How the model works

Most “value” tools work by stripping the margin out of a sharp bookmaker’s odds and calling what remains the true probability. That works where sharp books make real markets — but sharp books barely price fouls, tackles or cards. On player props there is no reliable market to borrow a probability from, so this product builds its own: a statistical projection for each player in each fixture, fitted on 120,409 completed player-match performances.

The same fact is why these markets are worth pricing. Books lean on season averages and recent form for props, adjust thinly for referee and opponent, and the result is the softest prices on the board. A model that measures what they skip is the entire bet this product is making.

Fouls, tackles and shots are counts, and player counts are streakier than a simple average suggests — the technical term is overdispersed. The model fits a negative binomial distribution per market, which carries a dispersion parameter for exactly that. The obvious simpler choice, Poisson, systematically underprices the extremes — and the extremes are where over bets live.

The negative binomial also earns its keep on minutes: it is a Gamma-mixed Poisson, so scaling the mean to a player’s expected minutes leaves the dispersion structure intact — a 60-minute projection is the same distribution at reduced exposure, not a different model. That property is what makes minutes-scaling legitimate rather than convenient.

The output is not one number but the full distribution: the probability of exactly 0, 1, 2, 3+ fouls. That is what the distribution ladders on the match pages show, and the probability of clearing a line is read straight off it. Where a line falls inside the ladder’s open tail and the split cannot be read honestly, the site shows a dash rather than an invented number.

A player averaging 1.4 fouls over his last five matches has told you almost nothing — at that sample size the measurement error swamps the signal. The market over-weights exactly this kind of streak, and that is a large part of why prop prices are soft. A model that chased the same streaks would have no edge by construction.

Instead, each player’s rate is estimated by empirical Bayes shrinkage: his observed rate is blended with a prior built from players in his position and league, weighted by how much evidence he has personally supplied. How strong that pull is — the prior weight — is fitted per market by cross-validation, not guessed, and the fitted values tell their own story: a goalkeeper’s save count shrinks hardest because it is mostly the opponent’s shot volume wearing his name.

Last-5 and last-10 figures are still shown across the site, because you expect to see them — always next to the season rate, so you can see when a streak is just a streak.

No rate survives a player who is substituted at half time. Every projection is built on expected minutes, and the site is explicit about how sure it is: confirmed once the lineup is out an hour before kickoff, expected when a probable lineup exists, provisional when neither does and minutes come from historical start rates.

Minutes are not one number. A rotation player’s match is a 78-minute start or a 20-minute cameo — almost never the 45-minute average of the two — so the projection is priced as a mixture of those two scenarios, each with its own distribution, rather than one distribution at the blended minutes. The blend has the same average and the wrong shape: too much weight on middling counts, too little on the tails, and the tails are where over bets live.

The mixture is also conditional on the player taking part. UK books void player props when a player takes no part in the match — stake returned, not lost — so the honest price for the bet is the probability given that he plays. Averaging in no-shows would price a refund as a loss and understate every rotation player.

Provisional is not a small print — it changes the rules. A provisional edge must clear a 10% bar where a confirmed-lineup edge clears 4%, because publishing uncertainty at the same threshold as knowledge would be pretending the difference away.

The model’s probability becomes a fair price (1 divided by the probability), and the edge is how far the book’s price beats it. Stakes are quarter Kelly capped at 2.5% of bankroll — never full Kelly, which is ruinous the moment the model is even slightly wrong, and every model is slightly wrong.

Per-bet sizing is not the whole story, because edges arrive in correlated clusters. A strict referee lifts every fouls projection in his match at once — if that spills six edges onto the board, they are one opinion wearing six names, and staking each as if it stood alone would put six independent-looking bets on a single judgement. So advised stakes are capped across correlated groups: all edges in one match share a 5%-of-bankroll budget, and all edges under one referee share 7.5% — measured across every fixture in the multi-day publication window, not within one match, since an official can take two matches in it. Inside a single match the 5% cap is the one that binds; the referee cap exists for the window, where two of one official’s matches could otherwise carry 10% of a bankroll on a single judgement about him. Stake figures live in the bankroll calculator and the downloadable record — a tool you point at your own bankroll, not advice printed beside a pick.

Whether an edge is published is a separate question with its own gates — minimum edge by confidence, sample floors, price freshness, sanity checks against other books, and a verified settlement rule per bookmaker. The full list is on the value board, and every rejection is logged with its reason.

Everything above prices player events. The match predictions come from a different model built for a different question: each league gets a Dixon-Coles goals model — an attack and a defence strength per team, a home advantage, and a correction for the low-scoring results that plain independence gets wrong — fitted with recent matches weighted more heavily, the weighting itself chosen by cross-validation rather than picked.

Multiplying the two sides’ expected goals through that model gives a probability for every scoreline, and those sum to the win, draw, both-teams-to-score and over/under figures on the cards. The headline number is each side’s expected goals because that is the model’s actual output; the “most likely score” is shown with its probability attached because even the likeliest football scoreline is a roughly one-in-eight event — a 1–1 or 1–0 favourite is a property of how goals distribute, not a hedge.

It faces the same discipline as the player models: it only renders after beating a naive baseline on held-out matches and calibrating within tolerance, and a side that changed division this summer is marked provisional — promoted teams enter at a deliberately below-average prior, relegated teams carry their old league’s strength translated down by a backtested gap, and real matches replace both within weeks.

Player prop markets are soft because they are small. The same thinness that leaves mispriced fouls lines on the board also means a line can move off a few hundred pounds of action. An edge published here is finite: take it, and you are part of what closes it. If this record ever has many readers, the closing line will start moving toward our fair price faster — which the CLV record would score as success, and which also shrinks what is left for the next reader. Both things are true at once.

And bookmakers limit winners. Soft books stay soft by restricting accounts that beat them, not by getting sharper — expect stake limits on these markets if you follow published edges and win, measured in months, not years. That is their business model working as designed, not a malfunction. Spreading across books extends the runway; nothing extends it indefinitely.

So this product scales as public measurement — a model, its calls, and its closing-line record, verifiable by anyone — not as a money tap that pours faster the more people hold a cup under it. Anyone selling the second thing is describing a product that cannot exist, and the honest version of this page says so before the record starts rather than after someone asks.