Metrics & Evaluation Interactive

MAE & RMSE

Measure regression model accuracy. MAE = average error, RMSE = penalizes large errors more. Essential for player projection evaluation.

📊 The Formulas

MAE

1/n × Σ|y - ŷ|

Mean Absolute Error. Average of absolute errors.

MSE

1/n × Σ(y - ŷ)²

Mean Squared Error. Squares penalize large errors.

RMSE

√MSE

Root MSE. Same units as target variable.

Error Parameters

-5 5

1 8

0 30

📊 Error Metrics

Mean Error -0.06

MAE 2.74 pts

RMSE 4.14 pts

RMSE / MAE 1.51 (outliers!)

Error Distribution

⚠️ High RMSE/MAE ratio suggests outliers

Metric Comparison

MAE

2.74

Linear penalty

Robust to outliers

MSE

17.10

Squared penalty

Differentiable

RMSE

4.14

Same units as target

Interpretable

🎯 When to Use Each

Use MAE When...

• Outliers are expected and shouldn't dominate
• All errors matter equally (cost is linear)
• You want median-like behavior
• Interpretability is key ("avg 3 pts off")

Use RMSE When...

• Large errors are especially bad
• Cost grows with error magnitude (squared)
• You need differentiable loss for training
• Data is relatively clean

R Code Equivalent

# Calculate error metrics
calculate_metrics <- function(actual, predicted) { 
  error <- predicted - actual
  
  mae <- mean(abs(error))
  mse <- mean(error^2)
  rmse <- sqrt(mse)
  me <- mean(error)  # Mean error (bias)
  
  list(
    mae = mae,
    mse = mse,
    rmse = rmse,
    bias = me,
    rmse_mae_ratio = rmse / mae  # >1.25 suggests outliers
  )
}

# Example
actual <- c(22.5, 18.3, 25.1, 20.8)
predicted <- c(23.1, 17.5, 26.0, 19.2)

metrics <- calculate_metrics(actual, predicted)
cat(sprintf("MAE: %.2f, RMSE: %.2f\n", metrics$mae, metrics$rmse))

✅ Key Takeaways

• MAE = average absolute error (robust)
• RMSE = penalizes large errors more
• RMSE ≥ MAE always (equality when all errors equal)

• High RMSE/MAE ratio → outliers present
• Check bias (mean error) separately
• For player props: MAE often more practical