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Visual Guides/Bias vs Variance
Statistics

Bias vs Variance: The Bullseye

Throw darts at a target while adjusting bias and variance. Watch how they trade off and understand why the ideal model is both accurate and consistent.

Dart sets thrown: 0/5
Quadrants explored: 0/3

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Dart Settings

Bias (systematic offset)0.00
Spread σ (per-axis std. dev.)0.20
Expected sq. error (bias² + 2σ²)0.080
Bias² component0.000
Variance component (2σ², both axes)0.080
Observed on this board0.000

Quick Presets

Dart Board

10203050

How to read this: each dart is one model trained on a different random sample of data, and the bullseye is the true value it should predict. Bias = how far the centroid (average model) sits from the bullseye. Variance = how scattered the darts are around their own centroid.

Dart
Centre (gold)
Centroid

Current Regime

Low Bias Low Variance

Accurate & consistent

← Ideal

Low Bias High Variance

Accurate but inconsistent

High Bias Low Variance

Consistent but wrong

High Bias High Variance

Worst of both worlds

The bias-variance tradeoff means reducing one often increases the other. Complex models have low bias but high variance; simple models the opposite.

MSE = Bias² + Variance + Irreducible Noise

Bias²0.000
Variance (2σ²)0.080
Irreducible noise (illustrative constant, not simulated on the board)0.050
Total MSE0.130

High Bias (Underfitting)

Model is too simple. Misses patterns in training data. High training AND test error.

High Variance (Overfitting)

Model memorizes training data. Works perfectly on training but fails on new data.

Sweet Spot

Regularization, cross-validation, and the right model complexity minimize total error.

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