# Optimized XI for 18/19 season

A basic idea of FPL is to pick a team that will score the most points through the season. Because of many constraints, we have to deal with, it is not as simply as it sounds. Apart from constraints, there are many risk factors and uncertainties which make our decision-making process difficult as we try to “predict” and evaluate future points for many players.

In this process, historical data about players points are very useful, and such an ex post analysis helps us to understand, which players we should have picked, which formation we should have used and so on. We can learn from this information and avoid similar mistakes in the future. And if we look at historical data, we can use some optimization techniques to solve what team would have scored the most points in some time period. Many people are using metric called points per million when they try to pick the best team, but I am not really fan of this metric because it does not really show how player’s points contribute to the global optima.

I used a genetic algorithm (optimization technique which is able to find global optimum of almost every optimization problem) and found a team that scored the most points in the 2018/19 season. My model respected all FPL constraints and was based on players prices from the beginning of the 18/19 season. It maximized points for a team of 11 players within the budget of 82,5m, which allowed to have bench of players that costed 4m/4,5m/4,5m/4,5m. To make it simple, I did not consider transfers, autosubs, chips, injuries and captain changes, so only one player was a captain for the whole season in this optimal team.

And here is the solution. If you had selected this team at the beginning of the 18/19 season, it would have scored 2469 points without autosubs and only with one captain. It would have been enough to be in top 900 at the end of the season.

## Goalkeeper

First, Alisson is not the goalkeeper because there are another 3 Liverpool players, otherwise he would be in the goal. So, we can see that optimal team consists of premium goalkeeper and not some 4,5m one. There is a first difference between selecting GK based on points per million metric and this optimization technique. Many people select a 4,5m goalkeeper because of the higher value (points per million) he offers. In the 18/19 season the highest scoring 4,5m goalkeeper was Etheridge with 154 points and value 34,22 points per million. Ederson’s value was “just” 30,73 points per million but as we can see, Ederson’s 169 points (despite his 5,5m price tag) made better points contribution to optimum than Etheridge’s 154 points. But this really depends on how the rest of the optimal team looks like. A lesson learned from this is that we shouldn’t make our decisions on goalkeepers only on points per million metric and we should always see a bigger picture.

## Defenders

It is not a surprise to see that at the back, there are three from top four scoring defenders of the season. There are no 4,5m or 5,0m million defenders because their points did not contribute to the points scored by the optimal team enough.

## Midfielders

Big at midfield. In last couple of years, the top scoring player was always a midfielder. It is clear that this is a area that offers a large amount of points and the algorithm recognized it. It shows us that we shouldn’t ignore expensive midfielders and despite their price, they are worthy. There were plenty of discussions about Mo Salah and his price tag throughout the last season. Nevertheless, he is here in the optimal team and with an armband. A captaincy is a huge factor when it comes to selecting the most expensive player in the game.

## Forwards

Just Jimenez and Wilson. No Aguero, Aubameyang, Lacazette, Firmino… They were expensive and they just didn’t score enough points to be there. Expensive defenders and midfielders were performing much better than them and it is something to have in mind at the beginning of the new season. After all, Robertson and Van Dijk outscored golden boot winner Aubameyang when it comes to FPL points.

## Comparison with points per million value

Now let’s compare the result with a value (points per million) metric. There is a list of 50 most valuable players from the 18/19 season (value is calculated as total points divided by player’s price from the beginning of the season).

 web_name cost_start total_points value Alexander-Arnold 5 185 37 Robertson 6 213 35,5 van Dijk 6 208 34,66667 Etheridge 4,5 154 34,22222 Fraser 5,5 181 32,90909 Jiménez 5,5 181 32,90909 Pickford 5 161 32,2 Laporte 5,5 177 32,18182 Alisson 5,5 176 32 Doherty 4,5 144 32 Fabianski 4,5 143 31,77778 Digne 5 158 31,6 Ederson 5,5 169 30,72727 Wan-Bissaka 4 120 30 David Luiz 5,5 164 29,81818 Pereira 5 146 29,2 Foster 4,5 129 28,66667 Wilson 6 168 28 Boly 4,5 120 26,66667 Lloris 5,5 145 26,36364 Patrício 4,5 118 26,22222 Dubravka 5 131 26,2 Kepa 5,5 142 25,81818 Keane 5 129 25,8 Duffy 4,5 115 25,55556 Milivojevic 6,5 166 25,53846 van Aanholt 5,5 140 25,45455 Redmond 5,5 137 24,90909 Alonso 6,5 161 24,76923 Westwood 4,5 111 24,66667 Rondón 6 148 24,66667 Brooks 5 123 24,6 Mané 9,5 231 24,31579 Azpilicueta 6,5 158 24,30769 Sigurdsson 7,5 182 24,26667 McArthur 5 121 24,2 Deulofeu 5,5 133 24,18182 Aké 5 120 24 Schmeichel 5 120 24 Chilwell 5 118 23,6 Camarasa 4,5 106 23,55556 Richarlison 6,5 153 23,53846 Kanté 5 116 23,2 Ryan 4,5 104 23,11111 Walker 6,5 150 23,07692 Jonny 4,5 103 22,88889 Coleman 5,5 125 22,72727 Hazard 10,5 238 22,66667 Townsend 6 135 22,5 Zouma 5 112 22,4

Players in green got also to the optimal team based on the genetic algorithm. Top value player in the last season was Alexander-Arnold with value 37. He had better value than other three Liverpool players which got to the optimal team and yet, despite his price, his total points scored was not enough to be there instead of one of his teammates. First places of the value table are full of defenders, but the algorithm found that formation that maximized points in last season had just three at the back.

Neither Etheridge’s or Pickford’s value was enough to get there and Ederson was the goalkeeper with the best points contribution to the maximum points scored by the optimal team.

Fraser, Jimenez and Wilson were the most valuable players in their positions and they also got to the optimal team, so in this case the value table had a right insight.

When it comes to midfielders other than Fraser, there were five more valuable midfielders than Sigurdsson: Milivojevič, Redmond, Westwood, Brooks and Mané. Unlike Sigy, neither of them got to the optimal team.

The likes of Camarasa or Kanté offered better value than Hazard, Sterling or Salah. Nevertheless, Salah, Sterling and Hazard made better contribution to the total points scored by the optimal team.

I did not mean to criticize the value – points per million matric. Great on this matric is that it helps us to identify unicorns in the midfield or attack like Fraser and Jimenez. I think we should be careful when we judge other players by their value because it could be misleading and we should always look at the bigger picture and consider player point’s contribution or captaincy factor.

## Lessons learned.

1. In the 18/19 season, selecting the optimal team from the beginning of the season would not have been enough to win the FPL, but enough to be around top 1k. Transfers and captaincy changes were key in winning it.
2. Unlike expensive forwards, expensive defenders and goalkeepers were worth the money.
3. Don’t be misled by the value – points per million and always look at the bigger picture and other factors.

Fantasy Football enthusiast with two top 1k finishes in FPL. Best FPL overall rank: 119th in 2019/20 season. Five top 500 finishes in UCL Fantasy, best overall rank: 23rd in 2018/19 season. Founder of Fantasy Football Reports.