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Exploiting the risk mechanics of bookmakers to profit from football

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Summary: Modern bookmakers often outsource the calculation of probabilities to specialized firms that provide white-labeled odds calculation services. These firms use advanced algorithms and extensive datasets to determine the probabilities of various outcomes, sold as proprietary API feeds. As a result, initial odds are similar across different platforms. Bookmakers adjust odds in real-time based on bet flow to hedge their positions, and skewed odds can indicate potential betting opportunities. By using Poisson regression, we can predict the number of goals scored in a game, identifying favorable bets with high expected value.



I can summarize this whole article very quickly here:

  1. Bookmakers outsource odds calculation to specialized firms.
  2. Odds adjust in real-time based on betting patterns to hedge positions.
  3. Skewed odds can indicate significant betting opportunities.
  4. Poisson regression helps predict the number of goals in a game.
  5. By combining the two, we can identify favorable bets with high expected value.

Modern Bookmakers and Odds Calculation:

Modern bookmakers rely on a few specialized firms for white-labeled odds calculation services. These firms use complex algorithms and vast datasets to determine probabilities, which are sold as proprietary API feeds to betting platforms worldwide. Consequently, when odds for a game are first published, they tend to be quite similar across different platforms due to the uniformity of the initial calculations. However, these odds are subject to change as market dynamics evolve.


Real-Time Adjustment of Bookmaker Data:

Bookmakers continuously adjust their odds in real-time based on the flow of bets they receive. This dynamic adjustment is crucial for hedging their positions and ensuring balanced books. When a large number of bets are placed on one side of an event, the bookmaker will adjust the odds to attract bets on the opposite side, minimizing potential losses. By analyzing the odds that have been adjusted in real-time, one can identify which bets have become skewed, indicating a shift from the initial probability calculation, often driven by public sentiment or insider information.


Delta and Statistical Outcome:

The delta represents the difference between the bookmaker's odds and the statistically probable outcome. A higher delta indicates a larger discrepancy, suggesting a stronger betting opportunity. This discrepancy can be quantified and ranked to identify the most favorable bets. The bets with the highest integer value in the delta column represent the greatest opportunities for profit, as they indicate the most significant deviation from the expected statistical outcomes.


Poisson Regression for Goal Prediction:

To predict the number of goals scored in a game, we can use Poisson regression. This statistical model is well-suited for modeling count data, such as the number of goals scored in a match. The Poisson distribution is used to model the number of events (goals) that occur within a fixed interval of time or space, characterized by the parameter λ, which represents the average rate (mean) of occurrence of the event. The probability mass function (PMF) of the Poisson distribution is given by:


\[P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!}\]

In a Poisson regression model, the log of the expected count (λ) is modeled as a linear combination of predictor variables (e.g., team strength, past performance, etc.). The model can be written as:


\[\log(\lambda_i) = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_p X_p\]

Using historical data, we can fit the Poisson regression model to estimate the coefficients. Once the model is fitted, we can use it to predict the expected number of goals (λ) for upcoming matches. With the estimated λ, we can calculate the probability of different goal outcomes. For instance, if λ for a team is 1.5, the probability of them scoring exactly 2 goals is:


\[P(X = 2) = \frac{1.5^2 e^{-1.5}}{2!} \approx 0.251\]

We can put all this knowledge together to identify favorable bets with high expected value. By comparing the bookmaker's odds with the predicted probabilities from the Poisson regression model, we can pinpoint bets where the bookmaker's odds are significantly higher than the model's expected probabilities. These bets represent opportunities for profit, as they offer positive expected value (EV) in the long run.