The optimal squad,
by the numbers.

Instead of last season's points — which bake in luck, penalties and one-off hauls — we rebuild each player from their underlying rates: how many chances they create and take per 90 minutes (xG andxA), then project those onto their actual upcoming fixtures.

A Poisson model turns each opponent's defensive strength into goal and clean-sheet probabilities, and FPL's per-position scoring converts it all into an expected-points figure for the gameweeks ahead.

From an empty squad and your full budget, a linear-programming solver picks the fifteen players that maximise total xP over your chosen horizon, subject to the real FPL rules: 2 GK / 5 DEF / 5 MID / 3 FWD, at most 3 per club, and the budget. The best legal starting XI is then chosen from those fifteen.

• Players without a trustworthy sample (new signings, academy graduates, rotation players) fall back to a shrinkage-blended position average— the explainer shows how much of each rate is a player's own data.
• Promoted clubs have no top-flight defensive rating yet, so their fixtures are treated as neutral until the model has data.
• An expected-minutes discount from ownership stops fringe and backup players (who'd otherwise bank clean-sheet points for free) from crowding out nailed starters.

Bonus points, defensive-contribution points, cards, saves, own goals and penalties are left out — they don't have a clean expected counterpart in the public data. This is a v1 forward-looking model: a strong signal for drafting, not a crystal ball.