Every method, one page each

Backing and laying, or backing every outcome across firms, so the same profit is locked in whatever happens.

Laying after backing (or backing after laying) to lock in an equal profit or loss on every outcome, known as greening up.

A rule for updating a probability when new evidence arrives, combining what you believed before with how telling the evidence is.

Why the total profit from many bets follows a bell curve, letting you put a realistic range on a season's results.

Comparing the odds you took with the final price before the off, the quickest reliable test of whether your bets have an edge.

Counting the ways outcomes can combine, used to price multiples, full-cover bets and forecast markets.

Expected value calculated with exchange commission built in, showing the true break-even price and how much edge survives.

The chance of something happening given that something else has already happened, the basis of every in-play price.

Splitting a stake across several selections so you win the same amount whichever of them wins.

The average profit or loss a bet would make if placed many times, the core test of whether a bet is worth taking.

The long-observed tendency for longshots to be overpriced relative to their real chances, and favourites to be slightly underpriced.

Turning decimal odds into the win chance the price is quoting, the first step in judging whether any bet is value.

Whether one outcome tells you anything about another, and why multiplying probabilities for linked bets can badly misprice them.

Why a real edge only shows up in your results after many bets, and how many you need before luck stops dominating.

Four ways to strip the bookmaker's margin from odds to estimate fair probabilities: proportional, Shin, power and odds-ratio.

How well betting prices already reflect all available information, and why beating a liquid exchange market is so hard.

How far a market's implied probabilities add up beyond 100%, which measures the built-in margin you pay on every bet.

Describes uncertainty about a probability, such as a strike rate, and updates cleanly as new winners and losers come in.

Gives the probability of a given number of winners from a fixed number of independent bets, ideal for checking whether results reflect skill or luck.

A Poisson model for both teams' goals together, with a shared component that lets the two scores move up and down together.

A Poisson football model with a correction for low scores and a time decay, so recent results count more than old ones.

Models the size and frequency of rare, extreme outcomes, such as your worst trading days, using only the tail of the data.

A family of waiting-time distributions for questions like when the next goal, wicket or price move will arrive.

Models positive, right-skewed quantities such as exchange prices and matched volume, where changes behave like percentages rather than fixed amounts.

Extends the binomial to more than two outcomes, such as home, draw and away, for pricing and for checking a model's results.

A count model like Poisson but with extra spread, suited to corners, cards and shots where totals vary more than Poisson allows.

The bell curve, used to price totals and margins in higher-scoring sports and to describe the spread of betting profits.

Turns win probabilities into probabilities for full finishing orders, used to price place, forecast and tricast markets in racing.

Turns an expected number of goals into the probability of 0, 1, 2 or more goals, the building block of most football pricing models.

The distribution of the difference between two Poisson counts, used to price goal handicaps and winning margins directly.

Count models that add an extra chance of zero, for markets where some zeros are structural, such as a player not starting.

A pairwise comparison model where each competitor has a strength and the chance of winning is your strength divided by the combined strength.

The standard horse racing win model: each runner gets a score, and win probabilities are each score's share of the field total.

A single number per team or player that rises after wins and falls after losses, sized by how surprising the result was.

A model that gives every shot a probability of being scored, so team and player quality can be judged on chances rather than noisy goals.

Regression models that let each input have a smooth, curved effect instead of a straight line, while staying interpretable.

A family of regressions that handle counts, probabilities and skewed data by pairing a linear score with a suitable distribution and link.

An upgrade to Elo that stores how uncertain each rating is, so new or inactive players move faster and are priced more cautiously.

Predicts a number, such as total corners or runs, as a weighted sum of inputs, fitted by minimising squared errors.

Predicts the probability of a yes/no outcome, such as a win, by passing a weighted sum of inputs through an S-shaped curve.

Two least-squares rating methods that solve for every team's strength at once, from goal margins (Massey) or wins and losses (Colley).

Regression models that treat teams, players or trainers as members of a group, shrinking small-sample estimates towards the group average.

Extensions of logistic regression that give probabilities for three or more outcomes, such as home, draw and away, summing to one.

A football rating system with separate home and away ratings per team, updated by how far the goal difference missed its prediction.

