Calculator Input
This page keeps a single-column page flow, while the calculator fields use 3 columns on large screens, 2 on medium screens, and 1 on mobile.
Example Data Table
These sample values assume independent games and a constant single-game win probability.
| Single-Game Win Probability | Series Format | Wins Needed | Series Win Probability |
|---|---|---|---|
| 55.00% | Best-of-3 | 2 | 57.4750% |
| 60.00% | Best-of-5 | 3 | 68.2560% |
| 60.00% | Best-of-7 | 4 | 71.0208% |
| 70.00% | Best-of-7 | 4 | 87.3965% |
Formula Used
wins needed = (best-of games + 1) / 2
P(exact final score r-l) = C(r + l - 1, l) × pr × (1 - p)l
where r is the wins needed, l is the number of losses before the final win, and p is the single-game win probability.
P(series win) = Σ from l = 0 to r - 1 of C(r + l - 1, l) × pr × (1 - p)l
P(final game) = C(n - 1, r - 1) × pr - 1 × (1 - p)r - 1
where n is the best-of number and r is the wins needed.
This calculator uses a constant win probability for every game. That makes it ideal for probability study, planning, simulation setup, and clean series comparisons.
How to Use This Calculator
- Enter labels for the team or scenario you want to analyze.
- Choose whether your single-game probability is a percent or decimal.
- Enter the single-game win probability.
- Type the odd best-of format, such as 3, 5, 7, or 9.
- Select how many decimal places you want in the output.
- Press the calculate button to show the result block above the form.
- Review the summary cards, exact score table, and Plotly graph.
- Use the CSV or PDF buttons to export the current results.
Frequently Asked Questions
1) What does this calculator measure?
It estimates the chance of winning a best-of series from a fixed single-game win probability. It also shows exact final score paths, expected games, sweep probability, and the chance that the series reaches the last game.
2) What assumption does the math use?
It assumes each game is independent and that the same win probability applies to every game. If home advantage, injuries, or lineup changes matter, use separate estimates or a more detailed simulation model.
3) Why must the series format be an odd number?
An odd best-of format guarantees that one side reaches a strict majority first. That prevents ties and makes the “first to r wins” rule clear for exact score and clinching probability calculations.
4) What does an exact score path mean?
An exact score path is the probability of a specific final result, such as 4-2 or 2-4 in a best-of-7 series. It includes the required clinching game and all valid orders before that final result.
5) Can I use decimal probabilities instead of percentages?
Yes. Choose decimal mode and enter values from 0 to 1. For example, 0.62 means a 62% single-game win probability. Percent mode accepts values from 0 to 100.
6) What does the expected games value show?
It is the average series length across all possible final score paths. Short sweeps lower the average, while balanced teams increase the chance of longer series and push the expected length upward.
7) What are the CSV and PDF exports for?
They let you save the current summary and exact distribution table for reporting, sharing, or later analysis. The CSV is easy for spreadsheets, while the PDF is convenient for clean presentation.
8) How should I choose the single-game probability?
Use your best estimate from historical data, ratings, market odds, or a predictive model. The result quality depends on that input, so better single-game estimates lead to better series-level conclusions.