On Zeroing

Last month I bored you with all the 10 shot groups that I shot. Now I’m going to unpack all the thought processes that went on in my mind while I was in the middle of collecting that data.

First of all, in the past I was a little careless on my zero. I paid more attention to precision (group size) than accuracy (actually hitting the target). The problem with that way of doing things comes when you actually do want to hit something. That gets frustrating.

What can be more frustrating is actually getting zeroed. When I started out rifle shooting I used three round groups to zero. In reference to that method, have you ever had the feeling that your sights must be moving around, or that someone must have messed with your turret since the last time? Assuming quality scope mounting components (no, that’s not a good place to use a low bidder part) that probably isn’t the case.

It was John Simpsons “Sniper’s Notebook” (and several follow up conversations with John) that clued me into what just seems like common sense. Each shot is a random event. Your rifle does not shoot all the shots through the same hole. It shoots groups, no matter how small they are. Because the shots are random, you don’t know what part of the group the shot you fire next will be. It could be the one that goes right where the crosshairs go, or it could be the one at the edge of your rifle’s group. This leads to the next question… what exactly is your rifle’s group?

Let’s consider the system. Your rifle, your scope, your ammo all fit together to form a shooting system. Normally I put the shooter in there as well, because someone has to shoot the rifle (except for those pesky ASSAULT WEAPONS, they shoot innocent people of their own accord). Consider that you had a single lot of ammunition, and that the rifle could stay in the same range of barrel cleanliness and temperature as you would normally keep it and shoot it, and that you could shoot a 5000 round group of ammo at the same target on the same day and suck all the life out of your barrel (I get that it’s not plausible, just bear with me). That group would be the total population of the rifle’s capability. You would know that the center of that group is where the rifle’s zero should have been, and you would know exactly what you could expect to hit with your rifle even at its very worst with any one of those 5000 shots.  

The three round groups that I used to zero my rifle with in the past are not as large as that 5000 round group would be.  So how does one predict the size of that theoretical group without actually shooting it.  You just have to have enough rounds to have a statistically significant sample. That’s a good thing because it would be a drag to wear the barrel out to figure out what it’s going to do next (replace the barrel and start over).

Consider a shooting system whose potential group size is 2 MOA. Three rounds from the system could go anywhere, but it’s more likely that a round will land near the center of the theoretical potential group than its edge. That means that it’s not likely that the three round group will be indicative of what the rifle will do over the course of many shots. The three round group could very likely be less than a minute. If that’s the case, then the center of that three round shot group, although it’s within the center of the rifle’s theoretical total population group, does not have the same center as the rifle’s total shot group would. So if you adjust your sights based on that 3 round group, what have you done? You’ve just started the beginning of a long train of confusion, pain, lost work, crumbled relationships, substance abuse, arrest after arrest, until finally you die face down in a ditch. OK, maybe I exaggerated slightly.

It may be obvious that I spent some time obsessing over this issue. I started noticing that even my 10 shot groups started to wander. It became clear that to follow each new twist and turn of the group center would take me down the same road of zero chasing as the three shot group.

One thing that has been helpful is the On Target program. They have a free version but I went ahead and bought the full version.  You may have noticed that the recent photos of my groups have the holes plotted and measured with a text box delineating all the relevant numbers. Another thing it does is calculates the mean point of impact, the mathematical center of the group, which is a lot nicer than eyeballing it.

Getting back to all the groups I posted last month. I posted 7 groups in all. 6 of them shared the same turret setting on my scope. Here they are again:

1-6-14 10 Shot FGMM 100

&1-11-14 100 Yard 10 Shots

1-13-14 10 rounds 100 Yards

1-19-14 FGMM 100 yards

1-20-14 FGMM 10 shots 100 yards

1-25-14 10 Shot FGMM 100 yards

So there we have 60 shots, all with the same zero (assuming my scope has solid tracking and returns to zero properly). I don’t know if 60 will tell me everything I need to know, but it’s better than 3, or even 5 shots. Notice that each group analysis has a mean point of impact. I started wondering about halfway through this what would it look like if I went just a little farther down the rabbit hole.

I took the file that I use to print my targets from, and opened it on Paint.net. I plotted each of the 6 different mean points of impact that On Target generated for each group. I saved that file, then opened the image in On Target. I plotted the mean points of impact just as if it were a shot group so I could get a look at the mean point of impact for all the groups. Here’s what that looked like:

Cumulative Mean 1-25-14

If you look at the individual groups, there is quite a bit of variance. If you were to pick any random three shots out of the 60, it might look like my zero was quite a bit off. I don’t know if this is my zero actually wandering around due to tolerances or ammo variance, or ???, or if it’s just indicative that 10 shots is not quite a large enough sample to really get it nailed down.  What the cumulative analysis shows is that over the long haul, I seem to be pretty much zeroed. That didn’t really tell me everything I wanted to know.

