On FPL, Optimization, and Ownership Weights

By Sertalp B. Cay | December 9, 2020

Robert Cialdini mentions scarcity as one of the 6 principles of persuasion. The nature of seeking something of great interest is embedded inside all of us. Our first reaction when we see other people do something is to follow them. Even though it does not make too much sense, we follow the herd even in a competitive game, like Fantasy Premier League.

Last week’s (GW11) unfortunate gold rush to Jota proved that we fear being left out. Of course the potential price changes further trigger and support our knee-jerk reactions, however it is important to separate what we want to do and feel forced to do.

This topic is of great interest to me right now, because I am at the other end of the spectrum: I am religiously following the results of my optimization model this season. Up until now, I never thought of including what other people are doing into my model, but it suddenly made sense to me. Perhaps our cognitive tendencies have something that I can benefit even in a purely mathematical model.

Analytics in FPL

Photo by Vlada Karpovich from Pexels

Analytics is once seen as an evil in sports. Many sports unwillingly embraced the edge analytics and data bring. Soccer/Football is still behind this transformation.1

As a fantasy sports leg of the puzzle, FPL is closely involved with data. The difficult part of FPL is the vast number of decisions you can give. Currently there are over 600 soccer players and an abundant volume of data available about each of them. You might be skeptical about whether analytics and data alone can solve the problem of decision-making each week in FPL. It depends how you look at it, but I do not think analytics and data have all the answers. However, they pave the road for well informed decisions like many sectors have been using for years.

Many of the managers are well aware of how to use basic tools and follow fixture difficulty ratings. After many hours of work, most of the time we end up with a prediction of what will happen next gameweek, however it might be away from the fact. Then, the question becomes: given this information, what is my best strategy? It is easy get overwhelmed with decisions, hence oversimplifying the most important step of the puzzle: decision-making. Unfortunately, neither statistics nor Machine Learning are decision making tools. They are called descriptive and predictive analytics tools, respectively. The last step of the analytics is what we call prescriptive, and the most common tool for this step is optimization.

MADS (Math-as-Decision-Support)

Before we go back to our original discussion about joining the bandwagons, let us define a simple problem to see why optimization is a great decision support tool you should be using. Using FPL Review’s estimated values for GW12 (as of 2020-12-08), let us try to pick 4 midfield players under a certain budget to maximize our expected FPL points.

Expected points of midfield players this GW are as follows:

