Probabilistic Forecasting in Energy: Reading a Missed Tail

A p90 of $96.15/MWh means the forecast puts about 90% of its probability at or below that price. It is not a maximum, and it does not promise the outcome stays under $96.15. A p10–p90 band is a nominal central 80% interval.

One outcome outside a band is consistent with a well-calibrated forecast. What counts over many comparable targets is how often outcomes escape the band, how wide the bands are, and whether certain horizons or market conditions fail more than others.

The forecast was issued at 12:45 UTC with model version L20260916b, for a target window of 22:50 to 23:05 UTC on September 17. In Central Daylight Time that is 7:45 a.m. and 5:50–6:05 p.m., a lead of 605 minutes to the start of the target.

That window is the forecast’s own native interval, not the 6:00–6:15 p.m. settlement interval, and the observation is an average of SCED prices inside it rather than a fifteen-minute settlement price. Relabeling it would change the question being scored.

The same issuance also published a p10, p50 and p90 path for the surrounding hours, and the chart keeps those levels together. It does not stitch a smoother fan from newer runs, because a newer issuance answers a different decision.

Quantile loss, also called pinball loss, makes the asymmetry explicit. At quantile level τ, the loss is τ × (actual − forecast) when the actual is above the quantile and (1 − τ) × (forecast − actual) when it is below. Lower is better.

For p90 here, 0.9 × ($336.34 − $96.15) is $216.18/MWh. A p90 set too low is penalized nine times as hard per dollar of error as one set too high, which is what separates a quantile from an ordinary point forecast.

Score the same target, price product, observation statistic and lead time across methods. A cleared day-ahead price is a fair point baseline, but it has no quantiles to score. For the underlying theory, see Gneiting, Balabdaoui and Raftery on calibration and sharpness and the distributional-accuracy chapter of Forecasting: Principles and Practice.

For scale, a hypothetical 100 MWh exposure priced at the observed average costs about $28,235 more than the same exposure priced at the median. That is an illustration of size, not a customer invoice.

The saved response includes a retrospective comparison at roughly the same 605-minute lead (within ±30 minutes), covering September 10 at 7:45 a.m. through September 17 at 7:45 a.m. It matched 143 target observations.

Only 97 of the 143 outcomes fell inside their p10–p90 bands: 67.8% coverage against an 80% nominal interval. The median’s mean absolute error was $52.56/MWh and its mean signed error was −$50.56/MWh, meaning the median sat below outcomes on average.

These diagnostics describe one location, one lead and one week. They are not a market-wide score or an annual claim, and errors in adjacent intervals are not independent. The forecast accuracy page carries broader evaluations with their own windows and comparison rules.

A buyer may care whether a high price breaches a cash limit. A generator cares whether low output coincides with expensive replacement energy. A battery needs the order of opportunities and its state of charge, not a distribution for one interval.

Quantiles at neighboring times do not describe the joint path. Multiplying independent interval probabilities, or building a whole-day schedule from a fan alone, invents dependence the model never supplied.

The battery study on this same day compares perfect foresight with a fixed day-ahead schedule and does not pretend either was chosen from this distribution. And the decision-time example explains why a later forecast vintage would change this evidence.