Fantasy Football Squad Optimizer
A constrained optimization problem for selecting the best 15-player fantasy football squad under budget and formation rules.
Given a pool of football players with associated prices, expected points, and minutes played, select an optimal 15-player squad (1 GK + 14 outfield) and a starting XI under:
- A total budget of £100m
- Valid formation constraints
- A points-maximization objective
| Variable |
Description |
x[i] |
Binary — player i is in the squad (15 players) |
y[i] |
Binary — player i is in the starting XI (11 players) |
f[k] |
Binary — formation k is selected |
One formation must be chosen for the starting XI. The squad always contains 1 GK + 10 outfield players (bench included). Valid formations:
| Formation |
DEF |
MID |
ATT |
| 3-4-3 |
3 |
4 |
3 |
| 3-5-2 |
3 |
5 |
2 |
| Formation |
DEF |
MID |
ATT |
| 4-3-3 |
4 |
3 |
3 |
| 4-4-2 |
4 |
4 |
2 |
| 4-5-1 |
4 |
5 |
1 |
| Formation |
DEF |
MID |
ATT |
| 5-4-1 |
5 |
4 |
1 |
| 5-3-2 |
5 |
3 |
2 |
| 5-2-3 |
5 |
2 |
3 |
Constraint: Exactly one formation f[k] = 1 must be active.
| Position |
Min Price |
Max Price |
| GK |
£4.0m |
£5.5m |
| DEF |
£4.0m |
£6.5m |
| MID |
£4.5m |
£14.5m |
| ATT |
£4.5m |
£14.5m |
Total Budget ≤ £100m
∑ price[i] · x[i] ≤ 100
| Condition |
Points |
| ≥ 60 mins played |
+2 |
| Event |
Points |
| Clean Sheet |
+4 |
| Event |
Points |
| Clean Sheet |
+4 |
| Goal |
+6 |
| Assist |
+3 |
| Event |
Points |
| Clean Sheet |
+1 |
| Goal |
+5 |
| Assist |
+3 |
| Event |
Points |
| Goal |
+4 |
| Assist |
+3 |
| Event |
Points |
| Yellow Card |
−1 |
| Red Card |
−3 |
Maximize total expected points of the starting XI:
maximize ∑ points[i] · y[i]
Where individual player points are estimated as:
points[i] = max(bookmaker_odds_implied_pts[i], xG[i] + xA[i])
And actual realized points follow:
actual_pts[i] = base_mins_pts[i] + goals[i] + assists[i] + clean_sheet[i] - card_penalty[i]
∑ x[i] = 15 # total squad size
∑ x[i] for GK = 2 # 2 goalkeepers in squad
∑ x[i] for DEF ∈ {5} # 5 defenders in squad
∑ x[i] for MID ∈ {5} # 5 midfielders in squad
∑ x[i] for ATT ∈ {3} # 3 attackers in squad
∑ y[i] = 11 # exactly 11 starters
y[i] ≤ x[i] for all i # can only start if in squad
∑ y[i] for GK = 1 # exactly 1 GK starts
∑ f[k] = 1 # exactly one formation active
∑ y[i] for DEF = ∑ def_count[k] · f[k] # DEF starters match formation
∑ y[i] for MID = ∑ mid_count[k] · f[k] # MID starters match formation
∑ y[i] for ATT = ∑ att_count[k] · f[k] # ATT starters match formation
If mins[i] > mins[j]: y[i] ≥ y[j] (soft constraint / priority ordering)
Players with more expected minutes are preferred as starters over those with fewer.
| Property |
Value |
| Problem Class |
Mixed-Integer Linear Program (MILP) |
| Decision Vars |
Binary (x[i], y[i], f[k]) |
| Objective |
Maximize expected points |
| Key Constraints |
Budget, formation, squad structure |
| Solver Options |
PuLP, OR-Tools, Gurobi, CVXPY |
fantasy-football-optimizer/
├── data/
│ ├── players.csv # player pool with price, position, xG, xA, mins
│ └── formations.json # valid formations config
├── src/
│ ├── optimizer.py # MILP model definition
│ ├── points.py # points calculation logic
│ └── scraper.py # data ingestion (odds, xG/xA feeds)
├── notebooks/
│ └── analysis.ipynb # squad analysis & visualization
├── tests/
│ └── test_optimizer.py # unit tests
├── requirements.txt
└── README.md
git clone https://github.com/your-username/fantasy-football-optimizer
cd fantasy-football-optimizer
pip install -r requirements.txt
python src/optimizer.py --budget 100 --formation auto
pulp>=2.7
pandas>=2.0
numpy>=1.24
requests>=2.31 # for data scraping
Optimal Squad (£99.2m / £100m)
Formation: 4-3-3
GK: Flekken (£4.5m) [bench: Flaherty £4.0m]
DEF: Alexander-Arnold (£6.5m), Pedro Porro (£5.5m), ...
MID: Salah (£13.5m), Palmer (£11.5m), ...
ATT: Haaland (£14.5m), ...
Expected Points (GW): 74.3
Risk Analysis Graph:
MIT License. See LICENSE for details.
