Penalty Shootout Simulator
"It's a lottery." Is it? Set how often each side's takers score, and see how much that edge is worth once the kicks are taken.
Conversion from 5% to 99%. Roughly three in four shootout penalties are scored.
Try an example
- Team A wins
- Team B wins
- Team A ahead after five kicks each
- Level, into sudden death
- Team B ahead after five kicks each
- Team A wins sudden death
- Sudden-death rounds, on average
How it works
A shootout stops as soon as one side can't catch up, but stopping early never changes who wins. So the first five kicks each work like five complete penalties, which is the Binomial distribution: each side's score out of five follows
$$P(k \text{ scored}) = \binom{5}{k}\, p^{k}\, (1 - p)^{5 - k}$$If the sides are level after five, sudden death begins. A round is decided when one side scores and the other misses, so Team A's chance of winning sudden death is
$$\begin{aligned} &P(\text{A wins sudden death}) \\ &= \frac{p_A (1 - p_B)}{p_A (1 - p_B) + p_B (1 - p_A)} \end{aligned}$$In plain football
- \(p_A\) and \(p_B\) are how often each side's takers score: 0.75 means three in four.
- \(p_A(1 - p_B)\) is a round Team A wins: their taker scores and Team B's misses.
- A round where both score or both miss changes nothing, so only the deciding rounds count.
So is it a lottery?
Between equally good takers, yes: it is exactly a coin toss. But a gap in quality counts for more than it looks. Takers who score 80% against 70% win about two shootouts in three, not the slim edge the ten-point gap might suggest, because every one of those extra goals can decide it. A goalkeeper who pushes a side's conversion down from 75% to 67% cuts their chance from a half to about three in eight.
Where it goes wrong
- Every kick is independent and each side has one conversion rate. Real takers differ, and managers put their best takers first.
- It ignores pressure. The fifth kick, to win or to stay alive, may not be scored as often as the first.
- Kicking order is assumed not to matter. Some studies have found an advantage for the side kicking first; others, with more data, found little or none.
These probabilities come from a statistical model and are for analysis and education. Football remains uncertain and model predictions will frequently be wrong.
The maths behind it: Five penalties, how many go in? The Binomial distribution