Metacognition & Confidence Calibration Simulator

Learner Parameters

Task Ability 60%

Metacognitive Insight 55%

Confidence Bias +0%

Run Trials

Calibration Readouts

Trials run

Accuracy

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Mean confidence

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Overconfidence

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Brier score

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Last outcome

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How it works

Metacognition is "thinking about your own thinking" — specifically, how well your confidence in an answer tracks whether that answer is actually correct. Each simulated trial draws a difficulty d and combines it with your Task Ability η into an evidence signal:

evidence e = 6·(η − 0.5) − 6·(d − 0.5) + noise(0,1.2)
correct = (e > 0)

The same evidence partly determines the learner's reported confidence — this link is the essence of metacognitive insight. A low-insight learner's confidence is driven mostly by independent noise instead:

signal = insight·e + (1 − insight)·noise(0,1)
confidence = clamp01( sigmoid(1.5·signal) + bias )

Every trial lands as a colored point in the 3D calibration chart (green = correct, red = incorrect) at its own confidence bin. The purple bars show the actual accuracy measured inside each confidence bin — perfectly calibrated judgment means bar height tracks the white diagonal reference line (accuracy = confidence) exactly. Bars sagging below the line reveal overconfidence; bars rising above it reveal underconfidence.

Task Ability — the learner's true skill; shifts overall accuracy up or down.
Metacognitive Insight — how much confidence is actually informed by the same evidence behind correctness, vs. noise; this is what calibration research calls resolution.
Confidence Bias — a flat offset added to every confidence report, independent of accuracy — this is overconfidence/underconfidence bias.
Brier score = mean((confidence − correct)²), the standard proper scoring rule for calibration; 0 is perfect, 0.25 is chance-level guessing at 50%.

Real-world relevance: this is the same calibration-curve method used to study exam confidence, medical-diagnosis certainty, eyewitness testimony, and the "Dunning–Kruger" overconfidence-at-low-skill effect.

Correct trial Incorrect trial Bin accuracy bar Perfect calibration line

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