Calculate a betting ROI confidence interval from your settled results. Use wins, total bets and decimal odds for equal-stake bets at one price, or paste a bet log with varied stakes and payouts. The calculator shows observed ROI, a 90%, 95% or 99% interval, and whether that interval includes break-even.
A positive return in your record is not proof of a lasting edge. This tool estimates uncertainty about expected ROI under its assumptions; it does not predict the profit of your next session.
How uncertain is your betting ROI?
Calculate a confidence interval from your record. Choose the mode that matches your bets.
The interval concerns expected ROI under the model, not your next session’s outcome. It does not prove skill or guarantee future profit. Correlated bets and a changing strategy can invalidate the calculation.
What went wrong?
How to calculate your betting ROI interval
- Choose the mode. Use Same odds and stake only for full wins and losses at one price. Use Bet log when stakes, odds or settlements differ.
- Enter the complete record. Include losing bets. In log mode, enter the stake and net profit after applicable commission, not the payout including the returned stake.
- Select a confidence level. The default is 95%; 99% produces a wider interval for the same data.
- Read the interval and diagnostics. Compare the endpoints with 0% and review any warnings. In log mode, check turnover, net profit and the counts of positive, negative and zero-profit bets against your records.
Which calculation mode should you use?
| Your record | Mode | Required information |
|---|---|---|
| Equal stakes, one decimal price, full wins or losses | Same odds and stake | Number of bets, number of wins and the common odds |
| Different odds or stakes, including pushes and partial settlements | Bet log | Stake and net profit for each settled back bet |
The first mode calculates a Wilson interval for the win probability and converts its endpoints to ROI. The second uses the observed variation in your record to build an approximate interval for total profit divided by total stakes. Neither mode corrects for correlated bets or a changing strategy.
ROI, win rate and return are different numbers
On this page, ROI = total net profit ÷ total amount staked. Multiply by 100 to express it as a percentage. The denominator is betting turnover, not your starting bankroll or deposits.
If a stake of 10 returns 19 including the original stake, net profit is 9. A losing stake of 10 has net profit −10. A push returns the stake and has net profit 0. For a simple calculation from total stakes and returns, use the Gambling ROI Calculator.
For equal-stake bets at the same decimal odds d, the relationship is ROI = d × win rate − 1. At odds of 2.00, a 51.5% win rate produces a 3% observed ROI. The break-even win rate is 1/d, or 50% in this example, before any additional fees.
Worked examples: 100 bets versus 5,000 bets
Both examples below use equal stakes, decimal odds of 2.00 and a two-sided 95% Wilson interval transformed to ROI.
| Bets | Wins | Observed ROI | 95% ROI interval |
|---|---|---|---|
| 100 | 55 | +10.00% | −9.51% to +28.77% |
| 5,000 | 2,575 | +3.00% | +0.23% to +5.77% |
The 100-bet record has the higher observed ROI, but its interval includes zero and negative values. The record does not distinguish positive expected ROI from break-even at this confidence level.
The 5,000-bet record has a narrower interval with a lower endpoint slightly above zero. Under the assumptions, it supports a positive expected ROI for the process represented by that record. It does not prove personal skill, guarantee future profits or rule out problems such as selecting only a favorable period.
How to read your ROI confidence interval
- Entirely above zero: the interval supports positive expected ROI under the selected model.
- Includes zero: the interval does not separate expected ROI from break-even. That is not proof of luck or proof that no edge exists.
- Entirely below zero: the interval supports negative expected ROI under the model, even though some sessions can be profitable.
A 95% confidence level describes the long-run coverage of an interval procedure across repeated comparable samples. Wilson coverage is approximate because win counts are discrete; the bet-log interval also relies on a large-sample approximation. It does not mean there is a 95% chance that you will win, or that the next session will finish inside the interval.
Raising the confidence level from 90% to 99% makes the interval wider. Choose the level before interpreting the result rather than switching levels until a preferred conclusion appears.
A positive ROI confidence interval is not a stake-sizing rule. The Kelly Criterion Calculator explores stake size from odds and an estimated win probability for a particular bet. Historical aggregate ROI does not supply that probability or establish that the next bet has an edge.
Why average odds are not enough
Two records can have the same ROI, number of bets and average odds but very different uncertainty. One may contain a few large longshot wins; another may consist of many modest returns. Stake sizes can further change how much each outcome contributes to the total.
For mixed bets, paste the actual stake and net profit for each bet. The tool uses sum of profits / sum of stakes, not the unweighted average of each bet’s percentage return.
Use two columns, optionally headed stake,net_profit or Stake and Net profit when pasting from Excel. Keep stake first and net profit second. Separate values with commas, semicolons or tabs, and use decimal points. For example:
stake,net_profit 10,9 10,-10 20,0
These three rows illustrate the format; the log mode requires at least 30 rows. Include pushes and partial settlements if they are part of your record, but exclude void bets, deposits, withdrawals and unrelated bonuses. Keep amounts in one currency or consistent units. This mode is for back bets whose loss cannot exceed the entered stake; exchange lay liability requires a different setup.
If commission is charged only on winnings, subtract it from each winning bet’s net profit. Records with extra charges that take a loss beyond the entered stake are outside this model. The fixed-odds mode assumes the stated payouts have no extra fees.
Worked bet-log example: mixed stakes and settlements
Select Bet log and click Load a mixed 100-bet example to reproduce this synthetic record. The CSV download contains the same 100 rows. The table groups identical rows for readability; it is not a record of real bets.
| Number of bets | Stake per bet | Net profit per bet | Settlement |
|---|---|---|---|
| 30 | 10 | +10 | Full win at 2.00 |
| 25 | 10 | −10 | Full loss |
| 15 | 20 | +30 | Full win at 2.50 |
| 15 | 20 | −20 | Full loss |
| 10 | 10 | 0 | Push |
| 5 | 20 | −10 | Half loss |
- Total staked: 1,350 units; net profit: 150 units.
