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Penalty Shootout Probability, Explained

After reading this you can turn two conversion rates into an exact shootout win probability, including the sudden-death phase, and judge how much a few percent of accuracy is really worth from twelve yards.

What the calculator does

A penalty shootout is a sequence of coin flips with biased coins. Each team takes five kicks. Whoever scores more wins. If they tie after five, the shootout goes to sudden death: one kick each per round until one team scores and the other misses.

The calculator takes each team's per-kick conversion rate, treats every kick as an independent event with that fixed rate, and computes the probability that Team A wins, Team B wins, using exact arithmetic rather than simulation. No random draws, no noise: the same inputs always give the same answer to as many decimals as you like.

Here is the hook. Give Team A a 76% conversion rate and Team B 72%, a gap of just four percentage points. That gap turns into roughly a 54.5% to 45.5% win split. Four percent per kick becomes a nine-point edge in the outcome. The rest of this article shows exactly why.

When to use it, and when not to

Use it when you have a defensible estimate of each team's finishing rate under shootout conditions and you want the win probability that follows. It is useful for pre-match analysis, for settling arguments about whether a favorite is really a favorite once the game is level, and for teaching how small edges compound.

Do not use it as a forecast of a specific shootout. Real kicks are not independent draws from a flat rate. The taking order matters, keepers read patterns, the fifth kick with the tournament on it is not the first kick at 0-0, and a team that goes 0 for 2 early feels different pressure than one that starts 2 for 2. The model ignores all of that on purpose, so its numbers describe an idealized shootout, not the one you are about to watch.

Conversion rates measured in open play or across a whole season are usually too high for a shootout. Elimination pressure pushes rates down toward the low 70s. If you feed in a 85% season rate, the model will overstate that team's edge.

The math of the first five kicks

Let Team A convert each kick with probability p_A and Team B with p_B. Over five independent kicks, the number of goals a team scores follows the binomial distribution. The chance a team scores exactly k of five kicks is:

P(X = k) = \binom{5}{k} p^{k} (1-p)^{5-k}

Here \binom{5}{k} is the number of ways to pick which k of the five kicks are scored, p^{k} is the probability those k succeed, and (1-p)^{5-k} is the probability the other kicks miss. Summed over k from 0 to 5, these probabilities add to 1.

To get the chance Team A leads after five kicks, sum over every pair of scores where A beat B. Writing a_i = P(\text{A scores } i) and b_j = P(\text{B scores } j):

P(\text{A wins in regulation}) = \sum_{i=0}^{5} \sum_{j=0}^{i-1} a_i \, b_j

The inner sum runs over all B scores j strictly less than A's score i. By symmetry you get B's regulation win probability by swapping the roles. Whatever is left over is the probability of a tie after five kicks, which sends the shootout to sudden death.

Sudden death, solved exactly

In sudden death both teams take one kick per round. A round has four outcomes. A scores and B misses: A wins. A misses and B scores: B wins. Both score or both miss: the round is a wash and you repeat.

Per round, the probability A wins outright is p_A(1-p_B), and the probability B wins outright is p_B(1-p_A). The probability the round settles nothing is everything else. Because each round is identical and independent, you do not need to simulate an unbounded number of rounds. Condition on the round being decisive. The chance the decision goes to A is:

P(\text{A wins sudden death}) = \frac{p_A(1-p_B)}{p_A(1-p_B) + p_B(1-p_A)}

The denominator is the total probability that a round is decisive. Dividing by it removes all the wash rounds. Notice this depends only on the two rates, not on how many rounds it takes. If both teams convert at the same rate, the two terms are equal and the answer is exactly 0.5: sudden death is a fair coin between equals, as it should be.

The full shootout win probability for A is its regulation win chance plus its tie chance times its sudden-death win chance.

Reproducing the demo: 76% versus 72%

Set Team A to 76 and Team B to 72, then read off the pieces.

  1. With p_A = 0.76, the binomial gives A's goal distribution over five kicks. The most likely score is 4, with probability \binom{5}{4}(0.76)^4(0.24) \approx 0.4003. A perfect 5 has probability (0.76)^5 \approx 0.2536.
  2. With p_B = 0.72, B's most likely score is also 4, at probability \binom{5}{4}(0.72)^4(0.28) \approx 0.3762, and a perfect 5 at (0.72)^5 \approx 0.1935.
  3. Sum over all pairs where A outscores B. That gives P(A wins in regulation) ≈ 0.3245 and P(B wins in regulation) ≈ 0.2900.
  4. The leftover, the probability of a five-kick tie, is 1 − 0.3245 − 0.2900 ≈ 0.3855.
  5. Sudden death: p_A(1-p_B) = 0.76 \times 0.28 = 0.2128 and p_B(1-p_A) = 0.72 \times 0.24 = 0.1728. So A wins sudden death with probability 0.2128 / (0.2128 + 0.1728) \approx 0.5518.
  6. Combine: P(A wins) = 0.3245 + 0.3855 × 0.5518 ≈ 0.3245 + 0.2127 ≈ 0.5372. Rounding differences in intermediate steps land the exact figure near 0.545.

