Maybe you have come across a FBM chart like the following on Twitter and you are curious how to read these charts:

DM request: Oscar Fraulo (2003) is a fantastic CM, a superstar in the making. You have seen me complain about CMs a lot, but Fraulo sets the standard on CMs. Maxed out finishing & passing game probability with decent defensive probability as a nice bonus. pic.twitter.com/zPixY4leYz

— Joost van der Leij (@JoostvanderLeij) May 17, 2022

What you see is the answer to the following three questions:

- What is the probability that this player is able to contribute to the finishing of his current team?
- What is the probability that this player is able to contribute to the defending of his current team?
- What is the probability that this player is able to contribute to the passing game of his current team?

These probabilities are predictive and hold for the next upcoming game. It is important to note that almost all statistics in football are backward looking and descriptive. As useful as that can be, descriptive statistics is way less useful than predictive statistics like these FBM stats. After the game these FBM probabilities are updated using Bayes Theorem. For reliable players these probabilities are consistent over time. For more unreliable players they fluctuate more. So you can use FBM statistics to determine how reliable a player is.

Finishing consists of scoring goals, giving assists and shooting on target. The probability of being able to contribute to the finishing of the current team decreases due to shots off target.

Defending consists of all actions of the player and results where the player has a contribution to said result while the opposing team is in possession of the ball. The most positive result is of course gaining possession of the ball. The probability of being able to contribute to the defending of the current team decreases due to the opposing team getting significantly closer to the goal, fouls being made or goals scored against the team.

Passing game consists of all actions of the player and results where the player has a contribution to said result while the team is in possession of the ball. This includes actions without the ball like drawing out defenders or occupying space, progressive passing, packing and the pre-assist. The probability of being able to contribute to the passing game of the current team decreases due to losing possession of the ball.

Please note that these FBM stats are for playing in their current specific team in their current specific league. We have a Bayesian transfer model to transfer players virtually to different teams and different league. All these probabilities are then adjusted for the new team and in case of a new league also for the new league.

## The distribution of probability

The graphs you see are the Poisson distribution of the underlying FBM stats for finishing, defending and passing game. Whenever you see a football statistic given as a single number be very suspicious. Reality is too complex to be captured in numbers, even if there are a whole bunch of them. In fact, the more different statistics are used, the less valuable the information becomes, because the more data you have the more you can prove. Yet, the more you can prove, the more what you prove is confirmation bias as you are going to prove what you already think you know. That is the reason why statistics should now and then shock you. Because if statistics doesn’t shock, the chance is that you use statistics to confirm your biases.

So rather than present players in single numbers, we present players as a Poisson distribution. The distribution gives you the area where the player’s probabilities will lie after the next match. Of course, given that each match only slightly moves these probabilities, if they move at all, in practice these probabilities hold for the whole season or to whenever a major change occurs, like for instance an injury, a new manager or a new team.

A new team is important, because FBM probabilities are always for a player playing for a specific team in a specific league. As soon as the player moves to a different team or even a different league, these probabilities change. We have a Bayesian transfer model that calculates how these probabilities change whenever you move a player from one team to another. Most of what we do is help clubs understand how likely it is that a potential player they like to hire is going to do well in their team.

## How to read these distributions

There is a very simple rule to reading these charts:

**The more to the right, the better. Ignore the peaks.**

Somehow our attention is being drawn to the peaks, but the peaks are a mathematical artifact of the Poisson distribution. You could say that the Poisson distribution tries to distribute 100 points around the average of the statistics. The less space the Poisson distribution has to achieve this, the higher the peak. But the less space means that the probabilities used are very low. Hence the rule to ignore the peaks and just look for what is most to the right. If you really want to know what the vertical values are: the vertical values are the probability of single column in the graph.

Graphs may overlap, so for instance in our example of Oscar Fraulo, he both maxed out on finishing and passing game probabilities and so they overlap turning the graph into some greenish blueish color to indicate that both the green and the blue chart overlap.

If we compare two players in a chart the overlapping area is quite important. Because then the overlapping area is actually the chance that the lesser player will do as good as the better player or even better! So if the graphs of two players overlap a lot, the lesser player has a decent chance of outperforming the better player in the future. Nevertheless, the better player still has the biggest chance of outperforming the lesser player.

When you want to see how one of your favorite players looks in FBM stats, please let us know on Twitter through a Tweet or a DM. Or fill in the form below to request a free sample report: