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

AA SLAA HLAI SLAI HL Solid Also in: Sport, Statistics

Research question

If the second team's conversion probability is lower because of pressure, how much advantage does the first team gain under the ABAB order, and does the ABBA order proposed by researchers remove it?

Adapt it: change the place, the data or the comparison until the question is yours.

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

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

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.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

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

Pitfalls that cost marks

Assuming constant p without discussing pressure.
Using too few real shoot-outs to estimate anything.
Not modelling the early finish (a team can become unable to catch up).

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.

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.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).