Log Loss Calculator
Calculate average log loss (binary cross-entropy) across a set of predicted probabilities and true labels.
Inputs
Actual binary labels for each sample.
Model's predicted probability of class 1 for each sample, same order as labels.
Average Log Loss
0.267821
Total Loss (Sum)
1.339105
Number of Samples
5
Worst Single-Sample Loss
0.4308
Step by step
Per-sample loss: −(y×ln(p) + (1−y)×ln(1−p))
−(y × ln(p) + (1−y) × ln(1−p))
= 0.1054, 0.2231, 0.4308, 0.2231, 0.3567
Total loss: sum over all samples
Σ [0.1054, 0.2231, 0.4308, 0.2231, 0.3567]
= 1.339105
Average log loss: total loss ÷ N
1.339105 ÷ 5
= 0.267821
How it works
Log loss is the dataset-level average of binary cross-entropy across N samples: LogLoss = (1/N)·Σ[y·ln(p) + (1−y)·ln(1−p)], negated. It's a standard classifier evaluation metric that, unlike accuracy, directly rewards well-calibrated probabilities — a model that confidently predicts the wrong class is penalized far more heavily than one that is uncertain, since ln(p) approaches −∞ as p approaches 0. Log loss is the metric minimized during training of most probabilistic binary classifiers, and is commonly reported for competition leaderboards (e.g. Kaggle) because it evaluates the quality of predicted probabilities, not just the final thresholded class.
Formula
LogLoss = -(1/N) × sum(y_i × ln(p_i) + (1 - y_i) × ln(1 - p_i))
- N
- Number of samples
- y_i
- True binary label for sample i
- p_i
- Predicted probability of class 1 for sample i
Frequently Asked Questions
Why is log loss preferred over accuracy for evaluating classifiers?
Accuracy only looks at whether the final thresholded prediction was right or wrong, ignoring how confident the model was — log loss directly penalizes overconfident wrong predictions and rewards well-calibrated probability estimates, which matters when probabilities themselves are used downstream (e.g. for ranking or risk scoring).
What is a 'good' log loss value?
It's problem-dependent, but as a reference, a model that always predicts p=0.5 achieves a log loss of ln(2) ≈ 0.693 regardless of the true labels — a well-performing model should score meaningfully below this baseline, with values closer to 0 indicating better calibrated, more confident correct predictions.
How does log loss punish a confident wrong prediction?
If a sample's true label is 1 but the model predicts p=0.01, the loss for that sample is −ln(0.01) ≈ 4.6 — dramatically higher than the ≈0.69 loss from an uncertain p=0.5 prediction, illustrating why log loss discourages overconfidence on samples the model might get wrong.