idnameteam_nameselected_by_percentpricexP
254SalahLiverpool32.212.37.732
4AubameyangArsenal9.411.55.86
251ManéLiverpool9.5125.808
272De BruyneMan City24.111.84.975
390SonSpurs58.59.54.893
468JotaLiverpool29.874.69
276SterlingMan City411.44.479
370Ward-ProwseSouthampton13.56.24.171
500HavertzChelsea3.38.34.033
469PodenceWolves3.45.44.032
231MaddisonLeicester2.773.988
37GrealishAston Villa38.97.73.958
275MahrezMan City9.18.43.937
570RaphinhaLeeds0.55.43.89
198KlichLeeds5.45.53.879
478WillianArsenal3.77.63.83
306RashfordMan Utd6.19.43.813
119PulisicChelsea2.18.23.79
302FernandesMan Utd4110.93.78
474NetoWolves4.75.63.765
120MountChelsea4.96.83.764
508RodríguezEverton22.27.73.761
203HarrisonLeeds1.35.43.488
465TraoréWolves6.36.23.471
24SakaArsenal2.45.23.367
69TrossardBrighton0.95.93.322
321ShelveyNewcastle0.15.33.305
141ZahaCrystal Palace16.87.43.235
445BowenWest Ham2.66.33.225
368ArmstrongSouthampton0.75.53.223
228TielemansLeicester2.96.43.095
57GroßBrighton0.35.83.009
244HendersonLiverpool15.42.98
449SoucekWest Ham3.94.92.961
466NevesWolves1.35.22.945
243WijnaldumLiverpool1.35.32.908
450FornalsWest Ham1.96.42.796
480Sean LongstaffNewcastle0.14.72.784
204PhillipsLeeds1.34.92.77
403Lo CelsoSpurs0.46.92.77
40TrézéguetAston Villa0.85.32.769
489EzeCrystal Palace0.75.82.765
100McNeilBurnley0.45.72.761
339AlmirónNewcastle0.45.62.752
113KantéChelsea3.44.92.725
446DianganaWest Brom0.35.32.696
464DendonckerWolves0.94.82.643
221AlbrightonLeicester0.15.32.626
454MoutinhoWolves1.25.22.623
396HøjbjergSpurs0.94.92.622
364Oriol RomeuSouthampton4.54.52.616
137TownsendCrystal Palace1.95.82.615
38McGinnAston Villa1.75.52.596
286RodrigoMan City0.55.42.559
360BergeSheffield Utd0.252.549
392Lucas MouraSpurs1.26.72.508
448RiceWest Ham2.54.82.5
544GallagherWest Brom0.15.52.498
89WestwoodBurnley0.45.32.486
65MarchBrighton1.352.472
253FabinhoLiverpool0.95.42.449
175CairneyFulham0.25.32.445
512DoucouréEverton1.15.32.394
355LundstramSheffield Utd2.452.384
52Douglas LuizAston Villa0.34.92.367
98BrownhillBurnley04.92.357
76BissoumaBrighton3.24.52.313
235BarnesLeicester3.96.92.27
346FleckSheffield Utd0.15.62.249
107KovacicChelsea0.35.32.202
271GündoganMan City0.35.42.19
148WalcottSouthampton0.85.82.153
315GreenwoodMan Utd2.27.12.142
133KouyatéCrystal Palace0.652.141
263JonesLiverpool0.74.42.14
555KrovinovicWest Brom052.14
159IwobiEverton0.25.92.134
382DjenepoSouthampton0.15.42.121
9XhakaArsenal0.55.22.088
236NdidiLeicester0.64.82.077
385SissokoSpurs0.54.82.064
411PhillipsWest Brom05.12.044
95BradyBurnley0.152.025
502AllanEverton0.95.31.99
400BergwijnSpurs0.471.977
130McArthurCrystal Palace0.15.31.964
413SawyersWest Brom04.81.944
261KeitaLiverpool0.25.21.939
191AnguissaFulham1.94.51.924
365RedmondSouthampton0.26.41.9
501CeballosArsenal1.14.81.87
115Loftus-CheekFulham0.25.91.832
296PogbaMan Utd1.17.71.826
309McTominayMan Utd0.34.91.818
526ElnenyArsenal1.34.41.814
485HendrickNewcastle2.44.81.809
405NdombeleSpurs0.45.91.793
540TraoréAston Villa05.91.783
557LookmanFulham0.651.753
225PraetLeicester0.45.51.695
205CostaLeeds4.95.41.646
187CavaleiroFulham0.15.31.633
142SchluppCrystal Palace0.15.41.601
349NorwoodSheffield Utd0.24.71.584
138MilivojevicCrystal Palace0.25.61.583
299FredMan Utd0.25.31.52
543BaleSpurs0.59.41.473
373ReedFulham0.64.41.403
290MataMan Utd0.25.91.388
190KamaraFulham04.81.368
424BurkeSheffield Utd1.24.31.361
106BarkleyAston Villa1.65.91.357
409LivermoreWest Brom0.14.81.336
33HourihaneAston Villa0.161.313
322RitchieNewcastle04.91.31
284FodenMan City5.26.41.307
336HaydenNewcastle0.14.81.297
150SigurdssonEverton0.86.81.272
497MurphyNewcastle0.14.91.27
281Bernardo SilvaMan City0.57.41.262
427NobleWest Ham0.44.71.253
518MendyLeicester3.14.51.228
144RiedewaldCrystal Palace1.94.41.215
71JahanbakhshBrighton05.41.2
287TorresMan City1.96.91.161
80Mac AllisterBrighton05.31.138
20WillockArsenal0.14.81.103
149DelphEverton04.91.079
229PérezLeicester0.861.061
439LanziniWest Ham0.16.41.019
495van de BeekMan Utd1.76.71.011
105JorginhoChelsea6.550.985
493LeminaFulham0.34.50.94
45El GhaziAston Villa0.15.70.882
21NelsonArsenal05.20.853
258MinaminoLiverpool0.160.824
206RobertsLeeds0.14.80.82
541ÜnderLeicester0.15.90.808
295MaticMan Utd0.24.80.725
131McCarthyCrystal Palace1.24.40.694
436YarmolenkoWest Ham0.15.60.658
90GudmundssonBurnley05.40.612
158André GomesEverton0.35.40.589
356OsbornSheffield Utd04.80.578
507FraserNewcastle0.25.60.555
338Saint-MaximinNewcastle4.25.20.498
587BenrahmaWest Ham0.260.473
79AlzateBrighton0.74.40.459
567ParteyArsenal0.550.447
209Poveda-OcampoLeeds0.44.40.447
55StephensBurnley5.34.30.434
565DialloSouthampton04.50.355
515VitinhaWolves04.80.338
154BernardEverton0.15.80.336
180KebanoFulham04.80.333
535BensonBurnley04.50.307
394AlliSpurs0.67.40.301
428SnodgrassWest Ham0.15.70.292
163DaviesEverton0.15.30.275
421EdwardsWest Brom04.80.275
311JamesMan Utd0.26.20.204
124GilmourChelsea0.14.40.196
44NakambaAston Villa0.44.30.189
397WinksSpurs0.15.20.167
550MolumbyBrighton04.50.136
122Hudson-OdoiChelsea0.25.70.113
554RamseyAston Villa0.14.50.108
59PröpperBrighton04.80.104
581OtasowieWolves04.50.103
423FieldWest Brom04.80.102
410GrosickiWest Brom05.30.091
72IzquierdoBrighton05.50.088
379SmallboneSouthampton0.24.50.087
553ShabaniWolves04.50.086
23Smith RoweArsenal0.24.40.082
143MeyerCrystal Palace04.70.074
551GoodridgeBurnley04.50.071
426HarperWest Brom0.54.40.035

