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A Trip Around the League: Winning at FPL with Math

Fair warning, this article is a bit math-heavy, and because you can be sure your mini-league competitors won’t read it, it’ll be your unfair advantage!

Einstein at blackboard with his equations
More FPL equations please!
Photo by Hulton Archive/Getty Images

I normally look forward to an international break with the same alacrity as, say, a commute to the office on a cool windy and rainy Tuesday morn (remember office commutes?).

This particular international break, however, is a great time to look at our FPL teams and make some changes; we now have almost enough sample size to make some important decisions and feel more confident in the data. For example, we’re now past the 37% threshold between the start of the season and the last game week deadline to use our first wild card. This means that, in this optimal stopping problem, the best time to use your wildcard is the first time it feels better than the week before. Confused? Doubtful? Rather than bore you with mathematical explanations, may I suggest you Google “37% rule” and/or “optimal stopping problem solutions”. Trust me, it’s math!

Let’s put this international break to good use! Let’s work just a bit harder and smarter than our competition to seek out those little gains that compound over a 38-game week slog.

Let us go then, you and I, on a trip around the league. For many of us, this particular trip will feel a bit like scaling Everest. It will not be easy. Most will not make it to the end. And if you do, you can expect to benefit from your accomplishment — you will have gained an unfair advantage over your mini-league opponents! My role is to serve as your Sherpa and guide you in your quest to make better decisions to achieve your FPL goals.

Our expedition has three stops and one summit. Let’s go!

First Stop: The Forwards

West Bromwich Albion v Tottenham Hotspur - Premier League
The HurriKane is the easy pick!
Photo by Tottenham Hotspur FC/Tottenham Hotspur FC via Getty Images

Our first stop in this expedition is to identify the best forwards to target for our FPL teams.

In order to do this, I propose we anchor ourselves on expected goal (xG) and assist (xA) metrics. While these two terms may be familiar to some, it is worth making sure we truly do understand what they mean (and what they don’t mean!).

Per Opta:

Expected goals (xG) measures the quality of a shot based on several variables such as assist type, shot angle and distance from goal. Whether it was a headed shot and whether it was defined as a big chance.

Adding up a player or team’s expected goals can give us an indication of how many goals a player or team should have scored on average, given the shots they have taken.

And again per Opta:

Expected assists (xA) measures the likelihood that a given pass will become a goal assist. It considers several factors including the type of pass, pass end-point and length of pass.

Adding up a player or team’s expected assists gives us an indication of how many assists a player of team should have had based on their build up and attacking play.

I like to take these two metrics one step further when trying to decide on a player to transfer in or out by removing as much randomness/luck as I can (while acknowledging that randomness and luck do play a huge role in any outcome!). This means I like to look at the xG for a player minus penalties (npxG). Further, I like to look at npxG per 90 minutes in order to make the data more consistent among all players (npxG/90).

While this still leaves some set piece randomness (like direct free kicks) in our metric, it does remove arguably the biggest statistical outlier that can skew our results. For example, a player like Jorginho could have a huge xG because each penalty is calculated at roughly .76 xG; but when you remove penalties you get, I feel, a more accurate representation of how desirable the player is as a fantasy asset (in Jorginho’s case, not very attractive). Armed with the npxG/90 metric, I then like to add xA/90 (i.e., npxG + xA/90) to get a number that tells me just how excited/not I should be about a given player in comparison to other prospective targets. Boiled down to its essence, in FPL we mostly care about two outcomes for attacking players: goals and assists.

Let’s take a look at how some of the more desirable forwards (sorted in descending order relative to FPL prices) stack up in npxG + xA/90 minutes - the higher the number the better (note: all data in this article, unless otherwise noted, is from FBref using Statsbomb data) :

Forwards: Expected Metrics

Name npxG + xA per 90
Name npxG + xA per 90
Kane 1.02
Vardy 0.59
Werner 0.47
Jesus 0.62
Jimenez 0.36
DCL 0.71
Richarlison 0.7
Abraham 0.64
Maupay 0.48
Bamford 0.72
Watkins 0.67
Adams 0.52

The data must always inform our beliefs. Despite what we may want to believe about, say, Raul Jimenez being a viable fantasy asset, a serious look at the data informs us that there are far better (and cheaper) assets to target. If we wanted to play a front three, the data tells us that the best players to target are Kane-Bamford-DCL.

