Betting Value, ROI and Risk: A Practical Calculation Guide
This guide keeps forecast quality, realised outcome and bankroll risk separate. Combining them into one "winning percentage" hides important errors.
Separate a forecast from a settled record
The first three fields estimate pre-bet value. The final two calculate historical yield from a complete settled record. Neither result predicts the next outcome.
- Raw implied probability
- 50.00%
- Estimated edge
- 5.00 points
- Expected profit / ROI
- 1.00 units / 10.00%
- Settled yield
- 4.00%
Expected profit equals stake multiplied by estimated probability multiplied by decimal odds, minus stake. Settled yield equals settled profit divided by total settled stakes.
Convert decimal odds into break-even probability
For decimal odds:
raw implied probability = 1 / decimal odds
Examples:
| Decimal odds | Raw implied probability |
|---|---|
| 1.50 | 66.67% |
| 2.00 | 50.00% |
| 2.50 | 40.00% |
| 4.00 | 25.00% |
At 2.00, a bettor needs to win half of equivalent bets to break even before fees and execution differences. Your probability estimate must be compared with the accepted price, not an earlier advertised price.
Why do implied probabilities sum above 100 percent?
In a two-outcome market priced at 1.80 and 2.10:
1 / 1.80 + 1 / 2.10 = 1.031746
The raw total is about 103.17 percent. The amount above 100 percent is the market overround under this simple calculation. It is not necessarily split equally between outcomes.
A basic normalisation divides each raw implied probability by their sum:
- first outcome:
(1 / 1.80) / 1.031746 = 53.85%; - second outcome:
(1 / 2.10) / 1.031746 = 46.15%.
This is a model assumption, not proof of the true probabilities. The cited market-efficiency research explains why raw inverse odds cannot simply be labelled true probabilities.
How is expected value calculated?
For a one-unit fixed-odds bet with estimated win probability p and decimal
odds d:
expected profit = p × (d - 1) - (1 - p)
This simplifies to:
expected profit = p × d - 1
If your estimate is 55 percent and the accepted price is 2.00:
0.55 × 2.00 - 1 = 0.10
The estimate is positive 0.10 units per unit staked before other costs. It is not a promise that the next bet returns 0.10. If the true probability is 48 percent, the same price has negative expected value.
ROI, yield and profit are different fields
For a settled betting record:
yield = settled profit / total settled stakes
If 1,000 units were staked and the settled result is positive 40:
40 / 1,000 = 4% yield
Some reports call this ROI. Others divide profit by starting bankroll or average capital at risk. State the denominator every time.
Do not:
- exclude losing bets;
- count open bets as settled;
- treat returned stakes as profit;
- ignore commission and transaction costs;
- combine currencies without conversion records;
- change the measurement period after seeing results.
What does closing-line value measure?
For this guide, closing-line comparison means comparing the accepted price with a predeclared closing reference. Define the operator or source, snapshot time, selection, line, period and settlement rules before collecting results. Also state whether the comparison uses raw or margin-adjusted prices. Then retain both prices even when the comparison looks unfavourable.
For example, accepting decimal odds of 2.10 before the same selection closes at 1.90 records a favourable price movement. It does not prove that 2.10 had positive expected value. The closing market can be wrong, the market definition may differ, and one comparison cannot establish calibration.
Do not replace the accepted price with the closing price in ROI calculations. Use the accepted price for realised settlement and the declared closing reference as a separate diagnostic field.
Measure risk as more than losing frequency
Useful fields include:
- maximum amount at risk on one bet;
- total simultaneous exposure;
- peak-to-trough drawdown;
- longest losing sequence;
- proportion of bankroll in one market or event;
- unmatched exchange liability;
- dependence between selections.
Ten bets on the same event are not ten independent risks. Multiples also concentrate several selections into one stake whose return depends on every required leg.
Use a stake policy that survives estimate error
A fixed-unit method is transparent:
- separate a finite betting bankroll from essential money;
- define a small fixed unit;
- cap total daily and event exposure;
- do not increase stakes after losses;
- pause when a personal limit is reached;
- review the model on a schedule, not during an emotional sequence.
Probability-based formulas can produce large stakes when the estimated edge is large. If the estimate is wrong or overconfident, the formula magnifies the mistake. Do not add complexity before calibration has been tested.
See responsible gambling for account limits and support controls.
Minimum evidence for a value or ROI claim
A reproducible record needs:
- timestamped selection rule;
- probability estimate made before the event;
- minimum and accepted price;
- stake and total exposure;
- fees, commission and currency;
- settlement result, including voids and resettlements;
- every qualifying bet, not a selected subset;
- frozen review period and metric definition.
Without those fields, describe the result as unknown rather than using a precise return claim.
Sources and update record
This guide was checked on 27 July 2026 against peer-reviewed market research and published exchange mechanics. The formulas are examples for decimal odds and do not establish a profitable method.
Primary sources mapped to this guide
Each source below is retained with the claims it supports. Operator sources describe published terms, not independent first-hand performance.
- Sports Economics Review market-efficiency study
- Raw inverse odds contain the bookmaker margin and are not automatically true probabilities
- Normalising implied probabilities is one defined way to compare prices within a market
- International Journal of Forecasting odds study
- Betting odds can be analysed as probability forecasts only under explicit assumptions
- Market properties differ across market types
- Betfair Exchange getting-started guide
- Exchange prices can be partially matched or unmatched
- Displayed available amounts can change before execution
Frequently asked questions
Is a value bet one that wins?
No. Value concerns price relative to probability before the result. A positive-value estimate can lose.
Is yield the same as win rate?
No. Yield uses monetary profit and stakes. Win rate ignores the prices and sizes of bets.
Can I use bookmaker odds as true probabilities?
Not without assumptions and margin treatment. Raw implied probabilities usually sum above 100 percent.
Does a positive historical ROI prove future profit?
No. It may reflect variance, selection bias, changing prices or model decay. Report the sample, method and uncertainty.
Is value betting risky?
Yes. A positive-value estimate can lose, and the probability estimate itself can be wrong. Stake and exposure limits remain necessary.