IA ideas library
Sports Maths IA ideas: from penalty kicks to world records
Sport is one of the easiest places to show genuine personal engagement: you know the game, you can collect your own data, and there are huge public databases of results. The challenge is finding a question with real mathematics in it, not just a table of averages.
These ideas cover modelling (projectiles, world-record progressions), statistics (home advantage, streaks), probability (scoring systems) and optimisation (angles, racing lines).
Next step: shortlist ideas with the free IA topic explorer, which filters starting points by course, interest and how easy the data is to get. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.
How sport explorations reach the top bands
Personal engagement (C)
Use your own sport: film yourself, collect your own statistics, or analyse the team you follow. Explain what you expected as a player or fan before you calculate.
Reflection (D)
Compare the model's answer with what real athletes do and explain the difference (biomechanics, rules, tactics). That comparison is the heart of the reflection.
Use of mathematics (E)
SL: A model derived from the situation (projectile, geometry, probability), optimised or tested with calculus or statistics, and checked against real data.
HL: HL techniques such as air resistance via differential equations, Markov chains for scoring, or rigorous inference on performance data.
An HL version
Add air resistance with a differential equation, model scoring as a Markov chain, or use inference to test whether an effect is real.
Sport ideas (10)
- What is the best angle to shoot a free throw?AA SLAA HLAI SLAI HLSolid
- Why don't long jumpers take off at 45°?AA SLAA HLAI SLAI HLSolid
- Is there a limit to how fast humans can run 100 m?AA SLAA HLAI SLAI HLSolid
- When should a Formula 1 driver pit? Modelling tyre degradationAA SLAI SLAA HLAI HLAmbitious
- Where should a winger shoot from? Maximising the angle to goalAA SLAA HLAI SLAI HLSolid
- Are cricket batting scores geometrically distributed?AI SLAI HLAA HLAA SLSolid
- Can a simple rating system predict football results?AI SLAI HLAA HLAmbitious
- Will women's Olympic times ever match men's?AI SLAI HLAA SLAA HLSolid
- Where should I aim on a dartboard?AI SLAI HLAA HLAmbitious
- Where should a pool ball hit the cushion? The geometry of bank shotsAA SLAI SLAccessible
Also relevant (20)
- How far does a bouncing ball really travel?AA SLAI SLAA HLAI HLAccessible
- Designing a smooth roller-coaster drop with piecewise functionsAA SLAA HLAI SLAI HLAmbitious
- The lifeguard problem: what is the fastest route to a swimmer?AA SLAA HLAI SLAI HLSolid
- How fast is a sprinter at each moment? Differentiating 100 m splitsAA SLAA HLAI SLAI HLSolid
- How long does a skydiver take to reach terminal velocity?AA HLAI HLAmbitious
- How much of cycling effort goes on air resistance? A coast-down testAA HLAI HLAmbitious
- Is home advantage in football disappearing?AI SLAI HLAA SLAA HLAccessible
- Do left-handed tennis players have an advantage?AI SLAI HLAA HLSolid
- Are elite footballers more likely to be born early in the selection year?AI SLAI HLAA SLAA HLAccessible
- Are NBA players getting taller?AI SLAI HLAA SLAA HLAccessible
- How much does a small edge on each point matter in tennis?AA SLAA HLAI SLAI HLSolid
- Is a penalty shoot-out fair to the team that shoots second?AA SLAA HLAI SLAI HLSolid
- Is the “hot hand” real? Streaks in my free throwsAI SLAI HLAA SLAA HLSolid
- How fast does my heart rate recover after exercise?AA SLAI SLAA HLAI HLAccessible
- Is BMI's “height squared” right? Evidence from OlympiansAI SLAI HLAA SLAA HLSolid
- Can height predict lung capacity?AI SLAI HLAA SLAccessible
- Does the best team win? Knockout cups versus leaguesAI SLAI HLAA SLAA HLSolid
- Ranking teams that haven't all played each other: the Colley matrixAI HLAA HLAmbitious
- How fast does a sledge go? Acceleration, friction and slopeAA SLAI SLAA HLSolid
- Left, right or centre? Game theory for penalty kicksAA SLAI SLAA HLAI HLSolid
Frequently asked questions
Is a sports IA taken seriously by examiners?
Yes — the context does not matter, the mathematics and the thinking do. Many excellent IAs are about sport because the student cares about the answer.
Where can I find sports data?
Football-Data.co.uk and FBref for football, Basketball Reference for the NBA, Statsguru for cricket, Jolpica-F1 for Formula 1, Olympedia and World Athletics for athletics, and Jeff Sackmann's repositories for tennis.
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Related types of IA: Kinematics & physics-style modelling
Taking SEHS? Maths IA ideas for sports, exercise and health science students
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