- Observed ROI: 150 / 1,350 = +11.11%.
- Profit counts: 45 positive, 45 negative and 10 zero-profit bets.
- Approximate 95% interval: −12.34% to +34.56%.
The record is profitable, but its interval includes break-even. The unweighted average of the 100 individual bet returns is +10.00%, which is not its turnover-based ROI. The larger stakes change each result’s contribution, so the calculator uses total profit divided by total stakes.
The two modes need not give identical intervals even for the same equal-stake record. For 55 wins from 100 bets at 2.00, Wilson gives −9.51% to +28.77%. Entering those outcomes as a log instead gives the symmetric approximate interval −9.84% to +29.84%. Use the fixed mode when its assumptions fit; the log method accommodates varied bets but is not an exact alternative to Wilson.
Calculation method
Same odds and stake: Wilson interval
Let n be the number of bets, w the wins, p̂ = w/n, and z the normal critical value for the selected confidence level. The calculator uses:
center = (p̂ + z²/(2n)) / (1 + z²/n)
half-width = z × √(p̂(1 − p̂)/n + z²/(4n²)) / (1 + z²/n)
The lower and upper win-probability limits are center minus and plus half-width. Each is then converted with ROI = d × p − 1. The method produces bounded win-probability intervals, including when all observed bets won or all lost. It assumes independent outcomes with a common win probability.
Bet log: approximate ratio interval
For stake sᵢ and net profit yᵢ, define the observed ratio r = Σyᵢ / Σsᵢ and residual eᵢ = yᵢ − r × sᵢ. The estimated standard error is:
SE(r) = √[n/(n − 1) × Σeᵢ²] / Σsᵢ
The interval is r ± t × SE(r), using a Student t critical value with n − 1 degrees of freedom. Results are converted to percentages for display. This is a linearized ratio estimate, not an exact small-sample interval. It assumes independent, representative stake/profit pairs from a stable process, with finite variance.
If every row has the same profit-to-stake ratio, the tool reports observed ROI without an interval: zero observed variation is not evidence of zero uncertainty. A very wide approximation can also extend below the feasible −100% ROI floor; the calculator flags this rather than silently changing its endpoints.
When the result can mislead
- Related bets: multiple bets on one match, shared parlay legs or common market exposures are not necessarily independent. Counting them as independent can overstate precision.
- Rare payouts: longshot returns can remain poorly represented even after hundreds of bets. Thirty rows is an input minimum, not a guarantee of statistical adequacy.
- Concentrated stakes: one large bet can dominate profit and uncertainty. The log mode flags a single stake above 10% of total turnover as a diagnostic, not a statistical cutoff.
- Selection and repeated checking: keeping the best-performing strategy or stopping the record when its interval becomes positive changes the interpretation. Ordinary intervals do not adjust for those choices.
- Changes over time: new odds, markets, staking rules or selection methods can make the historical record a poor guide to the current process.
More bets can reduce sampling uncertainty when the assumptions hold. They cannot repair missing losses, inaccurate records or dependence between outcomes. Do not place additional bets just to make a confidence interval narrower.
Uncertainty about expected ROI is also different from the risk of exhausting a bankroll. The Risk of Ruin Calculator explores how bankroll and stake size affect survival under its own assumptions. A positive expected return does not eliminate the risk of ruin.
Frequently asked questions
How many bets are enough to establish a positive ROI?
There is no universal count. It depends on the size of the edge, payout variability, stake concentration and independence of the results. Even a large record cannot establish future profitability if it is biased or the process has changed.
For a concrete scale, suppose stakes are equal, all decimal odds are 2.00, and outcomes are independent with a constant win probability. A two-sided 95% Wilson interval has a positive lower ROI limit when the positive observed ROI r satisfies n > (1.959964 / r)², with ROI written as a decimal.
| Observed ROI | Approximate cutoff in bets | Reproducible record: wins / bets |
|---|---|---|
| +2% | 9,604 | 4,947 / 9,700 |
| +3% | 4,269 | 2,266 / 4,400 |
| +5% | 1,537 | 819 / 1,560 |
| +10% | 385 | 220 / 400 |
The cutoff column rounds the formula up. Actual wins must be whole numbers, so the last column gives the first possible record above that cutoff with exactly the listed ROI. Enter these records at odds of 2.00 and 95% confidence to reproduce a lower endpoint above zero.
These are descriptive thresholds for an observed record, not sample sizes that guarantee detection of a true edge. Future observed ROI fluctuates. Planning a study requires a chosen detection probability (statistical power), and repeatedly checking until the interval turns positive changes the interpretation.
Why does the calculator ask for wins instead of an ROI percentage?
Wins and total bets define the fixed-odds sample without ambiguity. A rounded ROI may imply a fractional number of wins, and ROI alone does not describe variation in mixed bets. Use the log mode when the bets differ.
Is an interval above zero proof of skill?
No. An ROI confidence interval above zero supports positive expected ROI under assumptions about the record. Skill is a broader causal claim that the interval does not establish. Selection bias, correlated bets and changes in conditions still matter.
Can I use the interval to predict my next session?
No. It estimates uncertainty about expected ROI. A future session can finish well outside the interval, including at a loss when the entire confidence interval is positive.
Method references
- NIST: confidence intervals for a proportion — the Wilson calculation used in the fixed-odds mode.
- Penn State: auxiliary data and ratio estimation — background on ratio estimators and residual-based variance. The bet-log formula above uses independent observations without a finite-population correction.