Is a penalty shoot-out fair to the team that shoots second?

Why it makes a good exploration

Researchers have argued that the team shooting first wins more often, which led to trials of an ABBA order. Modelling both orders exactly shows how a small pressure effect becomes a real advantage.

The mathematics you'll need

• Probability trees and binomial probabilities
• Sudden death as a geometric series
• Conditional probability
• Simulation to check the exact result

Where the data comes from

Use published shoot-out records (e.g., major tournaments from FBref or competition reports) to estimate conversion rates, and cite any research you rely on.

• FBref — Football league tables, results and basic player stats. Advanced stats (xG, progressive passes) were removed in January 2026 — historical basic data is still there.
• Kaggle datasets — Community-uploaded datasets on almost any topic — check the licence and original source before you use one.

A possible outline

1. Define the model: equal skill, pressure reduces p for the team behind.
2. Calculate P(first team wins) under ABAB.
3. Repeat for ABBA and compare.
4. Estimate parameters from real shoot-outs and check.
5. Reflect on the evidence and why the ABBA trial was dropped.

Showing personal engagement

• Choose a shoot-out you watched and analyse it.
• Survey goalkeepers or players you know about pressure.
• Propose your own order and test it.

See Criterion C: personal engagement for what examiners look for.

Which course is it for?

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

Taking it further

Simulate thousands of shoot-outs and compare with your exact probabilities; discuss the size of sample needed to detect the effect in real data.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL probability exploration adds.