Statistics · Maths EE idea · Solid
The mathematics of rating players
A research question to start from
How does the Elo rating system turn results into ratings, and how well do its predicted win probabilities match outcomes?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
A model you can derive, analyse and test on results you collect.
Mathematics you would need
- Logistic function
- Expected scores
- Iterative updating
- Calibration of predictions
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Derive the expected-score formula and the update rule.
- Prove that rating points are conserved in a game.
- Test calibration on a set of results you collect.
Scope and difficulty
Solid. Solid.
Pitfalls
- A chess or sport essay.
- No test of predictions.
Where to start reading
Search a library catalogue or a university's open lecture notes for: Elo rating logistic expected score derivation; rating calibration. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).