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Quant Library · Markets and staking · Football

Game-State Strategy Solver

When to press and when to hold, by backward induction on the game state.

A finite-horizon Markov decision process over minute and score difference, with transition rates fitted on half-time and full-time states, solved exactly for the policy that maximises expected points.

Inputs

What it takes

3
NameTypeUnitsWhere it comes from
state ratesdictgoals per minute by leadfitted on your own match states
actionslist-press, hold, park, with their effect on both sides' rates
objective optionalstring-points, or win probability
Outputs

What it gives back

3
NameTypeUnitsNotes
policyaction per (minute, lead)-
valueexpected pointspoints
gain over holdingfloatpoints per match
Method

How it works

  1. Discretise the match into minutes and the score into a bounded lead.
  2. 2 further steps in the licensed specification
Assumptions
  • Actions change rates in the way your fit says they do, and a manager can actually execute them.
Limits
  • The gain over simply holding a balanced approach is a tenth or two of a point per match. It is real and it is small, and anyone claiming more is selling something.
Validation

What it was measured at

ok

From the fitted game-state model the Manager game plays against.

Fitted on14,504 half-time and full-time states
A side one goal downscores about 14% faster
Gain over holding0.1 to 0.2 points per match
Solutionexact backward induction
In the package
  • The full specification: inputs, method, assumptions and limits
  • The validation panel as measured on the day of purchase
  • A reference implementation extracted from the running source
  • Perpetual commercial use for one entity

Reference modules:

  • 2 module(s), named in the licensed specification and shipped in the package
Read this before you buy. The platform's own walk-forward tests say the closing line forecasts football better than these models do. What they give you is a coherent price for every market and match, before the market opens, with the band and the working attached. Any model here that has been beaten by something simpler says so in its limits, and the validation panel above is generated from the platform's result files rather than typed in.