexity.

Simplifying complexity

Obvious if you take both teams as the system, there are more variables than if you only look at your own team. More variables, means a higher level of complexity. But because we can’t control the opposing team directly, we chose to look only at our own team. In fact it is even easier to start with a team of only one player.

So let’s start with a single player. Imagine a match with only a single player. What can he do? Basically he can shoot the ball and run after it. Or he can dribble with the ball. There is not much else to do. So the complexity is relatively low. But as soon as we add another player, the complexity increases. Now they can pass to each other. One can give an assist as the other player scores. So team members increase complexity. Team members are variation amplifiers.

The more players we add to the team, the more complexity rises. In fact it rises exponential as all the possible different relations between the players add to the level of variation. A single team of eleven players without an opponent has the highest level of complexity. That sounds counter-intuitive. Doesn’t the opponent make the game more complex? The answer is: only if you make them part of the whole system. If the opponent is part of the environment, then the opponent is limiting the options of your team (the system in focus) and thus complexity decreases.

The opponent makes it more difficult to score. Obviously, It is much easier to score if there is no opponent on the field. Without an opponent it is very easy to score. But writing down all the options a team has, if there is no opponent, has become a much bigger task, than writing down all the options a team has when there is an actual opponent. Your opponent will diminish the options your players have. As such opposing team members are variation attenuators.  Your opponent only increases the complexity if it is part of the system. But because we have excluded the opposing team from the system, we only look at what the opposing team means for the options our team has.

Now let’s add an opposing player to our experiment. Immediately, it becomes clear that in this situation the team has less options to score. For one, they can’t run the ball through the opposing player as that would be a foul. The team has to play around the opposing player. In fact, by adding a single opposing player we proof that opposing players are indeed variation attenuators. They diminish complexity. The more opposing players there are on the field, the less options our team has. The more our team is forced to play in certain predictable patterns. And the more predictable our team becomes, the more difficult it becomes to score. The reason why it is difficult to score in football is not because the game is too complex, the reason is that the game is not complex enough.

If you are not yet convinced than reverse our little thought experiment. Now we start we only one player for ourside against eleven opponents. Scoring becomes almost impossible as the eleven opposing players limit the option of our one player to next to nothing. Again, we can increase our odds by either adding players to our own side as they are variation amplifiers. With more players our team gets more options, complexity rises and our chance to score increases as well. Or we could decrease the number of opponents. With less variation attenuators our options increase and again complexity rises together with our chance to score.

Real variables

Let’s see if we can calculate the level of complexity for a single player on an empty pitch. We will consider the following five variables (even though there are probably many more to consider):

• Position
• Direction
• Speed
• Timing
• With or without the ball

To calculate the complexity we have to determine how many different possible combinations of these five variables there. To do that we first determine how many possible settings each variable itself has. “With or without the ball” is easy as it is a binary variable with only two options: yes or no. For position we have to create a grid on the pitch. Let’s go for the smallest pitch allowed which is 100 by 64 meters. If we build a grid out of a single m2 then we have 100*64 = 6400 different positions on the field. For direction we have 360 degrees around us. But it is probably fine grained enough to use sections of 30 degrees so we can work with 12 directions as if we were to use a clock to determine our directions. Timing goes really fast in football so it is probably best to use a time scale of seconds. So in a football match we have 90 * 60 = 5400 seconds at least. Finally we have speed. Let’s go with 11 different speeds going from 0 m/s to 10m/s which is very fast.

So this gives the following number of options for a single player with or without the ball on an empty pitch. The formula is:

Options = position * direction * Speed * Timing * Ball

Which gives us:

6400 * 12 * 11 * 5400 * 2 = 9.123.840.000 options for a single player on an empty pitch. Over nine billion options is way to many options for people to handle conscious or unconsciously. That is why we need to decrease this number of options to make an interesting game that can actually be played by human beings.

