Best-of Series Probability Calculator (Playoffs: Best of 3, 5, 7)
The chance that a team wins a best-of-3, 5, 7 or 9 series, and how many games it is likely to take, from its chance of winning one game.
Results
The dashed line marks the value you entered.
What this tool does
In a best-of-7 the first side to win four games takes the series, so it is the same as a coin-flip race to four. A team that wins 60 % of single games wins a best-of-7 about 71 % of the time and a best-of-3 about 65 %: longer series favour the stronger side, but only gradually, which is why upsets still happen. The calculator assumes every game is independent and the chance does not change with home advantage or fatigue; with home and away alternating, use an average. The chart shows how a longer series stretches the single-game chance.
Formula
P(win series) = Σₖ C(w − 1 + k, k) pʷ qᵏ with w = (N + 1) ÷ 2 wins needed, k = games lost · expected games = Σ g · P(series lasts g games)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
pg | Chance of winning a single game | % |
bo | Series is a best of | — |
PW | Chance of winning the series | % |
PL | Chance of losing the series | % |
EG | Expected number of games played | — |
W | Wins needed | — |
SW | Chance of winning without losing a game | % |
FD | Chance it goes the full distance | % |
Worked example
- Chance of winning a single game60 %
- Series is a best of7
- Chance of winning the series71.02 %
- Chance of losing the series28.98 %
- Expected number of games played5.70
- Wins needed4
- Chance of winning without losing a game12.96 %
- Chance it goes the full distance27.65 %
Limitations
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.