Margin of error and confidence intervals

NYSEG posts a running list of substation transformer upgrades on its site. One entry from early 2026 shows the Amenia substation going from a 5.75 MVA transformer to a 37.3 MVA one, another shows Oakdale moving from 400 to 448 MVA. At these sites, a truck appeared, a transformer got swapped, and the hosting capacity increased.

If there are only two snapshots of a feeder's capacity, one from last spring, one from this spring, one would not be able to tell whether that’s a change or a trend. A step change from a transformer upgrade and a gradual trend from load growth produce the exact same evidence when you only have two points: a starting value, an ending value, and a straight line connecting them.

Three points are the minimum to detect a trend, and even then, it’s tenuous to claim one. With three points, you can at least check whether the middle one falls near the line the outer two would draw, but three points also have exactly enough freedom to fit a curve. A transformer upgrade that happens between your second and third snapshot will produce a chart that looks like accelerating load growth. The chart can't tell you what happened at that substation.

Research polls This is the same problem pollsters deal with. A Pew Research poll from the 2004 presidential election surveyed 1,925 likely voters and reported a margin of error of about 2.5 percentage points. As a rule of thumb, the margin of error scales with one over the square root of the sample size. From 1,925 respondents to 500, the margin of error doubles, because you're now dividing by the square root of a much smaller number. At a handful of respondents, the poll stops being able to say anything useful about the population.

Utility data refresh rates When it comes to utility data, most public hosting capacity data doesn't give enough snapshots to compute an honest margin of error. New York's Joint Utilities have committed to refreshing hosting capacity maps every six months for feeders where a significant amount of new generation has been added, with a full system refresh on a slower cadence, and Dominion Energy has said it plans to refresh its own hosting capacity data at least quarterly. Even at the faster end of that range, a year of history is four data points. Four snapshots is not a small sample of a trend. It's closer to a poll of four people, and no responsible pollster would publish a margin of error on that, let alone a confident claim about direction.

A proper confidence interval explains what happens under repetition. A 95% confidence interval means that if you redrew the sample and recomputed the interval many times, 95% of those intervals would contain the true value. Before reading a slope into a handful of points, consider what count of data points would be needed to distinguish that slope from noise.