Two hundred forecasts that say 0.75 when they lean one way and 0.25 when they lean the other, with thirty of them wrong. Log loss is 0.452474 and the Brier score is 0.137500. Switch to the next preset, which gets exactly the same thirty cases wrong on exactly the same rows but states 0.99 instead of 0.75, and watch which score notices. The two forecasters are indistinguishable on accuracy, on precision, on recall and on any measure built from a confusion matrix.
200 forecasts · base rate 0.5500
Log loss 0.452474 against a baseline of 0.688139
The worst ten per cent of cases carry 30.64% of the log-loss total against 40.91% of the Brier total. The Brier score on the same forecasts is 0.137500, against a base-rate baseline of 0.247500.
Log loss
0.452474
base rate would give 0.68814
Brier, same data
0.137500
base rate would give 0.24750
Worst decile carries
30.6%
40.9% of the Brier total
Clipped forecasts
0
none at the boundary
What a wrong call costs
The penalty each score applies to a wrong prediction at increasing confidence
Stated confidence
Log-loss penalty
Brier penalty
Ratio to 0.9
0.9
2.30259
0.81000
1.000× and 1.000×
0.99
4.60517
0.98010
2.000× and 1.210×
0.999
6.90776
0.99800
3.000× and 1.232×
0.99999
11.51293
0.99998
5.000× and 1.235×
Going from 90% confidence to 99.999% on a call that turns out wrong multiplies the log-loss penalty by 5.00 and the Brier penalty by 1.23. The Brier score saturates at 1; log loss has no upper bound, which is why it needs clipping and the Brier score does not.
Where the loss is concentrated
The single worst case and how much of each total it carries
Quantity
Log loss
Brier
Total
0.452474
0.137500
Base-rate baseline
0.688139
0.247500
Improvement on it
34.25%
44.44%
Worst decile’s share
30.64%
40.91%
Worst single case
row 4: forecast 0.2500, outcome 1, loss 1.3863
The two improvement figures are the useful comparison between the scores. When they disagree, the difference is about confidence rather than accuracy, and which one you should care about depends on whether a confident mistake costs you more than a hesitant one.
The Brier decomposition on the same forecasts gives a reliability of 0.010065 and a resolution of 0.120065. Log loss has no comparable exact decomposition, which is one practical argument for reporting the Brier score alongside it.
A forecast of exactly 0 or 1 that turns out wrong has an infinite log loss, so every implementation clips at some small epsilon — 1e-15 here. The penalty on such a case is then a property of the clip rather than of the forecast, and two libraries with different epsilons will report different scores for identical predictions.
Unbounded by design Brier alongside Proper scoring rule The clip is a choice
What this tool shows
Two forecasters get exactly the same thirty calls wrong out of two hundred, on exactly the same rows. One states 0.75, the other 0.99. Log loss: 0.452474 against 0.699318, a factor of 1.546. The Brier score: 0.137500 against 0.147100, a factor of 1.070. Every measure built from a confusion matrix — accuracy, precision, recall, F1 — scores them identically. Log loss punishes the over-confidence more than seven times as hard as the Brier score does, and that is the choice between them.
Log loss with the Brier score computed on the same forecasts, and both baselines
The penalty each score applies to a wrong call at 0.9, 0.99, 0.999 and 0.99999
How much of each total the worst decile and the single worst case carry
The clipping epsilon, how many forecasts hit it, and why two libraries can disagree on identical predictions
Two presets with identical accuracy and different confidence, so the gap is measured rather than described
Why both scores are safe to optimise, and where they diverge
Unbounded by design Brier alongside Proper scoring rule The clip is a choice
Unbounded means one case can carry the evaluation.
Updated 13 September 2026 · Works in any browser, no installation
Log loss is the average of −ln(forecast) on the cases that happened and −ln(1 − forecast) on the ones that did not. It is the negative log likelihood of the data under the forecast, which is why fitting a model by minimising it is the same thing as fitting it by maximum likelihood. And because the logarithm has no lower bound, a confident error costs without limit — which is its defining feature and its defining weakness.
At a glance
Formula shown
L = −(1/n)Σ[yᵢ·ln(pᵢ) + (1 − yᵢ)·ln(1 − pᵢ)]. Forecasting the base rate on every case gives −[p̄·ln(p̄) + (1 − p̄)·ln(1 − p̄)], the entropy of the base rate, which is the baseline to beat. A wrong call at confidence c costs −ln(1 − c): 2.30259 at 0.9, 4.60517 at 0.99, 11.51293 at 0.99999, and infinity at 1 — which is why every implementation clips at some small epsilon.
Scenario support
Evaluating probability forecasts where a confident mistake is expensive, comparing classifiers that output probabilities rather than labels, training and monitoring models where log loss is already the objective, and diagnosing over-confidence that accuracy cannot see.
Educational estimate
Planning support from the values you enter — not professional advice.
Identical accuracy, different scores
The first two presets are the same forecasts at two confidence levels, and the point is what a confusion matrix cannot see.
Thirty errors out of two hundred, on the same rows, both times. Accuracy, precision, recall and F1 are identical.
Stating 0.75: log loss 0.452474, Brier 0.137500. Stating 0.99: 0.699318 and 0.147100.
Log loss rises 54.6%; the Brier score rises 7.0%. A factor of nearly eight between how hard the two punish the same over-confidence.
So the choice of score is a statement about your costs. If a confident wrong answer is much worse than a hesitant one — an automated decision, a medical call, a trade — log loss encodes that. If the cost is roughly linear in how wrong you were, the Brier score is the better match.
It has no upper bound, and the Brier score does
The table on the page is the mechanism behind everything else, and it is worth reading a row at a time.
