I've updated the my Player Ratings model to show football players' potential career trajectories.

Back in 2016, I gave a presentation at the Opta Pro Forum discussing how to rate / rank footballers using a metric somewhat related to a plus/minus score. The presentation went down well with the audience and probably generated more feedback than all my other Opta Pro Forum appearances combined. A few years on, I've finally got around to refining the idea further to come up with version 2.0 of the algorithm and smooth out some of its wrinkles.

Although I've given the model a complete overhaul, the principles behind it are the same so I'm not going to repeat myself too much but the model is essentially looking at how well teams perform when a player is in the team compared when they are out of the team.

Unfortunately though, we can't just naively add up a teams goal difference with and without a specific player to calculate their plus/minus score. For example, stick an average player in Real Madrid's first team and they'd likely come out with a much better plus/minus than they would playing for Sheffield United.

So we need to account for the strength of a player's team mates and their opposition - this makes things get a bit more complicated though because to calculate the current player's score we now need to know the score of the other players around them, but to calculate those other players' scores we need to know the score of the current player. Circular!

Plus there are relatively few substitutions in football so we often don't get much data around how well teams perform with different combinations of players. To help alleviate this, the model incorporates a number of statistical priors that are used to inform the predictions where there is a lack of data.

As an example, imagine watching a footballer play for the first time - there’s a probability they may be the next Lionel Messi, there’s a probability they may be the next Lee ~~Badbuy~~ Bradbury and there’s a probability they may be average and be somewhere between the two.

This is essentially how the model works. Based on all the available data for each player, the model constructs a set of priors and uses them in conjunction with the observed data to estimate the player’s true talent compared with all the other footballers in the world. As the model gains more information about a player over the course of their career, the influence of these priors diminishes relative to the observed data.

If we calculate these scores over the course of a player's career, we can then visualise their career trajectory. As an example, here's the UK's future Prime Minister Marcus Rashford.

*Figure 1: Marcus Rashford's career trajectory to date*

The blue line shows Rashford's rating by the model over the course of his career. The scale of the rating is somewhat arbitrary as the number doesn't refer to anything specific, such as goals scored etc. Rather, it's used to compare footballers against each other and Rashford's current rating puts him comfortably in the top 200 footballers in the world. This is pretty impressive as there are currently around 100,000 players he's being compared against.

This chart is only looking at what has happened in his career so far though. Wouldn't it be more useful to get an idea about how the rest of his career is going to look?

Predicting how a player's career is going to pan out is tricky though. We have no idea about what will happen with injuries, managers, teams, transfers, motivation etc so we can't just give a single prediction. Instead, we need to provide a range of realistic possibilities that cover our uncertainty. The model does this be comparing the player with historical players to find those with the closest matching career trajectories to date.

As an example, here is Marcus Rashford again (in blue) alongside the closest matching career trajectories (in grey). Now, this isn't to say that Rashford will follow any particular one of those grey lines. All footballers are unique snowflakes and will all have their own unique career trajectory but it does give us a realistic range in which the player's career could develop.

*Figure 2: Marcus Rashford's potential career trajectories*

There's quite a wide range of potential trajectories there for Rashford, which shows how uncertain players' careers can be. At the top end, he is closest to Ivan Rakitic but at the bottom end there is Manuel Fernandes.

To be clear though, that doesn't mean Marcus Rashford and Ivan Rakitic or Manuel Fernandes are similar in how they play, but that they are similar (or could be similar) in the impact they have on their team's results.

Here's another example, this time for the in-demand Erling Braut Haaland.

*Figure 3: Erling Haaland's potential career trajectories*

We can already see that Haaland is at the upper end of all the similar trajectories, showing what a generational talent he potentially is. There are very few players who've careers have started as strongly as his so we don't have many careers to compare him with.

The most similar career is actually Mesut Özil's, who the model considers to have been one the greatest players I have data on. Again, this doesn't mean Haaland and Özil are similar in how they play, but that they are similar in the impact they have on their team's results.

At the opposite end of the career spectrum is Neymar who the model has been thoroughly unimpressed with recently. I don't follow Paris Saint Germain particularly closely but at one point Neymar was vying with Messi to be ranked the number one player in the world overall. However, it seems his impact has waned significantly over the past few years.

*Figure 4: Neymar's potential career trajectories*

And as a final example, here's Liverpool's Andrew Robertson. The reason for including Robertson is that it's a nice example showing a player that has probably reached his peak.

Although Robertson has steadily improved over the course of his career, based on the trajectories of similar players, it's likely that Liverpool will start to see him decline from here onwards. A slight positive from this though is that the expected drop off in impact looks to be fairly gradual compared with Neymar!

*Figure 5: Andrew Robertson's potential career trajectories*

This is a fairly short post just to introduce the idea of visualising players' potential career trajectories.

I'll expand on this topic in future articles but in the meantime, thanks for reading!

**hadisotudeh - July 28, 2021**

Hello,

First of all, it is a very interesting work!

How do you go about validating your plots in a way that the scout can also agree?

I also think they would like to know how the model works in a simple words, is it available somewhere?

Best,

Hadi

**Martin Eastwood - July 29, 2021**

Hi Hadi,

Thanks for the message - that's a really good question!

It's a tricky model to validate as football is quite subjective. Ask ten different scouts who the top ten players in the world are and you'll get ten slightly different answers.

I've done my own validation, which I'll continue to write up and publish on my blog but that's from more of a mathematical point of view so probably doesn't interest most scouts.

However, I've shown various iterations of this model to scouts / recruitment departments at professional teams. What has tended to get the most engagement is showing them things like who the best / worst players in their league are, who are the highest rated players aged under 21, who are the best strikers world wide, where Messi and Ronaldo rank etc.

The model also has dashboards for searching by age, position, nationality etc so I also let them have a play and then get their opinions on the results.

Thanks,

Martin

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