Adaptive Learning: Elo Matchmaking Engine

Adaptive Practice

P(correct) for the next item, from the Elo gap:

50%Δ = 0

Ratings

Learner ability θ

1000

Item pool spread

±350

Items answered

Rolling accuracy

—

K-factor (adaptation speed) 24

True skill (auto-practice) 55%

How it works

Every question in the pool carries a difficulty rating d, and the learner carries an ability rating θ, both on the same scale (Elo-style, same idea chess uses to rate players). Before each attempt the probability the learner answers correctly is given by the logistic curve:

P(correct) = 1 / (1 + 10^((d − θ) / 400))

After the outcome is observed, both ratings move — this is what makes it a matchmaking engine rather than a static test:

θ ← θ + K · (score − P)      score = 1 if correct, 0 if wrong
d ← d − K · (score − P)      (item moves opposite to the learner)

A correct answer nudges the learner's rating up and the item's rating down (it looks slightly easier next time); a wrong answer does the reverse. The next item is always drawn near the learner's current rating, so difficulty tracks ability continuously and the learner sits close to a 50% success rate — the zone shown to maximise engagement and long-run mastery, the same principle behind Duolingo's Birdbrain matchmaking and ALEKS' knowledge-space placement.

K-factor — how fast ratings react to a single result; high K adapts quickly but overshoots on noisy answers, low K is stable but slow to correct a bad early guess.
Auto-practice — simulates a learner with a fixed hidden "true skill" probability, so you can watch the tracked ability rating converge toward the correct level and the accuracy stream settle near 50%.
The 3D scene plots every item in the pool as a bead on the difficulty axis; the learner's marker glows and rises when correct, dims and lowers when wrong, and the item pool visibly compresses toward the learner over time.

Learner ability θ Item pool (difficulty) Next item served

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.