## Secondary statistic

Secondary statistics are all statistics that are used to derive the primary statistic.

## Subjectivity

Everything is subjective. Nothing is objective. People mistake high convergence for objectivity. Everything you see, hear and feel is subjective. It is your brain who creates your subjective experience. You have a Bayesian brain that creates expectations on the one hand and processes sense data on the other.

Given that everything you read and all the stories you hear, are also part of your subjective experience, there is no way to escape subjectivity. Nor is there a need to escape it. Everything you want to achieve with objectivity can be achieved with convergence.

That a ball shot in the air, falls back to the ground is not an objective truth, but only we can all agree on. So this is an example of high convergence.

That it is extremely unlikely that a ball once shot in the air, will continue to hover in the air, is again not objectively the case. It is only another example of high convergence.

That flipping a coin will have a 50% chance of heads, is not an objective truth, but again only an example of high convergence.

In every case where someone might want to use the label “objective”, in reality it only means high convergence.

But there is way less convergence on whether Manchester City is going to win the Champions League this season. So no matter whether you agree or disagree, your viewpoint is considered more subjective and less objective. In reality there is no difference to the level of subjectivity (all statements and situations are completely subjective), there is only a difference in the level of convergence.

The higher the convergence, the more people mistake that high convergence for objectivity. The lower the convergence, the more people mistake that low convergence for subjectivity. Again, in reality there is only subjectivity and high or low convergence. There is no objectivity.

## Subjectivity in football

In almost all cases there is a very high correlation between the level of convergence and whether people consider something, wrongly, subjective or objective. But this is less the case in football. Although there is very high convergence on match dates, teams involved in the match and the final outcome and result, there is way less convergence on almost everything else.

Many data providers claim to be objective. This is not the case at all, as we have seen. The best they could claim is that there is high convergence on their data. That is one of the reasons why the present themselves as objective and why they are so vigorously trying to convert people to adapt their way of looking at football. But in reality there is way less convergence about almost all their data.

Let’s look at passing. Can you objectively count all the passes in a match? No you can’t. First of all because there is no such thing as objectivity. But more importantly, to count passes you first have to define what a pass is. The easy way to see how much subjectivity there is in pass counting, is to try and define a cross pass, long pass or key pass. Depending on your definition you get a different count. Other people might disagree with your definition and thereby decreasing convergence. But even if they agree with your definition, they might disagree as which passes fall within your definitions and which fall outside of them, thereby decreasing convergence even further.

Even if you only look at simple passes there are tricky situations. Do you allow for passing to yourself? If not, would a pass to yourself then be considered a dribble? Again, all grounds for disagreement and a further decrease of convergence. Can I pass to another player by ricocheting the ball of an opponent? Would that still be counted as a pass or not? As you can see even such seemingly simple task as counting passes, leads to disagreement and a decrease of convergence.

Where passes are relatively easy, things get even more complicated when trying to count duels, interrupts or interceptions. But then we can even go to a higher level to find more disagreement by asking: is it really smart to count? Or should we weigh of judge players actions? And then we can look at a game at an even higher level and ask the question: are actions really important or do we need to look at results and player contributions to those results instead?

It doesn’t matter how you answer these questions. What matters is that within football many people come up with different answers. There is a lot of disagreement in football. That is a good thing by the way, because it makes football a very interesting activity. If we would all agree on everything than everybody would play the same and football would be much more boring. So disagreeing about these kinds of questions is a good thing! Yet, at the same time these differences also make clear how much disagreement there is and how little convergence

To sum up: everything is subjective, but our ideas about some things have a high convergence. This high convergence is often mistaken for objectivity. But in football we might even be wrong about the level of convergence. Convergence in football is much lower than some people assume. And that is a good thing: it makes football very interesting.

## System

In football there is a lot of talk about systems. But what is a system? Thinking in terms of systems started with cybernetics during World War II. Where Turing was busy inventing the digital computer that we still use today as our PCs and our phones are Turing machines, the cybernetic group tried to invent an analogue computer. Their task was to come up with a guidance system that would help anti-aircraft guns shoot down German fighter planes. The German jet fighters flew so fast that if you aimed and shot at where they were, by the time the bullet reached that spot the plane would be gone. So one needed to use probability calculations to determine the most likely spot where the plane would be and shoot at that spot so that the bullet and the plane would reach that spot at the same time.

