The method

The best wildcard squad, priced by the market

A wildcard is fifteen decisions that all touch each other: every pound on one player is a pound off another, every third pick from one club locks that club shut. Humans juggle this with rules of thumb. It is actually a small, well-defined optimisation problem — and it can be solved exactly.

The problem, stated properly

Choose fifteen players and eleven starters to maximise the starting eleven’s expected points, subject to the rules everyone knows: two goalkeepers, five defenders, five midfielders, three forwards; the budget; at most three per club; a legal formation on the pitch. The expected points come from this weekend’s match prices — de-vigged, fitted to a goal model, joined to each player’s share of his team’s output — so the objective is the market’s read, not last month’s form table.

Note what the objective is not: the sum of all fifteen. Value belongs with players who play. Maximise all fifteen equally and the solver buys a handsome bench that scores in theory and sits in practice. Maximise the eleven and the bench goes deliberately cheap — enablers, chosen so the budget flows to the pitch. That is not a shortcut; it is the correct objective.

Why exact beats eyeballing

The tool solves the problem as an integer program — the mathematician’s name for “pick the best combination when the choices constrain each other” — and returns a squad that is provably the best available for the prices entered, not a good-looking one. The interesting output is often not the stars (you could name those yourself) but the structure: which price bands the budget settles into, which cheap defender the market quietly rates, where the third-club slot goes. Eyeballing gets the stars right and the structure wrong.

Why this is a chip-week tool

The engine reads this weekend’s prices and deliberately nothing further — one gameweek is where the market is sharp, so one gameweek is the tool’s whole horizon. For week-to-week management that would be the wrong lens; you hold players across months. But on a wildcard or free hit you are rebuilding the lot and the question really is “what is the best squad for right now” — the one week the engine can honestly see is exactly the week you care about. Frame it as the chip tool and the horizon problem disappears.

Practical corollary: run it close to the deadline, when the prices have digested the team news, rather than on Tuesday.

The honest caveats

Exact optimisation, soft inputs: minutes and shares come from FPL history, and a model fed a wrong starter’s minutes will confidently optimise around the error. Availability uses FPL’s flags, which lag the news by hours. And the output re-expresses what the market thinks — it will not find you a player the market hasn’t priced. Treat the squad as the market’s answer, check the line-ups like everyone else, and overrule it where you actually know better.

Build the market’s squad