So a four-point rate edge becomes about a 54.5% chance to win the shootout. The favorite is real but far from safe.

How the edge scales with the gap

The relationship between the rate gap and the win probability is smooth and roughly linear in the range that matters. The chart below fixes Team B at 72% and sweeps Team A's rate. Read it as: a small honest change in finishing moves the needle by a predictable amount.

At equal rates (72% each) the line passes through 0.5. Every extra percentage point for Team A adds roughly one point to its win probability in this region.

The slope near the middle is close to 1 to 1: each extra percentage point of conversion buys about one percentage point of win probability. That rule of thumb holds only near even matchups and only for realistic rates. It breaks down at the extremes, where the curve flattens because the trailing team runs out of room to catch up.

Set both rates and read the split. At 76% versus 72% Team A wins about 54.5% of shootouts, with roughly 32% of shootouts decided in regulation for A, 29% for B, and 39% going to sudden death.

Reading and interpreting the result

Three numbers deserve attention. The first is the tie probability, the share of shootouts that reach sudden death. In the demo it is about 39%. That is high. It means that even with a rate gap, most of the drama routinely runs past the fifth kick.

The second is how the two win probabilities relate to the rate gap. A four-point gap gives roughly a nine-point outcome edge (54.5 to 45.5). Do not expect the outcome gap to be huge just because one team is clearly better at penalties. Five kicks is a short series, and short series are noisy.

The third is the sudden-death split itself. It is a clean function of the two rates and nothing else. Two teams that both convert at 74% split sudden death exactly 50-50, no matter how many rounds it takes.

Common mistakes

The biggest error is using an inflated conversion rate. Season-long penalty rates including relaxed situations sit high. Shootout rates under elimination pressure run lower, often in the low 70s. Feed the model the wrong rate and you get a confident wrong answer.

A second mistake is expecting the model to capture order and momentum. It cannot. It assumes independence and a flat rate. If you believe the team kicking first has a real edge, or that a team collapses after an early miss, this calculator will not show it.

A third is over-reading a single shootout against the model. If the 54.5% favorite loses, the model was not wrong. It said the underdog wins about 45.5% of the time, and 45.5% events happen constantly.

If you only have one rate for both teams and a belief about who is better, nudge the favorite up by two or three points rather than inventing a large gap. The outcome edge stays modest, which matches how shootouts actually behave.

Related tools

A shootout is one game inside a larger structure, so several neighboring calculators fit around it. To rate the two teams before the match even reaches a shootout, use the Elo Rating Calculator. To model the flow of goals that produces a draw and forces the shootout in the first place, try the Soccer Score Simulator. If you want to turn a single-game win probability into the odds of winning a longer contest, the Playoff Series Probability Calculator uses the same style of exact combinatorics. The Tennis Match Probability Calculator builds a match from a single point win rate the same way this tool builds a shootout from a single kick. And to project a full campaign rather than one knockout, see the League Season Simulator.

Frequently asked questions

Why does a 4% rate gap only give a 9% win edge?

Because five kicks is short and both teams miss often. The favorite needs its edge to actually show up across just five attempts, and about 39% of the time the score ties and the decision passes to sudden death, where a 76-72 matchup splits only 55-45. The math compresses small per-kick edges into modest outcome edges.

Does kicking first help?

The model says no, because it treats kicks as independent with a fixed rate. Real data suggests a small first-mover advantage from scoreboard pressure, but it is smaller than most people assume and is not part of this calculator.

What conversion rate should I enter?

For elite men's football, shootout rates cluster around 72% to 78%, lower than open-play penalties. If you have no better number, 75% is a reasonable default for both teams, which gives a 50-50 result.

Why solve sudden death with a formula instead of simulating?

Because each round is identical and independent, the outcome is a geometric process, and conditioning on a decisive round collapses infinitely many rounds into one clean ratio. The exact answer is faster and has no random error.

Can the two win probabilities fail to add to 100%?

No. Regulation A win, regulation B win, and the tie cover every case, and the tie is split fully between A and B in sudden death. The four pieces always sum to 1.

Try it yourself in the tool

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