The cyberneticians of that period tried to achieve this with chemical and natural processes that would use feedback loops. Unfortunately, they were never able to achieve this goal. But fortunately to compensate for the lack of practical progress, they made a lot of progress in information theory. Cybernetics became so successful helping organizing information systems in the fifties and sixties that more and more branches in sciences started to use cybernetics. Nowadays this has resulted in data science, cognitive science, neuroscience and philosophy (in the form of enactivism) now use cybernetics to understand their subject. See for instance Cybernetic Big Five Theory as the best explanation of the personality of players. Thinking in terms of a system is the main concept that has made cybernetics so attractive. Together with process feedback.

## What is a system according to cybernetics?

First of all you are completely free to subjectively decide what the boundaries of your system are. Once you have decided on the boundaries of the system, you would then treat the system as a black box. A black box approach means that you don’t really care what is inside the box. The only thing that you care about is how many ways you have to manipulate the system. And how these manipulations change the external behavior of the system. Once you have that down, then you can create a matrix of how the output of the system depends on changes to the input. This matrix gives you the number of variables that influence the system and the number of different values these variables can contain. Variables to the power of the number of different values these variables can have, determines the variation a system can have. The higher the variation, the higher the complexity of the system. Cybernetics has a lot to say about how much communication is possible between two systems depending on how much variation they can handle

With your system thusly defined, you can do all kinds of wonderful things. First of all, you can open the black box of your system by dividing your system into smaller systems. Now your black box has become a muddy box as you know more about what is happening inside your black box. Cyberneticians have done this all the way to the level of brain cells!

At the same time if you can divide a system into smaller subsystems, you can couple two or more systems to create a new higher level system. Again, this higher level system is not a black box, but a muddy box because you know something about what is happening inside the higher level system. Cyberenticians have used this to couple for instance coach and coachee, or a team or even a whole organization.

## How does this apply to football?

System talk is always highly abstract. So let’s see whether we can make it more concrete for football. First of all, the most obvious system we can define is the player himself. Humans are almost always considered a cybernetic system. We already know one subsystem of a player, i.e. his personality. But modern neuroscience considers the brain to be a cybernetic system.

Of course, system thinking in football is more interesting when we scale up rather than scale down. With the player as our basic system, we can then go on to define our defensive system as the coupling of the keeper and the defenders, our midfield system by coupling the defenders and our attacking system by coupling all defenders. From here it is quite a small step to go into formations.

Interesting enough, players that score high on transitioning contribution increase variation and complexity. If you combine those players with players that score high on attacking contribution so you have players that can finish the job, you increase the attacking strength of the team. As a rule of thumb you can say that higher complexity increases your chances to score, but you also increase your risk of the opposing team scoring. To lower the risk of the opposing team scoring, you decrease complexity by defending. Adding players who score high on defending contribution you are able to decrease complexity while defending, making it harder for your opponent to score. Then, once you have captured the ball, you increase complexity again in order to make it easier for your team to score. As you can see players who score high on all three contributions (attacking, defending and transitioning) are the most valuable players.

To see more applications of cybernetic systems, see the entry on feedback. There you’ll find the cyberentic cycle that describes any goal oriented system like football.

The next step in scaling up is the system becoming the whole match. At all levels a system is only cybernetic if it can be described with the cybernetic cycle. The cybernetic cycle has six steps to it:

1. Select a goal.
2. Select an action to achieve this goal.
3. Execute the selected action.
4. Interpret the results of the executed action.
5. Compare the interpreted result with the selected goal.
6. If the selected goal is achieved or achieving this goal takes too much time, go back to step 1. Otherwise, go back to step 2.

So if we take the whole match to be a system, then first goal our team selects is to win by scoring more goals. So the first action we decide to undertake is to attack. Then we actually attack. To be followed by interpreting the result of our attack. If we lose the ball we compare the result of our action with our goal. We did not achieve our goal so we select a new action to achieve our goal, which is to win the ball back. If we succeed at recapturing the ball, we still haven’t achieved our goal, so we select a new action, which is to attack again. We continue to do so until either we have won the match or not.