De-Vigged Odds (DVO) Explained: Why are they so important?
Ever wonder what odds really mean? Bookmakers don't just offer odds based on the true chances of an event happening. They build in a profit margin, often called the vigorish, vig, juice, or overround. This ensures that, ideally for them, they make money regardless of the outcome.
Understanding and removing this margin – a process called devigging – is crucial if you want to:
- See the bookmaker's (or the market's) underlying assessment of the "true" probabilities.
- Compare odds more accurately between different bookmakers.
- Develop your own betting models or analytical approaches.
What is the Overround (Vig)?
Imagine a perfect coin toss. The true odds for heads or tails are 50% each. In decimal odds, this would be 2.00 for heads and 2.00 for tails. If you convert these to implied probabilities (1 / decimal odds):
- Heads: 1 / 2.00 = 0.50 (or 50%)
- Tails: 1 / 2.00 = 0.50 (or 50%)
The sum of these probabilities is 50% + 50% = 100%.
However, a bookmaker needs to make a profit. They might offer odds like 1.91 for heads and 1.91 for tails. Let's calculate the implied probabilities now:
- Heads: 1 / 1.91 = 0.5236 (or 52.36%)
- Tails: 1 / 1.91 = 0.5236 (or 52.36%)
Now, the sum is 52.36% + 52.36% = 104.72%.
This extra 4.72% above 100% is the bookmaker's overround or vig. It's their built-in edge.
Why Devig?
Devigging aims to reverse this process. We take the bookmaker's odds (with the vig included) and try to strip out the margin to estimate the "fair" or "true" probabilities that add up to 100%. This gives us a clearer picture of the perceived likelihood of each outcome before the bookie added their cut.
How to Devig Odds: Common Methods
There are several ways to estimate the true probabilities. Here are three methods discussed in sports betting research, along with their pros and cons:
1. The Additive Method
- How it Works: This method assumes the bookmaker simply subtracts an equal slice of probability from each outcome. You calculate the total overround and divide it equally among all possible outcomes, subtracting that amount from each outcome's implied probability.
- Example: In our 1.91 / 1.91 coin toss example, the overround is 4.72%. There are 2 outcomes. So, subtract (4.72% / 2) = 2.36% from each implied probability:
- Heads: 52.36% - 2.36% = 50.00%
- Tails: 52.36% - 2.36% = 50.00%
- Strengths:
- Conceptually very simple.
- Weaknesses:
- Major Flaw: Can produce negative probabilities for longshots, especially when the overround is high or there are many competitors. A negative probability makes no sense!
- Rarely used in practice due to this significant flaw.
2. The Multiplicative Method (Normalization)
- How it Works: This is the most commonly used method due to its simplicity. It assumes the bookmaker applies their margin proportionally across all outcomes. You simply divide each outcome's implied probability by the total sum of all implied probabilities (the booksum).
- Example: Our coin toss booksum is 104.72% (or 1.0472).
- Heads: 52.36% / 1.0472 = 50.00%
- Tails: 52.36% / 1.0472 = 50.00%
- Strengths:
- Very easy to calculate.
- Always produces probabilities between 0% and 100%.
- Weaknesses:
- Doesn't account for the favorite-longshot bias. It's well-known that bookmakers often apply a larger effective margin to longshots than to favorites. This method ignores that nuance.
- Because it treats all outcomes the same proportionally, it might underestimate the true probability of favorites and overestimate the true probability of longshots compared to more sophisticated methods.
3. The Power Method
- How it Works: This method is more advanced. It raises each implied probability to a certain power (let's call it 'k'). The value 'k' is chosen (often through iteration - a computer trying values until it works) so that the resulting probabilities sum exactly to 100%. This method naturally removes more margin from longshots than favorites, better reflecting the favorite-longshot bias.
- Example: Calculating 'k' is complex, but imagine for our coin toss, the method finds a 'k' (which would be close to 1 in this symmetrical case) that adjusts 52.36% and 52.36% back to 50% and 50%. For a race with a strong favorite and several longshots, 'k' would typically be greater than 1, reducing the longshots' probabilities more significantly than the favorite's.
- Strengths:
- Mathematically sound: never produces probabilities outside the 0%-100% range.
- Can effectively model the favorite-longshot bias.
- Often performs better in tests compared to the Multiplicative method when predicting actual outcomes.
- Weaknesses:
- More complex to calculate.
A Real-World Example (Tennis Match)
Let's say Player A has odds of 1.50 and Player B has odds of 2.75.
- Implied P(A) = 1 / 1.50 = 66.67%
- Implied P(B) = 1 / 2.75 = 36.36%
- Booksum = 66.67% + 36.36% = 103.03% (Overround = 3.03%)
Let's devig using the Multiplicative Method:
- True P(A) ≈ 66.67% / 1.0303 = 64.71%
- True P(B) ≈ 36.36% / 1.0303 = 35.29%
- Sum = 64.71% + 35.29% = 100%
Using the Power Method (conceptual): It would likely assign a slightly higher probability to Player A (the favorite) and a slightly lower probability to Player B (the longshot) compared to the Multiplicative method, perhaps something like 65.0% / 35.0% (the exact numbers depend on finding 'k'), reflecting the favorite-longshot bias.
Conclusion: Why Bother?
Devigging odds is a fundamental step in moving beyond simply taking the prices offered and starting to analyze the underlying probabilities.
By understanding how bookmakers build their margin and using methods to remove it, you gain a clearer perspective on the events you're betting on. While no devigging method is perfect, applying one (especially the Power method for more serious analysis) helps you look "under the hood" of the betting market.
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