For a second assume that we have wildcard enabled, and trying to pick 4 out of these 179 feasible midfields. Under a budget of £28M, could you spot the best pick that will maximize your expected points (xP)?

The correct answer is:

Salah (12.3M), Podence (5.4M), Raphinha (5.4M), Soucek (4.9M)

The total xP? It is 18.61.

Well, with a limited budget this is what we can do best. I dare you to give it a try, but this is the true optimal solution under £28M.2

Somehow, it feels weird, right?

  • Raphinha (5.4M) has an xP of 3.89, but only selected by only 0.5% of all managers.
  • Rodríguez (7.7M) has an xP of 3.76, but selected by 22.2% of all managers.3

Total ownership ratio of these 4 players is 40%, with Salah dominating with 32.2% alone.

The picture changes as you would expect when we have more money to spare.

BudgetTotal xPPlayers
£24M16.783Jota, Ward-Prowse, Podence, Raphinha
£28M18.615Salah, Podence, Raphinha, Soucek
£32M20.625Salah, Jota, Ward-Prowse, Podence
£36M21.795Salah, Aubameyang, Ward-Prowse, Podence
£40M22.656Salah, Aubameyang, Son, Ward-Prowse
£44M24.090Salah, Mane, Aubameyang, Jota
£48M24.375Salah, Mane, De Bruyne, Aubameyang

Combining Math and Intuition

Analytics methods, including optimization, become powerful weapons at the hands of an expert. If you have an intuition about a particular subject, say FPL, then running these kind of analysis can only make you a better manager. Too often we have to simplify our decisions to “should I buy X and Y, or Z and W?” in the game. There are too many options out there, and we are trying to reduce our options to 2 or 3 when giving a final decision. Often, this is what happens when you are making other decisions, like buying a car or choosing a new phone, too. Since it is much better to use the correct tool at correct task, optimization can help us to find hidden insights.

Let me go back to the original discussion. What if there is something other managers know and you don’t?

Suppose you are running an optimization already like I mentioned, but do not think Aubameyang is the right choice when you have only £36M to spend on 4 midfield players. Why is that? It is possible that you share the feelings of 91% of managers: perhaps other popular assets worth more in your opinion despite what numbers tell you.

