Guide
Your 5-Shot SD Is a Rumor (the Math That Proves It)
Every handloader has done it: five shots over the chronograph, SD reads 9, and the load gets promoted. Here's the problem — the standard deviation of a small sample is itself wildly uncertain, and the uncertainty has a known shape.
The numbers
For a string of n shots, the sample SD follows a chi distribution. The 95% confidence range on the true SD, as a multiple of what you measured:
| Shots | True SD is likely between |
|---|---|
| 3 | 0.52× and 6.3× your SD |
| 5 | 0.60× and 3.7× your SD |
| 10 | 0.69× and 1.8× your SD |
| 20 | 0.76× and 1.5× your SD |
| 30 | 0.80× and 1.3× your SD |
So a 5-shot SD of 9 fps means the load's true SD is plausibly anywhere from about 5 to 26 fps. That range covers "excellent" and "mediocre" at the same time. The measurement isn't lying — it's just quiet about how little it knows.
What to do with this
- Never rank ladder rungs on 3–5 shot SDs. The ranking is noise wearing a lab coat. Use those strings for velocity only.
- 10 shots is the floor for an SD claim; 20 is a conclusion.
- ES is worse. Extreme spread grows with string length even for identical loads, so ES comparisons across different string lengths are meaningless.
- Report the range, not the point. Our string stats tool — and the Kit — always print the 95% range beside the SD.
None of this makes small strings useless. It makes them velocity data with a rumor attached. Load development gets honest the moment the rumor is labeled.