How we calculate the weather reference probability

Inputs

• The settlement station named in the market rules, such as New York Central Park or Chicago Midway. Each station is checked against the rules by hand before it gets a reference.
• The NWS point forecast for that station, daily and hourly, read every 15 minutes and stored with the time NWS issued it.
• On the day itself, the station observations reported so far.
• The highs each market settled on, used to measure how far the forecast tends to miss.

The calculation

The forecast high is the larger of the forecast daytime high and the warmest hour of the hourly forecast over the climate day, which runs midnight to midnight local standard time, as the NWS climate report does. That catches days whose high comes just after midnight, before a cold front.

The true high is treated as a normal distribution around the forecast high. Its spread starts at 2.5°F when the day is less than 24 hours away and 3.5°F beyond that. Once 30 days of stored forecasts at a given lead time have been matched with settled highs, the measured spread and the average forecast miss from those days replace the defaults: for the station once it has 30 days of its own, otherwise for all stations together. The spread never goes below 1°F.

Highs are reported in whole degrees, so a 75 to 76° bracket covers 74.5° to 76.5°. The probabilities across an event’s brackets are scaled to add up to 100%, and a market is skipped unless its brackets cover every possible high exactly once.

On the settlement day

• The highest temperature observed so far sets a floor, less 1°F because the observations we read are rounded differently from the official report.
• The rest of the hourly forecast is moved by how far the latest observation is from the forecast for that hour, by at most 8°F.
• Once the forecast no longer goes above the observed high, the day’s peak has passed and the spread narrows to 0.6°F around the observed high.

When no reference is shown

• The station has not been checked against the market rules.
• Some of the event’s brackets are missing, so the set does not cover every possible high.
• The latest reference is more than 3 hours old.

Limits

• Markets settle on the official climate report, and the observations we read can differ from it by a degree or two. At one station in our first check, the observations read 2°F below the reported high.
• The reference knows only what is in the NWS forecast. It does not weigh other weather models.
• Late in the settlement day, traders may already know the preliminary official high, so a gap then says more about our observations than about the market.

How well it does

Every reference is stored with the inputs behind it and the time it was computed, so any number shown can be reproduced. Once enough of these markets have settled, we will publish how the reference probability and the market price each scored against the actual outcomes, including where the reference does worse than the market.