Now if we add a single opponent, you can see the number of options for the first player drop only because there is 1 less position where he can be. Now our original player has the following number of options:

6399 * 12 * 11 * 5400 * 2 = 9.122.414.400 So now we see that by adding 1 extra inactive opponent, our original players has over a million option less. Now let’s add the other 20 players completely inactive with each player only taking up 1 space. The formula then becomes:

6379 * 12 * 11 * 5400 * 2 = 9.093.902.400 So that 29 million less options for our original player. Here you can see mathematically how adding more opponents actually decreases complexity. And this does not even take into account rules like off side where the opposing players can actively make large parts of the pitch inaccessible. Nor does it take into account all the seconds that the opposing team has the ball and the “with or without the ball” variable drops from 2 options to 1 option immediately limiting all available options for our original player for all those seconds by half.

With every second ticking away in a match, the number of options available to players decreases. One of the reasons why a formation helps players perform better is that a formation limits the number of positions where players can be, thus decreasing complexity.

Complexity and space

So far we have considered the whole pitch as the boundaries of the system. But we can actually look at smaller parts of the pitch. What goes for the whole pitch, goes for every part of the pitch: the less opponents there are in any given space, the more options you get and the more complex the game becomes. And the more complex the game becomes, the more chances you get to score. So once you have divided the pitch into zones, it becomes important to make sure that your team has more players in the important zones than your opponent. The better the ratio is between your players and the opposing players, the more options your players have. Complexity rises, but so do the chances to score.

This only works of course if your players are able to handle the increased complexity. A well known phenomena in football is that if a player gets too much space and time, he starts to overthink the situation and blunder and lose the ball. The problem here is that the brain and the unconscious mind are suddenly confronted with more options than it can handle. The brain and the unconscious mind need consciousness to help out with the increase in complexity. Unfortunately, for some players their conscious mind is not trained to solve this level of complexity and a blunder happens.

If your team is not in possession of the ball, you want to close down the space of your opponent. The less space your opponent gets, the less options he has, the less complex the system becomes and the more predictable the behavior of your opponent becomes. Which, in the end, lowers his chance to score. And makes it easier to recover the ball.

Yet, the moment your team captures the ball, space works the other way around. Then you want less opponents in your space so you get more options. That is why Ten Hag, for instance, wants all players to spread out when the ball is lost, except for the few players who are needed to recover the ball. That way, once the ball is recovered, the team has way more options. The game has become a lot more complex for the opposing team and your team has an increased chance to score.

Then, once you run into a packed defense you want as many of your own team mates closeby and into the same space that the player with the ball occupies. This makes the ratio between your players and opposing player more even and increases complexity.  Because if in the limited space where the ball is, the opposing team has more defenders than your team has attackers, these defenders diminish your options quickly, making your play more predictable and decreases your chances to score. The whole idea of parking the bus is to always have more defenders so to decrease complexity, make the game more predictable and decrease the chances of conceding a goal.  At the same time, you don’t want your players to be so close together that they start to limit each others options. Players still need room to manoeuvre and run.

Here is an example of six attackers flooding a relative small space to increase complexity, making it harder to defend and easier to score:

Sheffield United’s winning goal today shows how their famous overlapping centre backs work: O’Connell pushes the team forward and creates numerical advantage on the left wing with Stevens and Freeman. Scored by Lundstram after the first shot, by Freeman, is stopped. pic.twitter.com/ldih9IPhGy

— Last Row (@lastrowview) August 18, 2019

Complexity also explains why sometimes it looks as if a team playing with ten players, because a player was sent off the pitch, is easier than playing with eleven. Sometimes, the manager even comments on this after the match by saying that he ought to play more often with ten players as it seems as if the team was playing better with ten players than eleven. In fact, this not only seems to be the case, but often this really is the case. Complexity explains it. The team has a lot less options with ten players against eleven. So the complexity has decreased for the team. If the team was struggling with the level of complexity when they were still with eleven players, it could well be that now with the decreased level of complexity they can manage it.

