How Do You Do Value Betting? (Part 2)

Q: How can an individual bettor build a probability model?

For an individual bettor, building an accurate attacking and defensive coefficient model often faces several problems: narrow data sources, noisy data, and complicated calculation.

In fact, we do not need to repeat the bookmaker's entire workload. The odds themselves are already the final output of the bookmaker's mathematical model.

For a bettor, instead of guessing team strength directly, it is more practical to decode the probability behind the odds. In the industry, this method is called implied probability modeling.

Its core logic is: use existing market odds data to reverse-engineer the bookmaker's real judgment of the match.

1. From odds to implied probability: the first conversion

Decimal odds directly correspond to probability. The conversion formula is straightforward:

implied probability (pi) = 1 / odds

Practical example: In a Premier League match, mainstream bookmakers open with these 1X2 odds: home win 2.10, draw 3.40, away win 3.60.

  • Home-win implied probability: 1 / 2.10 ~= 47.62%
  • Draw implied probability: 1 / 3.40 ~= 29.41%
  • Away-win implied probability: 1 / 3.60 ~= 27.78%

At this point, the three probabilities add up to 104.81%.

The extra 4.81% is the bookmaker's overround, or profit margin. To get the bookmaker's internal "true probability", we must remove this margin.

2. De-vig: restore the true probability

The most common de-vig method is the multiplicative method. It divides each implied probability by the total implied probability and forces the result back to 100%.

true p_i = pi_i / sum(pi)

Using the same example:

  • Home-win true probability: 47.62% / 104.81% ~= 45.44%
  • Draw true probability: 29.41% / 104.81% ~= 28.06%
  • Away-win true probability: 27.78% / 104.81% ~= 26.50%

These numbers represent this bookmaker's best estimate of the match result. But data from one bookmaker can still be biased.

3. Build a "consensus probability": aggregate market wisdom

The key to individual modeling is not beating one bookmaker. It is capturing the collective wisdom of the market.

We should collect odds from 5 to 10 mainstream bookmakers, such as Pinnacle, Bet365, and William Hill. Then calculate each bookmaker's de-vigged true probability, and finally take a weighted average.

Weighting principles:

  • Higher weight: bookmakers with high payout rates, such as Pinnacle. Their odds are affected more by sharp money, so their pricing is usually more accurate.
  • Lower weight: smaller bookmakers with low payout rates. Their odds often react more slowly, are used more to balance betting volume, and contain more noise.

Result: Suppose after combining data from 5 mainstream bookmakers, the consensus probability for this match is: home win 45.8%, draw 27.6%, away win 26.6%.

This is the core output of your personal probability model: market consensus probability.

4. Expand data sources: cross-check different markets

Bookmakers offer many markets for the same match, such as Asian handicap, over/under, and half-time/full-time. These markets are not isolated. Mathematically, most of them come from the same underlying model, which is the expected goal distribution of lambda and mu.

In your model, you can use these related markets for cross-validation and improve the accuracy of the consensus probability.

  • 1X2 and over/under: If the 1X2 consensus says the home team has a very high win probability, but the over/under market strongly favors under 2.5, the market may be expecting a narrow 1-0 win. If the two markets conflict, it means the market has disagreement and you should be cautious.
  • Asian handicap: Asian handicap is essentially a variant of 1X2. For example, -0.5 is equivalent to backing the team to win. After converting Asian handicap back into win probability, it should be highly consistent with the 1X2 consensus probability. If the gap is large, it is often a value-betting signal.
  • Half-time/full-time: By analyzing HT/FT odds, you can infer the market's view of match tempo, such as whether the match is expected to start slowly or open with early pressure.

Note: For correct score, corners, yellow cards, and similar markets, the data may look rich, but their margins are often very high, or their distribution logic is relatively independent. For example, corners are only weakly related to goals.

So I do not recommend mixing them into the core match-result probability model. They should only be used as auxiliary observation indicators.

5. Find value: the final use of the model

After you have a consensus probability, your decision no longer depends on intuition. It depends on expected value, or EV.

EV = (consensus probability x odds) - 1

Suppose your model calculates the home-win consensus probability as 45.8%, while a smaller bookmaker keeps the home-win odds at 2.25 because its betting volume is unbalanced.

  • Calculation: EV = (0.458 x 2.25) - 1 = +0.0305, or +3.05%

This means that in the long run, for every 100 yuan you bet, your expected return is 3.05 yuan.

On the other hand, if EV is negative, then no matter how safe the bet feels, you should not place it.