Winning Streak Probability Calculator
Chance of winning n independent tries in a row, the chance that a streak of that length shows up somewhere in a season of games, the longest streak to expect, how many games it takes on average to see one, plus unbeaten and losing streaks with draws and a win rate taken from a team’s record.
How it works
P(n in a row) = sⁿ · P(streak breaks) = 1 − sⁿ · average tries to the first run of n = (1 − sⁿ) ÷ ((1 − s) sⁿ) · streak somewhere in N games = 1 − a(N), with a(t) = a(t−1) − (1 − s) sⁿ a(t−n−1), a(t) = 1 for t < n and a(n) = 1 − sⁿ · s = win chance (wins), win + draw chance (unbeaten) or loss chance (losses)
When each try is independent and has the same chance s, the chance of n successes in a row is s multiplied by itself n times. That number shrinks fast — a 60% edge gives under an 8% chance of five straight wins — and it answers the question “will the next five go my way?”. A different and often more useful question is whether a streak of that length will show up somewhere in a whole season. Because a streak can start at any game, that chance is much higher, and the calculator works it out exactly with a short recurrence that tracks the chance of having no such run yet. From the same recurrence it gives the whole distribution of the longest streak in the season, the expected longest streak, and how many tries it takes on average, or with 50% and 90% confidence, before the first streak of your length appears. You can ask about winning, unbeaten (win or draw) or losing streaks, add a draw chance under More options, or type in a won–lost–drawn record to estimate the chance per game from real results.
Worked example
A team wins 60% of its games. The chance it wins the next 5 is 0.6⁵ = 7.776%, about 1 in 12.86, so 92.224% of the time at least one of those five is lost. Over a 20-game season, though, a run of 5 straight wins turns up somewhere 47.8% of the time, and the longest winning streak averages 4.8 games (4 is the most likely). On average it takes 29.7 games to see the first 5-game winning run; half of the time it has happened by game 22 and 90% of the time by game 64.
Sources: Independence (probability theory) — Wikipedia · Schilling, M. F. (1990) “The Longest Run of Heads”, The College Mathematics Journal 21(3) · Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1, ch. XIII (runs of successes)
Frequently asked questions
Does this assume the tries are independent?
Yes. Every formula here assumes each try has the same chance and does not depend on the others — like fair coin flips or dice. Real sports results are only roughly like that, because form, injuries and opponents change.
Why is a streak somewhere in a season so much more likely than n in a row?
“n in a row” asks about one particular block of games. Over a season the streak can start at almost any game, so there are many chances for it to happen. With a 60% win rate, five straight wins from a given start is 7.8%, but in 20 games a five-win run appears about 48% of the time.
What does “1 in N” mean here?
It is the reciprocal of the streak probability: one particular block of n tries is a clean streak roughly once in every N such blocks. The “average tries until the first streak” is a different number, because streaks can overlap with the tries before them.
How do draws or ties change the answer?
A draw breaks a winning streak and also breaks a losing streak, but keeps an unbeaten streak going. Enter the draw chance under More options and pick Wins, Unbeaten or Losses as the streak type.
Can I use a team’s actual record?
Yes. Enter the wins, losses and draws under More options and the calculator uses wins ÷ games played as the win chance and draws ÷ games played as the draw chance. Short records give rough estimates.
What is the longest streak I should expect?
Over N tries with chance s, the longest run is usually close to log(N(1 − s)) ÷ log(1/s). The table under the results gives the exact chance of every longest-streak length, and the result shows the average and the most likely value.
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This calculator is for educational purposes. Double-check important results before acting on them.