A wrong call at 90% confidence costs 2.30259 in log loss and 0.81000 in Brier.
At 99.999% it costs 11.51293 and 0.99998. The log-loss penalty has multiplied by 5.00; the Brier penalty by 1.23.
The Brier score saturates at 1 because it squares a bounded difference. Log loss takes a logarithm of something approaching zero, and goes to infinity.
Which is why log loss needs a clip and the Brier score does not. A forecast of exactly 0 that turns out to be 1 has an infinite log loss, so every library replaces it with some small epsilon — and the penalty on that case is then a property of the library.
One case can carry the whole evaluation
The third preset makes the fragility concrete: two hundred forecasts, one of them certain and wrong.
Without that case the log loss is 0.105361. With it, 0.277528. One case out of two hundred multiplies the score by 2.63.
It carries 62.23% of the total. The Brier score moves from 0.010000 to 0.014950, and that same case carries 33.44% of its total.
The loss on it is 34.5388, which is −ln(1e-15) — the clip, not the data. Change the epsilon and the headline score changes.
So a log-loss comparison needs the concentration reported beside it. A model that wins on log loss because its rival made one over-confident mistake has not won on anything generalisable, and the worst-decile share on this page is there to make that visible.
It is the likelihood, which is why models minimise it
Log loss is not an arbitrary choice of penalty. It is the same quantity a logistic regression is already maximising, with a sign flipped and a division by n.
Minimising log loss is maximum likelihood estimation. The two are the same optimisation problem.
Which is why it is the default training objective for logistic regression, gradient boosting on binary outcomes and neural network classifiers alike.
And why a model trained on it should be evaluated on it, at least alongside anything else — evaluating on accuracy a model that was trained on log loss compares two different objectives.
The link runs both ways. A logistic regression’s log likelihood divided by n is exactly the negative log loss of its fitted probabilities, which is one way to check an implementation of either.
Both scores are safe to optimise
Log loss and the Brier score are both strictly proper, and it is worth being precise about what that guarantees.
Your expected score is minimised by reporting your true belief. Shading towards 0 or 1 to look decisive makes your expected score worse, not better.
Accuracy is not proper. It rewards rounding every forecast to 0 or 1, which destroys the information a probability carries.
Neither is F1 or any threshold-based measure. They all reward confident reporting whether or not the confidence is earned.
The verification suite checks properness directly, scanning the forecast across a grid at seven true probabilities and requiring the expected score to be minimised at the truth, for both rules.
The clipping epsilon is not a detail
Every implementation clips, most do not say what to, and on data with confident errors the choice moves the headline number.
This page clips at 1e-15, which is the common default and gives a maximum single penalty of 34.5388.
A library clipping at 1e-7 would give 16.1181 for the same case. Less than half, on identical predictions.
The page reports how many forecasts were clipped, so a score driven by the clip rather than by the data is visible rather than silent.
The real fix is upstream. A model that outputs exact zeros and ones is over-confident by construction, and calibrating it — or simply bounding its outputs away from the extremes before scoring — is more honest than choosing an epsilon that flatters it.
Reporting a log loss
Four items, and the second is the one that makes a number from one paper comparable to a number from another.
Give the base-rate baseline. Log loss has no natural scale; the entropy of the base rate is what a forecast has to beat.
Give the clipping epsilon. Two libraries with different defaults report different scores for identical predictions.
Give the concentration. If the worst ten per cent carry most of the total, the score is telling you about a handful of cases rather than about the forecast.
And report the Brier score too. They agree when confidence is calibrated and diverge when it is not, and the divergence is itself the finding.
Sources and methodology
References for the score and the class it belongs to.
Method. Log loss and the Brier score are computed from the same cleaned pairs so the comparison on the page is exact rather than approximate, and the Brier figure is cross-checked against the separate Brier engine in the verification suite. Forecasts are clipped at 1e-15 by default and the number clipped is reported, because a score driven by the clip rather than the data should be visible. The concentration figures — the worst decile’s share of each total, and the single worst case — are computed by sorting the per-case losses, which is what makes a comparison between two models interpretable when one of them made a single catastrophic call. The verification suite checks properness directly for both rules, scanning the forecast across a grid at seven true probabilities and requiring the expected score to be minimised at the truth, and asserts on 120 generated sets that log loss is never negative and the Brier score never leaves 0 to 1. That engine is verified on every change against 100 assertions. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
Brier ScoreThe Brier score split into reliability, resolution and uncertainty, with the term the decomposition drops printed rather than absorbed, plus a skill score and a calibration table.
Logistic RegressionLogistic regression with odds ratios converted to risk ratios at your own event rate, a likelihood ratio test, AUC, and separation reported rather than hidden.
Hosmer-LemeshowThe Hosmer-Lemeshow calibration test with the group count swept from five to fifteen, per-group promised-against-observed rates, and the Brier reliability alongside.
ROC Curve & AUCBuilds the curve from raw scores with every threshold enumerated, and computes the AUC twice — trapezoid and Mann-Whitney U — which agree to 1.11e-16 across 300 datasets.
Sensitivity and SpecificitySensitivity, specificity, PPV, NPV, likelihood ratios and MCC from a 2×2 table, with predictive values recomputed across the prevalence range — a 99%/99% test has a PPV of 50% at 1% prevalence and 9% at 0.1%.
An educational tool. Log loss is unbounded, so a single confident error can dominate an entire evaluation — the concentration figures on this page are there to make that visible. A forecast of exactly 0 or 1 that turns out wrong has an infinite loss and must be clipped, which means two implementations with different clipping thresholds will report different scores for identical predictions.