It is indeed quite easy to involve the common belief of other 7 million FPL managers into your own optimization model. The original objective was simply this:

$$ \sum_{e \in E} \text{pick}_e \cdot \text{xP}_e $$

Here, E is the set of all players (elements), pick is a binary value, either takes 1 or 0, depending on you do or do not have the player, respectively. xP is the expected points of players. This sum gives you the total objective I have mentioned above.

Assume that you are playing against a single person (consider your mini league, for example). You can calculate the points difference as

$$ \sum_{e \in E} \text{pick}_e \cdot \text{xP}_e - \sum_{e \in E} \text{opp}_e \cdot \text{xP}_e$$

In this one, denote opp as a binary multiplier whether your opponent has the player e or not.

For a second, assume all FPL managers are united against you! Imagine them as single boss you need to defeat :) The objective can now be written as

$$ \sum_{e \in E} \text{pick}_e \cdot \text{xP}_e - \sum_{e \in E}(1-\text{pick}_e) \cdot \text{own}_e \cdot \text{xP}_e$$

The second term here becomes how much you are being penalized compared to other players. Here, own is the percentage ownership of a player. At the extreme, if no one has a particular player, then you cannot lose anything by not choosing him. At the other extreme, if everyone has a player and you don’t, you are going to be at a disadvantage as much as xP of that particular player.4

Deciding strategy

The final piece of the puzzle is to re-running optimization model with this objective. This means that the optimization algorithm will bring you closer to what is called template as much as possible.

Instead of running it directly, let us put a weight parameter for how much you believe other managers know the game.

  • Weight=0 means that you don’t value other manager’s picks at all, so you have no faith on others.
  • Weight=1 means that you value their opinions as much as your predictions for this week.
  • A significantly higher value means you value their opinions more than your own predictions for the week. You can play the GW really aggressive (weight=0) or really passive and safe (weight >> 1)5

Here is how the optimal solution changes:

On the other side of the coin, our squad gets closer to the “template”. This means our decision is more “passive” as we will less likely to get affected by wild swings.

Right at this point is where your expertise should come into play. Depending on your current rank, you might want to play it safe, and go for a moderate or very passive approach. Instead of overall ownership, you can use ownership ratios of top 1000 players, or your FPL mini-league, depending on what you are trying to achieve. If you are in need for a good jump in your rank, you can take the risk and pick the “differentials”. Of course if you fall, you might fall hard.


If you are going to remember 2 things from this post, remember these:

  1. Optimization is a great tool that you should have under your belt to gain an edge in FPL.
  2. It is not surprising that more budget gives you more freedom, hence expected points. However, it is equally important to trust your own instincts. As you get closer to template, you are playing it safe, meaning that you will probably stuck with your current rank.

What’s next?

While you are here, let me point out that I’m keeping a website for those wondering what is at the end of the spectrum. “FPL Optimized” (as I call it) gives you the best 11 and squad picks for the week, purely on expected points from FPL Review, updated every day:

https://sertalpbilal.github.io/fpl_optimized/

A final note: Quite a bit number of FPL websites claim they do “optimization”, but most of the time they are simplifying and approximating without actual mathematical optimization behind, as it tends to be computationally expensive. If FPL community is interested, next time I can write about ways to run mathematical optimization on tools you commonly use, such as MS Excel or Python with open-source packages.

Until next time, I wish all of you luck!


  1. I’m reading Chris Anderson and David Sally’s book “The Number Game” nowadays. It is a great book that I strongly suggest. ↩︎

  2. I have the optimization formulation available for this simple problem. Reach out to me if you are interested. ↩︎

  3. Of course Rodríguez’s upcoming GW points are better, which could explain the higher pick rate. Still, 0.5% vs 22.2% is a huge difference. ↩︎

  4. Here, we are using what is known as multi-objective optimization. We are combining two different objectives into a single one. ↩︎

  5. You can also choose a negative weight, meaning that you think everyone is wrong! Might be a good way to differentiate your team from others actively. High risk / high reward. ↩︎