For accurate data, sample size matters.
How many shots do you need to determine the accuracy of your rifle?
Three shots? Five? Ten?
Try 30, and 50 is even better.
“We’ve learned a lot in the last couple of years in statistics and probability and how they apply to what we do as precision rifle shooters,” said Seth Swerczek, marketing communications manager for Hornady®.
“We conducted a huge amount of large-sample-size testing and said, ‘Well, what’s good enough?’” said Jayden Quinlan, senior ballistician.
While it depends somewhat on the situation, the short answer is that more is better.
Most shooters will take three- to 10-shot samples.
Go big or go home.
“But the minimum sample size to get fairly accurate data is generally around 30 to 35,” said Miles Neville, project engineer.
How does he know?
“I just really burned out a couple of barrels shooting 35-, 50- and 100-shot groups just to see what is actually there,” Neville said.
He found that the results a shooter might get from a five-shot string just weren’t repeating with 50 shots.
“You’re getting taken for a loop because you believe in this small sample data, but it isn’t necessarily repeatable,” Neville said.
Enough for a bell curve
The key is standard deviation — in this case, how far off the average the shots in a group are.
“We can use the recorded standard deviation to get an idea of what the future performance could be, if it’s valid,” Quinlan said.
A normal distribution of data should look like a bell curve, but if a shooter has three or five shots worth of data, it probably won’t.
“It takes a certain minimum threshold before that really starts to develop its shape,” Neville said. “Standard deviation, as a predictive tool, the way it’s meant to be used, only works if you have a histogram of data that represents a normal distribution.”
“If you’re going to do small sample sizes, the predictive tool of standard deviation really isn’t valid,” Quinlan said.
Go for decreased variability
In his tests, Neville looked at what happened to extreme spread, standard deviation, group size and group mean radius and then plotted those as a function of how many shots were in the group.
“I’ll shoot 50 shots, and then at two shots, what’s my standard deviation? At three, at four, at five, at six, at seven, all the way down to 50, and then plot those out,” he said.
Test results found that, the more shots in a sample, the wider the spread of shots will be, but variability will decrease, so the data will be more accurate.
Neville said a shooter should expect 40% to 50% variability with five-shot tests.
“If I take exactly the same ammunition and I repeat that same five-shot group over and over and over again, I can expect 40% to 50% variability in the results,” he said.
A shooter could pull out the best of those five-shot groups and focus on that, but tests show that those results are not repeatable over the long term.
Strike the right balance
Of course, the average shooter needs to strike a balance between obtaining accurate data and the time and money required.
“We’re saying that we try to get to a sample size of 20, because if you look at those numbers, that’s kind of the trade-off point,” Quinlan said. “With a 20-shot sample, your variation is 20% to 25%.”
If time and money are lesser factors, shooting 30 — or even 50 — is even better. In their testing, Hornady ballisticians went as high as a 500-shot group.
“Once you got to 50, you had established that normal distribution,” Quinlan said. “That bell curve pretty much stayed there after 50.”
“We’re not here telling you what to do. We’re telling you what we found,” he said. “If you increase your sample size, you’re going to get better data.”
“It seems that 10 gives you a good look, 20 gives you a better look, 30 will pretty much tell you,” Swerczek said, “and anything after that is a bonus.”
For more information on assessing a rifle’s performance using data that’s statistically significant, watch these podcast videos for an in-depth discussion on how statistics play a role in rifle and load analysis.
