How Proper Scoring Rules Shape LLM Forecasting

Forecasters are evaluated by backtesting, which replays resolved questions and grades the probability the system would have assigned before the outcome was known. For LLMs, two channels leak the answer into this test. A model that retrieves can surface reports written after the event, turning forecasting into a lookup, and each new model is trained on data closer to the event, so a question that lay in the future for last year's models sits inside this year's training data. Either way, the test grades recall while claiming to grade foresight. We introduce Hindcast, which closes both leaks by grading a model as if it stood at a chosen past date $t_0$, before the outcome existed in either channel. Hindcast replays resolved Polymarket prediction markets against a frozen snapshot of public Reddit, lets the model read only posts written before $t_0$, and scores each forecast against both what happened and the market's own price at $t_0$, itself a human forecast made from the same past information. Because the cutoff is set per market and the snapshot never changes, the evaluation re-runs on new markets as models improve, without going stale. Once the leak is closed, retrieval still helps most models, but only where Reddit discussed the event beforehand. Where the archive carried only speculation, retrieval hurts.

Probabilistic forecasting estimates the likelihood of uncertain future events. To improve LLM forecasting, existing methods typically learn from binary outcomes to output verbalized forecasts. However, while aggregated human forecasts contain rich information in both the crowd probability estimate and the degree of agreement among forecasters, how to utilize these signals remains underexplored. To address this, we propose the Beta-Bernoulli Calibrator (BBC), which converts an initial point estimate forecast from any model into a distribution over event likelihood, using supervision from both binary outcomes and human forecasts. BBC models event likelihood $p \sim \text{Beta}(α, β)$ and outcome $y \sim \text{Bernoulli}(p)$, with the mean as the calibrated point forecast and the variance as the epistemic uncertainty. Our results show that BBC generally provides better calibrated and more accurate forecasts than both traditional post-hoc calibration methods and models fine-tuned specifically for forecasting, while remaining lightweight and having good generalization. We also show that the epistemic uncertainty captured by BBC is a more reliable predictor of forecasting error than verbalized confidence.

Reinforcement learning with verifiable rewards can in principle train calibrated probabilistic forecasters, since a proper scoring rule such as the Brier score is computed from outcomes alone and is minimized in expectation by the true probability. In practice it degrades calibration, and existing remedies address epistemic uncertainty, where a model's confidence accompanies a verifiably correct or incorrect answer. We study aleatoric forecasting, where the forecast itself is the output and the label is one stochastic outcome, taking NFL in-game win probability as a testbed with the betting market as a reference. Rewarding the realized per-play outcome fails, because the single outcome is a noisy target and the policy gradient corrupts the chain of thought. We introduce a verifiable, label-free reward, a state-conditioned empirical win rate estimated from past outcomes, that removes the label noise, and we keep the gradient off the reasoning, by direct prediction or a gradient mask, so it cannot be corrupted. Trained with this reward alone, without human labels or supervised fine-tuning, a 7B model reaches the calibration of the betting market by direct prediction and is better calibrated than a zero-shot frontier model. That frontier model and a tabular estimator reach the same Brier score as this model, identifying the market's small remaining edge as live in-game information beyond their shared inputs. Masking the gradient, rather than dropping the chain of thought, preserves reasoning from which the forecast follows, which ordinary chain-of-thought training corrupts.