While that is true at this moment, and those three are my front three, I am always going to look to optimize by replacing my weakest link with a stronger one. Remember, expected metrics change with every match! Therefore, I am constantly monitoring prospective replacements, which currently include Ollie Watkins (great fixtures to boot!), Richarlison and even Tammy Abraham (with the caveats of uncertain playing time and resulting smaller sample size).

Arsenal v Aston Villa - Premier League
If I have two good FPL FWDs, will Ollie be my third?
Photo by Visionhaus

What about penalties, you ask? Well, in Ollie Watkins’ case he does take them and adding them to his score yields an xG + xA /90 of 0.77 which could get him over the likes of Bamford and DCL (neither is their team’s designated penalty taker) in the coming game weeks. Adding in penalties can be a handy tie-breaker (e.g., Watkins v DCL; Kane v Vardy).

if you got this far, well done! Let’s keep going!

Next Stop: The Midfielders

Applying the same methodology as we did to the Forward cohort (after all, goals and assists are the same outcomes we seek for both FWD and MID assets), the midfielder data shows:

This means that Sadio Mane is the most unplayable midfielder in EPL and is thus a wonderful FPL asset to own. He is significantly outplaying his counterpart (and FPL royalty) Mo Salah in open play. The data also tells us that, despite passing the “eye test”, Harvey Barnes is overrated relative to many other midfielders (similar situation with Wolves’ Podence and Neto, by the way).

We also notice from the data that Aston Villa features two of the most promising midfielders in Jack Grealish and Ross Barkley. Given their affordable prices and wonderful upcoming fixtures, the data will forgive you if you want to double up on Villa mids and even triple up alongside Watkins!

One aside: What we don’t see in the data is a premium player I chose to ignore — Arsenal’s Pierre-Emerick Aubemeyang. Why did I leave him off the Midfield charts entirely? Because, ugh; take a look at his shot volume/90 and npxG/shot data for the past four seasons:

Now that we’re into meatier specific player analyses, let’s jump into some FPL polemic and see what the data tells us is the optimal course of action.


Salah v Mane:

Manchester City v Liverpool - Premier League
Salah or Mane is the question
Photo by Simon Stacpoole/Offside/Offside via Getty Images

The short answer is ideally we’d want both! But life being life and resources being finite we most likely must chose only one. I’ve already outed myself as a huge fan of npxG + xA as a decision-making tool. So if that is the case, why do I own Salah and not Mane? In this instance I am probably being a little irrational and, well, gambling on good luck. Let me explain:

  • Salah has shown me exceptional past performance for a few consecutive years;
  • Salah, unlike Mane, takes penalties and Liverpool is such a dominant attacking team that I want the penalty taker on the best attacking team on my side; and
  • if we factor in the xG tie-breaker (i.e., penalties) + xA /90 we get: Salah (0.98) v Mane (0.87).

Verdict: While Mane has been the better real life player, Salah is the FPL asset I still want to own.


Son - Keep or Toss:

West Bromwich Albion v Tottenham Hotspur - Premier League
Son: keep for more goals or give him the boot?
Photo by Laurence Griffiths/Getty Images

As the data shows, Son is an elite attacking midfielder. While he has blanked in his last two matches, I don’t put a lot of weight on that in my decision-making process because it is small sample size and, well, blanking is a very probable outcome for any player on any given game week. It is also true that Son’s fixtures are turning really bad and this is a real worry.

Most serious FPL managers will already own a premium mid (Salah or similar), Son, and at least one of the mid-tiers like James “Hamez” Rodriguez or Jack Grealish, so I am not going to advocate for a trade up or down to one of these assets. Rather, I am going to look at two intriguing, lower-ownership candidates: Bruno and Ziyech.

Because Son is not his team’s designated penalty taker, his npxG + xA/90 and his xG + xA/90 remain the same (0.75); same story with Ziyech (0.84 with a statistically significant smaller sample size); and Bruno, who does take penalties, shows a resultant split of npxG + xA/90 (0.37) and a xG + xA/90 (0.74).

Verdict: The data informs us that Bruno without penalties 0.37 npxG + xA) is about half the player Son is (0.75); and even with penalties (0.74) Bruno’s about equal to Son but more expensive. While Ziyech comes out ahead in this comparison (0.84) - and is cheaper than both - the small sample size is significant (Ziyech has played 191 minutes to Son’s 639). In short, I am going to keep hold of Son for at least another game week or two in order to give Ziyech’s statistics more time to mature. Bruno is not a player I am interested in at this point (but if his numbers pick up I will gladly follow the data). Worth noting: If it’s penalties you’re after, then it’s Vardy who is the cheaper and better alternative to Bruno on your FPL team!

