Then and Now: What’s Changed- #8 The Price of Hard Data

I think it’s amazing that when I started the blog I didn’t really even know what to expect, performance-wise, from my shooting. I really hadn’t taken the time to shoot static groups of sufficient sample size (number of shots in the group) to know how I shot until those first fateful offhand groups in July of 2011 where I showed the world that I wasn’t afraid to put up realistically sized (euphemism for amazing huge) groups. Maybe starting with offhand wasn’t such a great idea either.

My ability to analyze my shooting at that time was extremely primitive. Like everyone else, I was only looking at the two worst shots in my group. I was doing ten shot groups because it seemed like the right thing to do, but I didn’t really understand the relation of sample size to what my capabilities were. That was part of what the blog was really for in the beginning, but there was so much data in the targets that I wasn’t seeing.

In the past year my curiosity in analyzing my shooting has grown. I realized that knowing about how big my worst shots in a 5 or 10 shot group was really wasn’t telling me what I want to know. I want to be able to predict the probability of a hit from a given position at a given distance. That was really the tough part of the goal that I set for myself (and am overdue in evaluating), which was to be able to hit a 4” target inside 200 yards on demand regardless of conditions, terrain, stress, exertion, or if the target doesn’t want me to shoot it. How do I evaluate, from a shot group, if I can make a hit on demand?

The scope testing project I did over the spring and summer also tested my ability to evaluate my own shooting, but forced me to integrate different measures of performance into the total analysis to give me an idea of how easily I was able to do different things with different scopes. I had to figure out ways to pull out and separate accuracy from precision, and how time factored into each of those things as well. Then I had to try to figure out how to present the data so it could it could be understood.

What I’ve learned is that it’s a ton of work to really get a handle on aspects of shooting performance, and I’m not to the point yet where I’m utilizing my data to make predictions about my ability to hit on demand. I’ve also learned that my pageviews plummet when I get into stats.  I mentioned recently how I’ve been learning more lately about statistical analysis of shot groups from resources like John Simpson’s “Sniper’s Notebook” and the Ballistipedia website. I’m hoping that through some collaborative work with Jeff Block, who created the On Target TDS program, some easier ways to get at meaningful and useful data will come to light. I need to point out that I’m not a business partner with Jeff, and having nothing to gain from plugging his program, other than hopefully other people learning more about their shooting.

The point of all this number crunching is to predict with a reasonable degree of confidence, “Can I make this shot? Should I take it? Is it the ethical thing to do? Is it the safe thing to do? What are my chances of actually hitting my target, and what odds am I willing to risk under the circumstances?” The answers need to be known ahead of time, and what it should boil down to is a quick “shoot” or “don’t shoot”. Next month, when the blog goes back to “normal” mode and I start posting actual shooting results, hopefully I’ll be able to do that with my own shooting. Maybe my work can help you figure that out too.

8 thoughts on “Then and Now: What’s Changed- #8 The Price of Hard Data

  1. Your summary (last paragraph) should be in every serious rifleman’s mission statement, I do not recall having seen or heard it together with such brevity and clarity
    Well done Slinger

    • Agreed. Pretty much my thoughts on ‘programming your fire control computer’. You should be able to look at the target and know immediately.

  2. I’ve given what you have mentioned some serious though over the years. I think I have a way to calculate it. If you have a large set (say 100 data points but we can work with smaller data sets) of values of shots and we have the measurement between point if aim and point of impact for a given position and a given distance, we can enter the data into a simple spreadsheet program. From this, we can get the standard deviation. One standard deviation will tell you the group size for 66% if your shots. Two standard deviations will tell you the group size for 95% of your shots. Three standard deviations will tell you the group size for 99% of your shots.

    There are a few details that are important to capture for the way we measure but it isn’t that hard.

    Anyway, that’s how I’ve though of doing it.

    Then, I can say that shooting offhand at ZZ yards, 95% of my shots are x MOA; kneeling it is y MOA, and prone it is a MOA.

      • I’ve actually thought about that and think I have a solution. Give one direction (say all holes right of zero) a positive value and the other direction (say all holes left of zero) a negative value. In essence you are dividing a circle in half. Half are positive and half are negative. Yes, the average will net to zero or close to it. But the standard deviation will give you a real number.

        I also have ideas on how to handle a rifle that isn’t quite zeroed.

        I think it would work. What do you think?

        • Unfortunately the statistics are not that easy. I’ll show you where your approach will lead: Suppose the standard deviation in each axis is 1MOA. If you only consider one dimension the odds of a shot being within 1 standard deviation of the center of impact is 68%. However when you account for the fact that the shot has dispersion in two dimensions, and if you assert that each dimension is uncorrelated and normally distributed with standard deviation of 1MOA, you discover (via the bivariate normal distribution) that only 39% of shots are within 1MOA of the center of impact.

          The math is at Ballistipedia to support the results and recommended approaches for those who want to delve into it, but that page I linked to alone was the product of several months of (part-time) work by expert statisticians who already knew the general form of the solution in this scenario. You’ve got a long road ahead of you if you want to reproduce it from scratch!

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