Log loss is a scoring rule that measures how good a set of probability forecasts was, rewarding calibrated confidence and punishing confident predictions that turn out wrong.
Last reviewed 5 November 2025 · Educational, not advice
Log loss, also called logarithmic loss or the logarithmic scoring rule, judges forecasts stated as probabilities. For each event you assigned a probability to the outcome that actually happened, and log loss takes the logarithm of that probability and averages the penalty across many forecasts. A lower score is better. Because of the logarithm, being very confident and wrong is punished sharply, while honest uncertainty is treated gently.
Its key property is that it is a proper scoring rule. That means your expected score is best when you report your true probability, so the rule gives no reason to exaggerate or shade a forecast. This is why log loss, alongside the Brier score, is a standard way to grade forecasters and probabilistic models. It rewards being well calibrated, meaning the things you call seventy percent likely happen about seventy percent of the time.
The sharp penalty for confident errors is the point, not a flaw. Saying something is ninety nine percent certain and being wrong incurs a large loss, which discourages overconfidence. It also means a single extreme miss can dominate a record, so a careful forecaster avoids stating near certainty without strong reason. Because prediction market prices can be read as implied probabilities, log loss is one way to ask after the fact how well those prices were calibrated.
Log loss is a measure, not a strategy or a guarantee. A good score over a sample does not promise future accuracy, and it says nothing about whether trading on those forecasts would have made money once prices and costs are included. It is a tool for honest self assessment, best read over a large number of forecasts rather than a handful.
If you said an outcome was eighty percent likely and it happened, the term in your score uses the logarithm of zero point eight, a small penalty. If you had said ninety nine percent and it did not happen, the score uses the logarithm of zero point zero one, a very large penalty. Average those terms over many forecasts, and a lower total means better calibrated probabilities.
Illustrative only. Numbers are examples, not a quote or a prediction, and exclude fees.
A good score grades the accuracy of forecasts, not the profitability of trading them, and past calibration does not promise future results. Any position on these venues can lose, and a contract can settle worthless. Stake only what you can afford to lose, never to chase a loss, and never on borrowed money. If it stops feeling like a free choice, step back. In the United States you can call or text the helpline on 1-800-GAMBLER or visit ncpgambling.org.
A scoring rule that grades probability forecasts, giving a lower score for better calibrated predictions and a heavy penalty for confident mistakes.
Because your expected score is best when you report your honest probability, so the rule does not reward exaggeration or hedging.
Both are proper scoring rules for probabilities. Log loss uses a logarithm and punishes confident errors more sharply, while the Brier score uses squared error and is gentler at the extremes.
No. It measures forecast accuracy, not trading profit. Prices, fees, and execution decide whether a forecast would have paid.
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