Now, I know you’re tired and that your eyes must be glazing over. I promise we’re almost there!

Third Stop: The Defenders

When it comes to defenders we still want to focus on goals and assists as key metrics and we can also add clean sheets to the equation. Clean sheets, of course, are practically impossible to predict; a helpful shortcut is to look at what teams have statistically been the most robust based on team expected goals against metrics (xGA).

Per Understat, the five best defensive teams in xGA so far this season are 1) Chelsea; 2) Burnley; 3) Aston Villa; 4) Tottenham; 5) Brighton.

The stats tell us we want at least one or two of our defenders to come from these teams. The next step is to figure out which players we might want. For this we can apply the same metrics-driven process to figure out who the standout FPL defenders are: nxpG + xA per 90!

Defenders: Expected Metrics

Name npxG + xA per 90
Name npxG + xA per 90
Robertson 0.24
Digne 0.18
Walker 0.04
Chilwell 0.29
Reguilon 0.24
Semedo 0.11
Cancelo 0.28
Tarkowski 0.1
Tierney 0.1
Van Aanholt 0.22
Mings 0.12
Zouma 0.06
Bellerin 0.07
Cresswell 0.22
Coady 0.01
Lamptey 0.2
Ayling 0.17
Dallas 0.13
Coufal 0.08
Masuaku 0.22
Furlong 0.19
KWP 0.04

The clear leader is Ben Chilwell, while Tariq Lamptey looks a credible option given his price point, expected metrics and team defensive solidity. So that’s two of our four FPL defenders right there!

Chelsea v Sheffield United - Premier League
Run, don’t walk, to pick up Ben Chilwell!
Photo by Chris Lee - Chelsea FC/Chelsea FC via Getty Images

The big question on a lot of FPL managers minds is what to do with the Liverpool fullbacks. Unfortunately for TAA, who is apparently out injured for at least a month, half of the question has already been answered. The other half, however, is a bit more complicated. Andrew Robertson is a fantastic player and has been a fantastic FPL asset for a couple of years. But with Liverpool’s defense ravaged by injuries (we can now add Joe Gomez to the injury list alongside TAA and Virgil van Dijk), clean sheets for the Reds are at a premium. And with the emergence of Jota, it is possible (though unclear how probable) that Robbo’s role in the attacking third could be altered and diminished. Furthermore, we were all witness to the level of exhaustion exhibited by Liverpool and many Man City players in their match last game week. Tired legs are no joke!

It might not be a bad idea, then to “downgrade” Robbo’s price point to bring in a more affordable statistical facsimile such as Joao Cancelo or even Patrick Van Aanholt. While I am not quite ready to go there just yet, I am starting to think about it. My links to Robbo as an FPL asset are mathematically-based but there is some (irrational) emotion attached. Point being, there are options to step in for your Robbo-sized roster spot!

Well done dear reader for making it this far; you are elite!

The Summit:

Congratulations, you made it!

We are now at the end of our expedition. I hope it hasn’t been too onerous. We do have to make one final exertion before we are ready to enjoy the fruits of our labor.

If last season was the year of the premium defender, this year sure seems like the year of the mid-priced forward. For this reason I am playing a 3-4-3 formation.

I should note here that the math-driven and probabilistic decision-making process I described is a relatively entry-level version of what I’m working on. I should also confess to some early-season mistakes, mostly driven by an itchy transfer trigger finger and incomplete data poisoned by small sample sizes. Big failures have included owning James Ward-Prowse for every game week except his two best ones. Yes, I transferred him out before his 11 and 17 point explosions and promptly wildcarded him back in for his 3 pointer last week. I am already thinking about upgrading him to Ross Barkley.

As the data becomes more reliable and predictive, I plan on severely restricting my transfers to focus not on the shiny new toy, but on more pedestrian and utilitarian upgrades to my weakest links.

One last piece of advice before I leave you to play with the data. User beware, adjusting for “per 90 minutes” can yield some wacky results for players with very limited playing time who scored or assisted a random goal in garbage time (small sample size). For example, Leicester’s Cengiz Under who’s played all of 72 minutes and registered two assists looks like the best player on earth by the npxG + xA/90 metric!

Good luck and have fun winning with math!

Let us know how you found this article! Was it too math-heavy or not enough? If you are a regular reader of A Trip Around the League and you found this new version too much of a stylistic departure from the expected -think: Radiohead’s Kid A - I hope you can overcome your initial shock and disappointment and learn to appreciate the new! Data-driven optimized decision-making is the way forward my friends. Thank you for reading and please share your comments below!