Predicts chosen percentiles of an outcome, not just the average, so you can price over/under lines when outcomes are skewed.

Adding a penalty for large coefficients so a model stops fitting noise, trading a little bias for much more reliable predictions.

Horse racing ratings that turn finishing times into a single number, adjusted for course, distance, going and beaten distance.

Models the time until an event, such as the next goal or wicket, and how match conditions speed it up or slow it down.

A Bayesian rating system that tracks each player's skill as a bell curve and updates it after each result, including team and multi-player events.

A classic forecasting model that predicts the next price move from recent moves and recent forecast errors, useful mainly for measuring bounce-back.

Blend several models' probabilities, weighting each by how well it has explained past results, instead of betting on whichever one looks best today.

Start with a sensible belief, then adjust it by exactly the right amount as each new result, price or piece of news arrives.

Spot the moment a price trend, team's form or strategy's results really shift, rather than reacting to every wobble.

Trade the gap between two linked Betfair markets, such as Over 2.5 goals and Both Teams to Score, when it stretches unusually wide.

Matched pairs of prior and data model that make Bayesian updates a matter of adding counts, ideal for fast strike-rate and goal-rate estimates.

Use the whole population of trainers, jockeys or teams to set a prior, then shrink each individual's record towards it by the right amount.

Models how price volatility clusters, so big moves are followed by more big moves, helping you size stops and stakes to current conditions.

Infer which hidden state a market or match is in, such as calm versus informed money, from the patterns you can actually observe.

Models that let teams, horses or players borrow strength from their group, shrinking noisy individual estimates towards a sensible league-wide average.

A recursive filter that separates a runner's underlying price from noisy trades, updating its estimate and its confidence every tick.

A simulation engine that draws thousands of plausible parameter values from a Bayesian model when the maths is too messy to solve directly.

The idea that a price pushed away from its fair level tends to drift back, and how to measure how fast before trading it.

The tendency of prices already moving in one direction to keep going, the logic behind following steamers and drifters on the exchange.

Average recent prices or results to strip out noise and reveal the underlying trend, at the cost of reacting a little late.

Tracks a hidden, changing quantity using a cloud of weighted guesses, coping with jumps and odd shapes that a Kalman filter cannot.

Break a price or volume series into repeating cycles to see whether any regular rhythm exists, such as the serve-by-serve swing in tennis.

Models a count that grows and shrinks one step at a time, such as the number of unmatched bets queued at a Betfair price.

Treats price moves as random steps, the baseline for judging whether a trading pattern is real or just noise.

Solves multi-step betting decisions by working backwards from the end, such as when to take a price before kick-off.

Explains why the gap between back and lay prices exists: whoever offers prices must protect themselves against better-informed traders.

Models in-play prices as slow drift plus sudden jumps, such as goals or wickets, so you can price the risk of a shock.

Estimates how much worse your average odds get when a large bet eats through several levels of the Betfair ladder.

Models a match as a series of states with fixed chances of moving between them, ideal for in-play football pricing from any score and minute.

Measures whether more unmatched money is waiting on one side of the Betfair ladder than the other, as a short-term price pressure signal.

Treats goals, trades or other events as arriving randomly at a steady average rate, so you can price what happens in the time left.

Estimates how long your unmatched Betfair bet will wait, and how likely it is to be matched, given the money queued ahead of it.

How Betfair's uneven price increments change what a one-tick move is worth in probability and in pounds across the ladder.

Measures how one-sided matched volume is, bucket by bucket, as a warning sign that informed money may be moving a market.

Compares unmatched money on each side of the ladder and summarises traded prices with a volume-weighted average price.

Simulates a market as many individual traders with simple rules, to see how prices and liquidity emerge from their behaviour.

Flags prices, volumes or results that are unusually far from normal, such as sudden steamers or suspicious markets.

Resamples your own betting record thousands of times to show how much of your profit could simply be luck.

Groups similar runners, teams or markets together without being told the answer, to reveal types and styles.

A flowchart of yes/no questions learned from data that sorts runners or matches into groups with different win rates.

Squeezes many overlapping stats into a few summary scores, cutting noise and overfitting risk before modelling.

Combines several models' probabilities, by simple averaging or a learned blend, to get a forecast better than any one alone.

