Fantasy Premier league team optimisation

This is an attempt to optimise my fantasy football squad selection, picking an initial team and subsequent transfers. I've used data from https://github.com/vaastav/Fantasy-Premier-League/ which includes an 'xP' field, which isn't exactly what's required but is a good enough placeholder until the season starts with more accurate player predictions.

Player points prediction is probably the most technical element of a task like this. It would involve not only gathering the most common data but also searching for alternative data that could improve accuracy, such as betting odds for various markets or even something as stupid as the tweets of the player may improve accuracy. There are a number of available models currently out there, put together by people who have thought a lot more about the problem than I have, so initially this project is purely an optimisation problem based on the predicted points and any other factors useful for creating a team.

The optimisation is carried out using pulp. I'd considered converting the problem into pytorch to crunch the numbers on a GPU, but it's only taking 5 seconds or so to run over a CPU for 6 gameweeks which is fast enough for now.

Single gameweek optimisation

Here's the optimised output for the first gameweek of the 2023-24 season, based on maximising the xP value within the constraints of the game. This gives total xP of 47.1 and uses all of the 100 budget. We can see that the bench players are simply the cheapest options as they are not important when only optimising a single week.

name	pos	team	price	xP	lineup	captain	vicecaptain
Trent Alexander-Arnold	DEF	Liverpool	80	4.5	1	0	0
João Cancelo	DEF	Man City	60	4.3	1	0	0
Kieran Trippier	DEF	Newcastle	65	3.6	1	0	0
Andrew Robertson	DEF	Liverpool	65	3.6	1	0	0
Virgil van Dijk	DEF	Liverpool	60	3.4	1	0	0
Callum Wilson	FWD	Newcastle	80	3.1	1	0	0
Ederson Santana de Moraes	GK	Man City	55	5.5	1	1	0
Kevin De Bruyne	MID	Man City	105	4.9	1	0	1
Bruno Borges Fernandes	MID	Man Utd	85	3.4	1	0	0
Bukayo Saka	MID	Arsenal	85	3.4	1	0	0
Martin Ødegaard	MID	Arsenal	85	3.4	1	0	0
Andi Zeqiri	FWD	Brighton	45	1.5	0	0	0
Ellis Simms	FWD	Everton	45	0	0	0	0
Mark Gillespie	GK	Newcastle	40	1.5	0	0	0
Tyrese Francois	MID	Fulham	45	1	0	0	0

Multi gameweek optimisation

Below shows an example of the optimisation for the first 6 gameweeks of the 2023-24 season, which has a total expected points of 518. The xP is 45.4 for the first gameweek, less than the 47.1 as in the single week optimised team above. This is obviously as expected due to more consideration being made for subs that we may actually find benefit in using in order to not spend points on additional transfers.

First Gameweek Team

name	pos	team	price	xP	lineup	captain	vicecaptain
Kieran Trippier	DEF	Newcastle	65	3.6	1	0	0
Andrew Robertson	DEF	Liverpool	65	3.6	1	0	0
Pervis Estupiñán	DEF	Brighton	50	2.9	1	0	0
Raphaël Varane	DEF	Man Utd	50	2.8	1	0	0
Erling Haaland	FWD	Man City	140	5.5	1	1	0
Julián Álvarez	FWD	Man City	65	3.7	1	0	0
Alisson Ramses Becker	GK	Liverpool	55	4.5	1	0	1
Rodrigo Hernandez	MID	Man City	55	3.6	1	0	0
Bukayo Saka	MID	Arsenal	85	3.4	1	0	0
Son Heung-min	MID	Spurs	90	3	1	0	0
Solly March	MID	Brighton	65	2.8	1	0	0
Matty Cash	DEF	Aston Villa	45	1.5	0	0	0
Yoane Wissa	FWD	Brentford	60	2.1	0	0	0
Alphonse Areola	GK	West Ham	40	1	0	0	0
Bryan Mbeumo	MID	Brentford	65	2.3	0	0	0

Transfers

Gameweek	Transfers In	Transfers Out
2	Cristian Romero	Andrew Robertson
3	Destiny Udogie	Raphaël Varane
4	Darwin Núñez Ribeiro	Yoane Wissa
5	Pedro Lomba Neto	Bryan Mbeumo
6	Anthony Gordon	Solly March

Optimising based on the actual points the players scored leads the model to make far more transfers as the cost of 4 points is more than offset by the foresight of knowing the player will score more than 4 points. The selection over the first 6 gameweeks of the 2023-24 season, based on actual points scored, leads to a total of 695 points (177 more than previous) and takes 7 hits for an additional transfer.

Gameweek 1 Picks

name	pos	team	price	xP	lineup	captain	vicecaptain
Pedro Porro	DEF	TOT	5.5	4.7	1	0	0
Romero	DEF	TOT	5	4.4	1	0	0
Gvardiol	DEF	MCI	6	4.3	1	0	0
Watkins	FWD	AVL	9	5.2	1	0	0
Bowen	FWD	WHM	8	5.2	1	0	0
A.Becker	GK	LIV	5.5	3.9	1	0	0
M.Salah	MID	LIV	14.5	7.5	1	1	0
Palmer	MID	CHE	10.5	6.8	1	0	1
Mitoma	MID	BRI	6.5	4.9	1	0	0
McNeil	MID	EVE	6	4.1	1	0	0
Tielemans	MID	AVL	6	4	1	0	0
Senesi	DEF	BOU	4.5	2.3	0	0	0
Toti	DEF	WOL	4.5	2.3	0	0	0
Barnes	FWD	BUR	4.5	0.3	0	0	0
Foderingham	GK	WHM	4	0.1	0	0	0

