Then and Now: What’s Changed- #3 Measuring Groups

Some of the more substantial changes came along this year when I started to look for better ways to evaluate my performance. One of the most significant things happened was being introduced to On Target TDS. I had already been using the free version of On Target to measure my groups. My friend at U.S. Optics got me in contact with Jeff Block, the person who wrote the On Target program. I spoke with Jeff a few times about his premium program, On Target TDS (Target Data System). He wanted some input from me on how to improve it, and actually incorporated some of my suggestions, one of them being the feature that I’ve been using to make composite target composed of shots from different target and shooting sessions.

Jeff also told me about Ballistipedia. We’d been talking about statistics, and how to integrate his program into something that would run more powerful statistical analyses. I was not able to figure out how to make that happen, but the Ballistipedia site had some information about different statistics, and advantages and disadvantages. This was finally the “aha” moment for me that measuring group size using extreme spread wasn’t telling me very much about my total performance.

What’s strange is that I had already been introduced to other ways of measuring, and was aware of mean radius. I’d known about that for quite a while and just ignored it. John Simpson’s book (Sniper’s Notebook), which I’d gotten in 2013, discussed that and other statistical measures, such as CEP (Circular Error Probable), the 99% circle, radial standard deviation, and probably others. Sometimes it just takes one thing to finally click things into place. In this case, it was a description in Ballistipedia of the difference between invariant measures (Mean Radius, CEP, Variance, Standard Deviation) and range statistics (extreme spread, diagonal, figure of merit, covering circle radius). A big difference between the two is that invariant measures “do not vary with group size. I.e., taking more shots tightens their confidence interval but doesn’t change their expected value,” while range statistics “increase with group size. They are more commonly used because they are easier to calculate. But they are statistically far weaker because they virtually ignore inner data points.” (Quoted from the page at Ballistipedia linked above.)

Last spring and summer I went through an obsession about my precision. My rifle would almost be sub-minute for a few shots and then one would just go crazy. It makes a person go through a quasi-bipolar emotional cycle with the rifle. Using extreme spread as a group measure exacerbates this, as it only measures the worst shots. Statistically speaking, the very worst shots are less likely, so you might see a decent group or two before things go completely haywire, which for me made me start thinking I’d finally fixed my shooting problem (which turned out to be a rifle problem), before having my hopes smashed against the rocks with a wild shot.

When using what Ballistipedia describes as an invariant measure, the outlier really won’t affect the numbers that much. It’s just part of the total performance. Additionally, it’s easier to spot small differences in performance over the long term, for example, between the 155 grain Amax and the 168 grain Match King.

Since I’ve been primarily using mean radius to evaluate my performance, I’m much more practical and even keeled in evaluating my shooting. Realizing that “dispersion happens” has really removed most of the emotional baggage that I still see most shooters dealing with. I feel sorry for them, but it’s hard to get people to realize sometimes how something just a little different can change how they think and feel about things. Sometimes, just a little different perspective from which to view things can make the picture so much more clear.

9 thoughts on “Then and Now: What’s Changed- #3 Measuring Groups

  1. Mongo glad Sheriff Rifleslinger do number magic so Mongo not have to, but Mongo head hurt again anyway.

    Mongo only care about three things: can Mongo hit target with first shot, how long it takes, and if target tastes good (Mongo eat target regardless, but still good to know).

  2. I have a booklet, “Statistical Measures of Accuracy for Riflemen and Missile Engineers” by Frank Chubb, PhD. In it he compares a whole lot of different measures:
    Standard deviation of x or of y
    Extreme vertical and horizontal dispersion
    Mean vertical and horizontal dispersion
    Radial Standard Deviation
    Figure of merit
    Mean Radius
    Extreme Spread (aka “group size”)
    Radius of covering circle

    The best is Radial Standard Deviation, and I have used it in the past. Most of these measures require you to get the x and y distance from the bullet holes to some reference lines like the left and bottom edges of the target, then just plug it in to the formulas using a calculator or a spreadsheet. Mean Radius is almost as good as RSD. WIth measures like RSD and MR, all shots contribute to the measure, not just two of them as in Extreme Spread.

    I doubt this booklet is available from the author any more as last time I contacted him was 1993 and I think he was old then. The Library of Congress number is A751662 if that is any help. I might copy the book for you if you are really interested. Contact me through email if so.

  3. Woops, I see your link shows another link to Chubb’s booklet, which is available as a pdf. Strangely they have some argument with RSD and also say it is difficult to calculate. I guess I don’t see why, since the radii are not difficult to calculate. If you have a list of numbers, you can certainly get the standard deviation of the list.

    • I’m what you might call “math challenged”. The main problem I have when reading the Ballistipedia pages, or John Simpson’s “Sniper’s Notebook”, is even when they start out in familiar (or even really easy) territory, it quickly goes over my head with formulas and such. This “sigma” stuff is all Greek to me 🙂

      From what I can understand, I think that their objection to RSD, and it would also appear to apply to CEP (and MR?), is that the math assumes that the vertical deviation and horizontal deviation are equal. From what it sounds like, they (the Ballistipedia authors) assume that vertical deviation is the product of load performance and horizontal deviation is wind error, and therefore an elliptical shot group with a larger vertical deviation is more likely to be the case. I don’t know about that, but I guess I can see that vertical deviation and horizontal deviation are not likely to be exactly equal in any given shot group. They do make reference to “elliptical error probable”, but I don’t have the math chops to see what the difference is.

      At this point I do enjoy MR for at least the ability to have a more reliable “apples to apples” type number to look at. I would like to also see RDS, CEP, and a 3 sigma CEP for the “99% circle”. Do you have any others you would like to see in a shot group stats calculator?

    • The problem with RSD (“Radial Standard Deviation”) is that it has been given a few definitions over the years, and the one that has stuck most often is not “standard deviation of radii,” but rather, “average of orthogonal standard deviations.” The former is extremely hard to calculate in the general case. In the special case we assume for most of the math modelling at Ballistipedia either definition is easy to calculate but they are straight up different numbers.

      When it comes down to it either definition of RSD does not provide any information not contained in MR, CEP, or any other invariant measure. That’s why we suggest steering clear of it and just talking about the hit probability you’re interested in.


      • I still don’t see the problem calculating RSD, or at any rate the standard deviation of the list of radii (if that has any connection to what we call RSD), but I can think of cases where it would not work very well so I guess I will move on to MR as the best practical measure. It’s also very easy to visualize.

        • I flew them not fixed them, while it sounds like you men designed them. More pertinent to keeping on glide slope and runway centerline, is keeping the difference in the two major paradigms properly factored…i.e. the variance in vertical vs. difference in deflection ( horizontal ). ES of velocity showing up in vertical, I think should be factored less than deflection for crosswind component as it is much more dynamic. A rifleman’s wind reading skills require almost Zen calibre SA.

    • I’m working through that. Almost done with the bit initial “load up”. I’m ’bout ready to see what I need to do to put on more weights and make the bar move (figure of speech and literal).

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