Builds hundreds of small trees in sequence, each correcting the errors of the ones before, for strong tabular predictions.

Neural networks that learn from connections, such as teams that have played each other or players who share a pitch.

Predicts an outcome by finding the most similar past matches and seeing how they turned out.

Estimates probabilities by simulating an event thousands of times with random numbers and counting the outcomes.

Layers of simple weighted sums and switches that can learn complex patterns, but need lots of data and careful checking.

Turns text such as team news, press conferences and social posts into numbers a betting model can use.

Hundreds of decision trees, each trained on a random slice of data, averaged into one steadier probability.

Neural networks with a memory that read sequences, such as price ticks or in-play match events, one step at a time.

An agent learns a trading or staking policy by trial and error, chasing reward; powerful in theory, fragile in real markets.

Simulates every remaining fixture many times to price outright markets like title, top four, relegation and tournament winner.

Draws the widest possible boundary between winners and losers; needs extra calibration before its scores become usable probabilities.

Neural networks that use attention to decide which past events matter most, powering modern language models and sequence forecasting.

Measures how far your bank falls from its previous peak, and how long it takes to recover, so you know what normal pain looks like.

Staking the same amount, or the same share of bank, on every bet: simple, transparent and easy to evaluate.

Staking a fixed share of the full Kelly amount, trading a little growth for much smaller drawdowns and protection against overestimated edges.

A search method that breeds and mutates candidate strategies over many generations, powerful for messy problems but prone to overfitting.

Systematically searching for the best settings of a model or betting rule, and the serious overfitting risk that comes with it.

Sizes each bet as a fraction of your bank that maximises long-run bank growth, given your edge and the odds.

Finds the best stakes or bet selection subject to hard limits such as budget, stakes already placed and exposure, using an optimisation solver.

Splits your bank across strategies or bets to get the best balance of expected return against the size of the swings.

The probability that a run of bad results wipes out your betting bank before your edge has time to show.

Risk-adjusted performance measures: average return divided by the size of the swings, or by the size of the losing swings only.

Extends Kelly staking to several bets that are open at the same time, including several outcomes in one market.

Systems that raise stakes after losses cannot change expected value; they only swap frequent small wins for rare, bank-destroying losses.

Estimates how much you could lose on a bad day at a chosen confidence level, and the average loss when that bad day comes.

A checklist of the common ways a betting backtest overstates profit, from look-ahead data to ignored commission, and how to catch each one.

The predictable mental shortcuts that distort betting prices and bettors' own decisions, and how to test whether any of them are still exploitable.

A simple average squared error that scores how close your probability forecasts were to what actually happened. Lower is better.

Checks whether events you rate at 40% really happen about 40% of the time, the property that makes a model's probabilities safe to bet on.

A structured way to ask whether a betting record shows real skill or could easily be luck, by testing it against a no-edge assumption.

Measures uncertainty and the difference between your probabilities and the market's, and links that difference directly to how fast a Kelly bank can grow.

A scoring rule that punishes confident wrong forecasts very hard, closely tied to how a Kelly bettor's bank grows or shrinks.

Offering both back and lay prices on the exchange to earn the gap between them, while managing the risk of trading against better-informed money.

Tests whether your model adds anything beyond the Betfair price, and how much weight to give each when they disagree.

Adjusts for the fact that if you test enough betting systems, some will look profitable by pure luck.

Game theory's stable strategy mix where no player gains by changing alone, useful for pricing penalties, serves and competitive trading.

A p-value measures how surprising your record is if you had no edge; a confidence interval gives a plausible range for your true ROI.

Tests whether a betting filter or system beats chance by reshuffling results many times and seeing how often random groupings do as well.

Two ways to repair a model whose probabilities are biased, by learning a mapping from raw scores to realistic probabilities on held-out data.

Works out how many bets you need before a real edge of a given size is likely to show up clearly, before you start.

A Brier-style score for ordered outcomes such as home, draw, away, which gives credit for being close as well as being right.

Measures how well a model ranks winners above losers, regardless of whether its probabilities are accurate.

Checks a strategy after every bet, with stop rules that control false alarms and usually need fewer bets than a fixed test.

Tests a betting model as it would have been used live: train on the past, bet the next period, then roll forward.