Gameweek 2 Picks

name	pos	team	price	xP	lineup	captain	vicecaptain
Gvardiol	DEF	MCI	6	4.2	1	0	0
Senesi	DEF	BOU	4.5	4.2	1	0	0
Lacroix	DEF	CRY	5	4	1	0	0
Watkins	FWD	AVL	9	5.1	1	0	0
Bowen	FWD	WHM	8	4.4	1	0	0
A.Becker	GK	LIV	5.5	3.4	1	0	0
Palmer	MID	CHE	10.5	6.1	1	1	0
M.Salah	MID	LIV	14.5	5.8	1	0	1
Mitoma	MID	BRI	6.5	4.2	1	0	0
McNeil	MID	EVE	6	4.2	1	0	0
Tielemans	MID	AVL	6	3.9	1	0	0
Toti	DEF	WOL	4.5	2.5	0	0	0
Pedro Porro	DEF	TOT	5.5	2.1	0	0	0
Barnes	FWD	BUR	4.5	0.3	0	0	0
Foderingham	GK	WHM	4	0.1	0	0	0

Gameweek 3 Picks

name	pos	team	price	xP	lineup	captain	vicecaptain
Pedro Porro	DEF	TOT	5.5	3.7	1	0	0
Toti	DEF	WOL	4.5	3.7	1	0	0
Virgil	DEF	LIV	6	3.5	1	0	0
Watkins	FWD	AVL	9	5.5	1	0	1
Bowen	FWD	WHM	8	4.3	1	0	0
A.Becker	GK	LIV	5.5	3.6	1	0	0
Palmer	MID	CHE	10.5	6.8	1	1	0
M.Salah	MID	LIV	14.5	5.5	1	0	0
Tielemans	MID	AVL	6	4.2	1	0	0
Mitoma	MID	BRI	6.5	4	1	0	0
McNeil	MID	EVE	6	3.9	1	0	0
Lacroix	DEF	CRY	5	3.1	0	0	0
Senesi	DEF	BOU	4.5	2.8	0	0	0
Barnes	FWD	BUR	4.5	0.3	0	0	0
Foderingham	GK	WHM	4	0.1	0	0	0

Gameweek 4 Picks

name	pos	team	price	xP	lineup	captain	vicecaptain
Munoz	DEF	CRY	5.5	4.8	1	0	0
Lacroix	DEF	CRY	5	4.5	1	0	0
Virgil	DEF	LIV	6	4.4	1	0	0
Bowen	FWD	WHM	8	4.7	1	0	0
Watkins	FWD	AVL	9	4.6	1	0	0
A.Becker	GK	LIV	5.5	4.2	1	0	0
M.Salah	MID	LIV	14.5	7.7	1	1	0
Palmer	MID	CHE	10.5	6.2	1	0	1
Mitoma	MID	BRI	6.5	4.2	1	0	0
McNeil	MID	EVE	6	4.1	1	0	0
Tielemans	MID	AVL	6	3.8	1	0	0
Senesi	DEF	BOU	4.5	3.4	0	0	0
Toti	DEF	WOL	4.5	2.3	0	0	0
Barnes	FWD	BUR	4.5	0.3	0	0	0
Foderingham	GK	WHM	4	0.1	0	0	0

Gameweek 5 Picks

name	pos	team	price	xP	lineup	captain	vicecaptain
Virgil	DEF	LIV	6	4.5	1	0	0
Milenkovic	DEF	Nott'm Forest	5.5	3.8	1	0	0
Toti	DEF	WOL	4.5	3.6	1	0	0
Lacroix	DEF	CRY	5	3.5	1	0	0
Watkins	FWD	AVL	9	5.8	1	0	1
Bowen	FWD	WHM	8	4.8	1	0	0
A.Becker	GK	LIV	5.5	4.3	1	0	0
M.Salah	MID	LIV	14.5	7.1	1	1	0
Palmer	MID	CHE	10.5	5.4	1	0	0
Mitoma	MID	BRI	6.5	4.6	1	0	0
Tielemans	MID	AVL	6	4.3	1	0	0
Senesi	DEF	BOU	4.5	3.1	0	0	0
Barnes	FWD	BUR	4.5	0.3	0	0	0
Foderingham	GK	WHM	4	0.1	0	0	0
McNeil	MID	EVE	6	3.2	0	0	0

Gameweek 6 Picks

name	pos	team	price	xP	lineup	captain	vicecaptain
Gvardiol	DEF	MCI	6	5.3	1	0	0
Milenkovic	DEF	Nott'm Forest	5.5	4.4	1	0	0
Senesi	DEF	BOU	4.5	3.3	1	0	0
Watkins	FWD	AVL	9	5.5	1	0	0
Bowen	FWD	WHM	8	4.1	1	0	0
A.Becker	GK	LIV	5.5	3.8	1	0	0
Palmer	MID	CHE	10.5	6.6	1	1	0
M.Salah	MID	LIV	14.5	6.2	1	0	1
McNeil	MID	EVE	6	4.4	1	0	0
Tielemans	MID	AVL	6	4.1	1	0	0
Mitoma	MID	BRI	6.5	3.7	1	0	0
Lacroix	DEF	CRY	5	3	0	0	0
Toti	DEF	WOL	4.5	2.5	0	0	0
Barnes	FWD	BUR	4.5	0.3	0	0	0
Foderingham	GK	WHM	4	0.1	0	0	0

Transfers Summary

Gameweek	Transfers In	Transfers Out
2	Lacroix	Romero
3	Virgil	Gvardiol
4	Munoz	Pedro Porro
5	Milenkovic	Munoz
6	Gvardiol	Virgil