New member Q -- How Many Shots to Set Zero?

[stats_guy]

Since statistics and life never match 100% of the time, rarely 95% of the time…….

If you shoot a 100 shot group, and randomly select 10, 10 shot or 20, 5 shot groups.
How many “true zeros” would your app show?
How many of those would be the same as the 100 shot “true zero”?
How far off would they be?

This is actually a great question and I will try my best to answer.

By "true zero" I mean the center of a very large sample group shot with same rifle, load, shooter, and environmental conditions.

Let's take the 20 5-shot groups example, and let's say we hold a 95% confidence level.

Each group will have a slightly different center and an "uncertainty circle" associated with it. The circles will have significant overlaps with each other, and 95% of those circles (so 19 out of 20 groups) will contain the "true zero".

The same idea applies for different confidence levels - at 80%, the the circle will be smaller, but it's also less likely to contain the true zero, and at 99% the circle gets pretty huge.

 

[dellet]

This is actually a great question and I will try my best to answer.

By "true zero" I mean the center of a very large sample group shot with same rifle, load, shooter, and environmental conditions.

Let's take the 20 5-shot groups example, and let's say we hold a 95% confidence level.

Each group will have a slightly different center and an "uncertainty circle" associated with it. The circles will have significant overlaps with each other, and 95% of those circles (so 19 out of 20 groups) will contain the "true zero".

The same idea applies for different confidence levels - at 80%, the the circle will be smaller, but it's also less likely to contain the true zero, and at 99% the circle gets pretty huge.

I think if you were to use your example 10 shot group and simply use shots 1-5 and 6-10 as two five shot groups, your theoretical numbers would tell a different story. With something like 250, 5 shot combinations available from that single group, it could get interesting how much different the centers are.

 

[stats_guy]

Yeah, if I split my 10 shot group into 2 5 shot groups, I'd end up with 2 circles, each larger than the current circle (because there's more uncertainty with only 5 shots), but both circles would overlap the 10-shot group's center.

With more and more combinations, it's all about the confidence level selected. So with 250, 5-shot combinations, each with a slightly different center, 95% of those circles would overlap the true zero point.

 

[Fast14riot]

One aspect I've always held as truth for load dev, sighting in, any form of low sample statistics in shooting, previous experience plays a big part of the decisions we make. Even though previous data is not part of the sample lot, it affects our mental filter for making decisions.

When I spin up a new barrel in the same chambering, I can normally have a great shooting load to take to 1000y in about 20 shots. A totally new chambering, I need more to establish my boundaries of load and seating depth, however previous experience tells me what it looks like when I'm not optimized in just a couple shots instead of firing 5 rounds "just for the data."

 

[stats_guy]

One aspect I've always held as truth for load dev, sighting in, any form of low sample statistics in shooting, previous experience plays a big part of the decisions we make. Even though previous data is not part of the sample lot, it affects our mental filter for making decisions.

When I spin up a new barrel in the same chambering, I can normally have a great shooting load to take to 1000y in about 20 shots. A totally new chambering, I need more to establish my boundaries of load and seating depth, however previous experience tells me what it looks like when I'm not optimized in just a couple shots instead of firing 5 rounds "just for the data."

Thanks for bringing this up because it's a great point that's often missing from these statistical analyses - they don't incorporate prior knowledge into the calculations. Whether it's previous groups that the rifle has shot, or in your case previous experience with reaming a chamber where you have a decent idea of how it should shoot.

There's the field of Bayesian statistics which does take prior knowledge into account - the whole idea is that you "update your priors" based on new information. It's a little tricky to get right, but it's something I'm working on incorporating for group variance comparison (where the goal is to determine if one group is truly more precise than another). The idea is to add a level of statistical rigor to load development while maintaining ease of use and showing results that are intuitive. I've been doing group comparisons for my own load development using Excel, but that is very tedious and was part of the motivation for creating this app. Here is an example of two 10-shot groups compared using Bayesian statistics.

 

[swd]

I can put a new barrel on, bore site it at 1K and usually have a good zero in 3-6 rounds or so.

A year or so ago I was at our local 100 range watching a guy try and sight in a hunting rifle. He couldn’t get it on paper after a lot of shooting. I asked him if he wanted some help to which he said yes. I took the bolt out, bore sighted it and had it zeroed in 2 shots. We’ll call it 3 with a third to confirm the second shot. He just looked completely amazed and befuddled at the same time, but was very thankful, LOL