THE STAT MAN

Three calculations the whole book rests on

Every figure below is taken from The Stat Man and recomputed here. Follow them with a calculator and you can already do the three things most bettors never do: read a price as a probability, see the margin, and build a number of your own to argue with it.

Convert a price into a probability

Every price is a claim about how often something happens. One division tells you what the claim is.

The odds Rosetta Stone: the same probability written as fractional, decimal and American odds.
Figure 2.1The odds Rosetta Stone: the same probability written as fractional, decimal and American odds.

  1. Read the price as a ratio

    Fractional odds are written a/b, so 13/8 means you win 13 for every 8 staked. The two numbers are all you need.

  2. Add both numbers together

    13 plus 8 is 21. That total represents every unit at risk in the transaction, your stake included.

  3. Divide the stake by the total

    8 divided by 21 is 0.3810. Multiply by 100 and the price 13/8 is claiming a 38.10 per cent chance.

  4. Compare it with your own number

    If you believe the outcome happens more often than 38.10 per cent of the time, the price is generous. If less, it is short. That comparison, and nothing else, is what value means.

The answer

13/8 = 38.10 per cent

Strip the bookmaker's margin out

A book that sums above 100 per cent is charging rent on every outcome. Here is how to see it and remove it.

Four ways to strip the margin from a market, and how much each one changes the answer.
Figure 8.1Four ways to strip the margin from a market, and how much each one changes the answer.

  1. Convert every price to a probability

    Take a three-way market priced 4/6, 14/5 and 9/2. Those convert to 60.00 per cent, 26.32 per cent and 18.18 per cent.

  2. Add them up

    60.00 plus 26.32 plus 18.18 is 104.50 per cent. A fair book sums to exactly 100, so this book carries 4.50 percentage points of margin.

  3. Divide each probability by the total

    60.00 divided by 1.0450 is 57.42 per cent. The other two become 25.18 per cent and 17.40 per cent, and the three now sum to 100.

  4. Read the fair prices

    Those margin-free probabilities are what the market actually believes. Anything you are offered above them is the house's head start, and it is charged on every outcome, not just the one you back.

The answer

Booksum 104.50 per cent, so 4.50 points of margin

Turn goal expectancies into a price

Two numbers, one distribution, and the whole match odds board falls out of the arithmetic.

From expected goals to a match price: the full pipeline as it appears in the book.
Figure 19.1From expected goals to a match price: the full pipeline as it appears in the book.

  1. Estimate each side's goal expectancy

    Start with the two numbers the whole model rests on: how many goals you expect each side to score. Take a home expectancy of 1.47 and an away expectancy of 0.93.

  2. Apply the Poisson formula to each scoreline

    For a given expectancy, the probability of exactly k goals is e to the power of minus the expectancy, multiplied by the expectancy to the power k, divided by k factorial. Run it for 0, 1, 2, 3 goals and beyond for both sides.

  3. Multiply the two sides together for every scoreline

    The probability of 1-0 is the chance the home side scores exactly one multiplied by the chance the away side scores none: 13.34 per cent. Do this for the whole grid of scorelines.

  4. Add the cells into the three outcomes

    Sum every cell where the home score is higher for the home win, every cell where they match for the draw, and the rest for the away win. Here that gives 49.7 per cent, 26.4 per cent and 23.9 per cent.

  5. Convert to fair prices and compare

    Those probabilities are fair decimal odds of 2.01, 3.79 and 4.19. Compare them with the market and you have a disagreement you can measure. The book then patches the model's known weaknesses, because raw Poisson underrates draws and low-scoring games.

The answer

49.7 / 26.4 / 23.9 per cent, or 2.01, 3.79 and 4.19

Questions

Questions about the modelling

Is Poisson good enough to price a football match on its own?

No, and the book is explicit about it. A plain Poisson model treats the two teams' goals as independent and underrates draws and low-scoring matches as a result. The Dixon-Coles correction adjusts exactly those low-scoring cells, and time decay weights recent matches more heavily. Poisson is the foundation, not the finished machine.

What margin do bookmakers usually build into a football market?

It varies by market and competition. A competitive three-way market on a major league might carry a few percentage points, while accumulator and bet-builder markets compound margin leg by leg: a four-leg accumulator at 8 per cent per leg works out at just over 26 per cent in aggregate before a ball is kicked.

Can I do this without programming?

The conversions and the margin arithmetic need nothing more than a calculator. Building and calibrating a full match model is more comfortable in a spreadsheet, and the book's appendices include a model-building checklist and a bet-tracking template for exactly that.

These three are the foundation. The book takes them through Dixon-Coles corrections, expected goals, team ratings, Monte Carlo simulation and fractional Kelly staking across 32 chapters.

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