To be clear: for the opposing team, who still play with eleven players, the complexity has risen. This is why it is easier to score against a team of ten players than against a team of eleven players. But only if the players of this team are able to cope with the increase in complexity. Sometimes this is not the case.

Complexity and risk

Ten Hag’s approach of attacking by making the space even smaller and adding more attackers into that small space, is one way to break through a defense by increasing complexity. Another example is to add one or more creative players to the lineup. 

Why is a player called creative? Because he has more diversity in his play. He is less predictable than other players. The reason is that he has more variation. Adding a creative player to the team increases the complexity of the system. That is the reason why a creative player increases the chances to score. 

But the more options you have, the more that can go wrong. Increasing complexity, also increases your chances to score. But it also increases the risks you take. For not only are there more ways in which things can go wrong, often the additional options creative players have, are also harder to execute. So the creative player needs more game intelligence and more technique than the average player. For all players, it is important to check to see whether they have a positive error ratio, but for creative players even more so. For a creative player might also increase the risk the team runs to an unacceptable high level.

Ten Hag’s strategy of spreading out on ball loss and concentrating attacks, does increase the chance of his team winning. It also increases the risks as the higher level of complexity might bite him. That is why you see him sometimes lose a game out of nowhere.

The difference between complexity and difficulty

One can argue that scoring in a match without an opponent is very easy. And they would be correct. But the fact that scoring is easy with no opponent, doesn’t mean that it is not complex. For there is a difference between complexity and difficulty. Activities can be both complex and difficult. Or they can both be without much complexity and difficulty. Or they can be either complex and easy or having less complexity and yet be difficult to execute.

Complexity has to do with how many options you have. Not whether those options are easy or difficult to perform. In football there is a difference between decision making and executing decisions. The more complex the situation, the more options you have, the harder it becomes to make a decision. The less complex the situation is, the less options you have the easier it becomes to choose. In the example of a match against no opponent, even though most complex, it is easy to choose, because although there are so many options, a few options present themselves as most attractive because they are the easiest to perform. For instance, dribbling to the goal and score. But this is only the case if you think about the match as a single action. As soon as you understand that the players of your team have to enjoy themselves for 90 minutes, it becomes clear that they will entertain and probably do a lot of the other, less easy, options in that situation.

The difference between difficulty and complexity can also be seen in the following example:

Let’s do another experiment. This time taking a penalty. But before we take the penalty, we are going to strongly limit the number of options as to where to shoot by boarding up the goal with wooden planks. We will only leave a small hole in the middle of the goal just big enough to let the ball through. This is a real life example of a system with a very low complexity (as there is only one option to score), yet where the chosen action is very difficult to execute.

Now we can expand this example by creating a second hole in one of the corners of the goal. We make the second hole a bit bigger than the first hole so that the difficulty of the exercise stays the same. Although the difficulty is the same as in our previous experiment, the complexity has risen as now there are two options. And this proves that there is a difference between the difficulty of the execution of the decision and the complexity of the decision itself.

Of course we can continue to create more holes in the goal to increase complexity. Or we can remove all the planks and put a goalkeeper in the goal instead. Suddenly, a whole lot more options are available, complexity has risen, but it has also become easier to score. Some players will turn out to be better at handling the complexity of taking a penalty in the same way that other players will turn out to be better at executing the penalty. Ideally, you have a player in your team who is both good at dealing with the complexity of a penalty and at the execution of a penalty.

Example of complexity in football

Here is another great tweet that explains complexity:

Espacio y Tiempo pic.twitter.com/PbmzOgEAOl

— Caño Football (@CanoFootball) September 5, 2019

What is so great about it is that it explains that if you give Messi space, he also gets time to think and he becomes very dangerous. But why does he become so dangerous if he has time to think? It is because he now has more options (more variation) and time to go through these options. So the complexity for Messi rises. Lesser players might be overwhelmed by this increase in complexity. But Messi is such a good player that he uses the increased complexity to become a lot more dangerous. So this is another great example of why more space and time increase complexity.