Sample size in sports betting: count evidence, not just tickets
A short run can swing sharply. More observations can reduce sampling uncertainty under a suitable model, but they cannot repair selective reporting, dependent outcomes or a method changed after seeing results.
Compare the same observed rate at different counts
| Wins / decided tickets | Observed rate | Approximate interval |
|---|---|---|
| 12 / 20 | 60% | 38.7%–78.1% |
| 120 / 200 | 60% | 53.1%–66.5% |
| 1,200 / 2,000 | 60% | 57.8%–62.1% |
These intervals use an independent Bernoulli model with one fixed underlying success probability. With p̂ = wins ÷ n and z ≈ 1.96, the Wilson center is (p̂ + z² ÷ 2n) ÷ (1 + z² ÷ n). Its half-width is z × √(p̂(1 − p̂) ÷ n + z² ÷ 4n²) ÷ (1 + z² ÷ n).
The table illustrates sampling uncertainty under that model. It is not a 95% probability that a particular future bet falls inside the interval, and it is not a confidence interval for ROI. The method’s coverage describes repeated samples under its assumptions.
Ticket count is not independent evidence count
Ten copies of the same selection produce ten tickets but one shared sporting result. Several props from the same player can also depend on the same minutes and game conditions. Treating these as independent observations can make uncertainty look too small.
Define the unit of analysis and preserve event IDs. A method that groups correlated observations by game or date answers a different question from a simple binomial calculation. The table above does not implement such a correction, and no universal conversion from tickets to “effective bets” is supplied here.
A larger selected sample is still selected
Imagine evaluating 100 unrelated toy strategies and reporting only the best observed run. That winner was selected using its results. An interval calculated as though the strategy had been chosen beforehand does not account for the selection process.
Freeze inclusion rules, odds treatment, model version and reporting windows before evaluating later data. Retain failed methods and dropped markets in the research log. Separate development samples from genuinely later evaluation; repeatedly tuning on the evaluation period makes it part of development.
Tie the sample to the claim
In the first row, 12 wins and eight losses at +100 with $10 on each ticket produce $240 returned from $200 staked: +$40 and 20% ROI. That exact accounting result can coexist with a wide uncertainty interval. The calculator reproduces the money totals, not the statistical interval.
There is no single ticket count that proves every strategy. Prices, dependence, effect size, stability and the proposed claim matter. A large historical sample from an obsolete player role or changed model may not describe the current method. State the sample, dates, assumptions and gaps instead of declaring a universal “proven after N bets” threshold.
Try the numbers yourself.
Open the calculator with this guide’s example inputs. Change one assumption at a time and see what changes.
Open roi calculatorCommon questions
Does 2,000 bets prove a winning method?
No fixed count proves every claim. The sampling process, prices, dependence, selection rules and stability still matter.
Can I use this table for changing odds and probabilities?
Not as a complete uncertainty analysis. It assumes independent binary outcomes with a common probability and does not model varying payouts or ROI.
Sources and example scope
NIST supplies the Wilson interval method. The three interval calculations, ticket-dependence examples, selection scenario and accounting case are original illustrations; no real strategy is statistically validated here.