How odds are calculated
A complete walkthrough of the math: implied probability, the vig, true odds, expected value, and Kelly sizing.
1. What odds actually mean
Every betting market is a translation of probabilities into a price. The odds you see are not random — they are a mathematical statement: "the market thinks this outcome has an X% chance of happening." Once you can read odds as probabilities, everything else follows.
The decimal format
Decimal odds are the most direct format. The number tells you what you get back for every 1 unit staked.
- Odds of
2.00→ for every $1 you bet, you receive $2 back (your $1 stake + $1 profit). - Odds of
3.50→ bet $1, receive $3.50 back ($2.50 profit). - Odds of
1.20→ bet $1, receive $1.20 back (only $0.20 profit — a heavy favourite).
Implied probability
The most important formula in this entire field:
Implied probability = 1 / decimal odds
Examples:
| Decimal odds | Implied probability |
|---|---|
| 1.50 | 66.67% |
| 2.00 | 50.00% |
| 2.50 | 40.00% |
| 5.00 | 20.00% |
| 10.00 | 10.00% |
If a coin flip were a betting market, the fair odds would be exactly 2.00 on each side (50% × 2 = 100%). Anything else means the bookmaker has added a margin.
2. The vig (bookmaker margin)
Bookmakers do not offer fair odds. They build in a margin — called the vig, overround, or juice — that guarantees a profit if their book is balanced.
How to spot it
Sum the implied probabilities of every outcome. In a fair market the sum equals 100%. In a real market it always exceeds 100%.
Example: a coin flip offered at 1.91 / 1.91:
- 1 / 1.91 = 52.36%
- 1 / 1.91 = 52.36%
- Total: 104.71% → 4.71% margin built into the market
Stripping the vig — the "true" probability
To recover the bookmaker's true probability estimate, divide each implied probability by the total overround:
True P(outcome) = (1 / odds) / Σ(1 / odds)
This is what the Vig Remover calculator does for you. The result is what the bookmaker actually believes the probability is — without the markup.
3. Expected value (EV)
EV is the single number that tells you whether a bet is rational or not, over the long run.
EV = (Probability of winning × profit if you win) − (Probability of losing × stake)
If EV is positive, the bet is +EV. If negative, it is −EV. The casino, the bookmaker, the lottery — all rely on selling −EV bets.
You can only beat a market by finding situations where your true probability estimate differs from the market's implied probability — by enough to overcome the vig.
4. The Kelly Criterion
Once you have a +EV opportunity, the next question is: how much should you stake? Kelly's formula gives the bet size that maximises long-term bankroll growth.
f* = (b × p − q) / b
Where:
f*= fraction of bankroll to stakeb= decimal odds minus 1 (net profit ratio)p= your estimated true probabilityq= 1 − p
Most professionals use half Kelly or quarter Kelly — the long-term growth is slightly lower but the variance (bankroll swings) is much smaller, and the model is robust to small errors in probability estimation.
5. Poisson distribution for football
Football scoring follows a Poisson distribution reasonably well. If you know each team's expected goals (xG), you can derive the probability of every possible scoreline:
P(k goals | rate λ) = (λ^k × e^−λ) / k!
From the matrix of scoreline probabilities you can extract 1X2, Over/Under, Both Teams to Score, and exact-score odds. The Poisson calculator does this automatically.
6. Putting it together
The workflow looks like this:
- Take the market odds.
- Strip the vig to find the bookmaker's true probability estimate.
- Form your own probability estimate using a model (Poisson, ELO, your own analysis).
- If your probability is meaningfully higher than the bookmaker's, you have a +EV opportunity.
- Size the bet using fractional Kelly.
- Track your bankroll over time to confirm the edge is real, not noise.
Reminder: 9Ja Odds is an educational tool. The presence of an apparent +EV opportunity does not guarantee profit, and consistent profitability requires accurate probability estimation, discipline, and bankroll management. Past results do not predict future returns.