After I had five 10 shot groups I wanted to know what the worst case scenario was for my group size. Essentially, I wanted to know my cumulative extreme spread. I plotted the worst shots from each group and ran them through On Target.

Cumulative Extreme Spreads 2

There are better ways to figure out hit probabilities than extreme spreads, but this was a nice way to look at the worst case scenario based on shots that I had actually taken.  Also, it seems to be a very happy group, and who doesn’t like that?

Coincidentally, the maker of On Target also has an upgraded version of the software called On Target TDS (Target Data System) that is meant to combine large numbers of shots into an aggregate group.  I’m going to be giving that a try soon to see if it saves me some work and makes the cumulative results a bit more accurate and easier to get to.

To sum up on this whole zeroing/shot group thing… while I have taken this rifle out and shot a four round 0.25 MOA group within the last few months…


…it really isn’t indicative of how the rifle is likely to perform.  There’s no way I would ever call this a quarter minute gun.  All the stars just happen to line up that day. It was just four rounds out of the last 3500 or so that randomly landed in nearly the same spot.  I should have bought a lotto ticket too.

What this has shown me is that, as John said during a conversation with him, it’s a convenient fallacy to say that the gun is “zeroed”.  It takes a while to even begin to get a handle on getting it close.  Having said that, at some point you have to have it in your mind that your gun is zeroed so you can go out, leave the minutiae behind, and use the rifle to do some good work.

Why go to all this trouble if my goal is only as modest as hitting a 4″ target within 200 yards?  I’ll explain later.  Thanks for reading.


8 thoughts on “On Zeroing

  1. As always, a great insight.

    I recently picked up On Target, based on seeing you using it on here.

    I do find it interesting that some people seem to be constant ‘knob twiddlers’ – firing a string of 3 shots down range, then adjusting their scope, 3 more, adjust again, 3 more, adjust back to where they started. What also amazes me, is bagged, on a bench, they still are shooting bigger groups than us on a mound with a bipod. There seems to be a correlation between the amount of knob twidling being done, the cost of gear, and the more removed from practical shooting they get.

    Anyhow – I should have stopped at my cold bore shot on the weekend – 4mm from dead center. Statistics be damned! Just put that 1 shot up on the wall and brag!

    Unfortunately, the rest of the shooting was more in line with my skill level, so much more practise to do.

    I have had a look through the site – but have you ever put up the specific dry fire drills you go through? I am essentially just working through positional shooting positions at the moment, but wondering if you have any other specific exercises you run through?

    • You don’t seem like the type of guy to play it safe and stop at one round. Better to keep shooting and risk ruining the perfect shot than to be too timid to press the trigger again.

      Most of my dry fire is offhand. I think it’s more fun, and it’s easier to do. I like to find something I can barely see and try to “hit” it. Lately I’ve been working for speed, so it’s offhand again trying to get a fast hit on a relatively large target. For other positions I might take one shot, get up again, and take another. Then another, and so on. Other times I might try to slow down and find my natural point of aim just to really try to get the feeling burned into my brain and take a few really good shots. Other times I might just concentrate on trigger control with the bipod.

      • Too much fun to be had when you press the trigger to stop!

        I don’t get out to the range as much as I would really like too – costs and time – but certainly the dry fire has helped with the comfort level of the mechanics. Thank’s for the insight. Will keep at it!

  2. RS,

    Another thing to consider is your parallax. Most people don’t really remove all the parallax and so comparing one group to another can be less than informative. Even within one shot string, if you’re readjusting your position or cheekweld every shot, you are not getting the level of consistency needed for top level accuracy. I think that your article is correct as far as it goes, but I also think that more people’s groups and day to day consistency suffer more from their interface with the gun, rather than the inherent accuracy of their gun/ammo/scope. That assumes of course, that the equipment is reasonably well made and assembled.

    • I have wondered for a while how much of my group size was parallax, especially when I went through all that obsessiveness with the FN. Now would be a good time to test that. I have an SWFA 3-15 on loan. It’s basically an upgrade from my 3-9×42, which has no side focus, so it would be as direct a comparator as I could find if I just keep it on 9X. The hard part is getting the rifle back in a timely manner.

  3. Greetings RS,

    I just wanted to say that I’ve found this quite informative. I’ve always had the feeling that getting a zero was not quite as simple as verifying where my rifle was hitting with a three shot (or 5 shot) group. But my relatively poorly developed skills as a shooter mean that ten shot groups have generally been so disappointing that I willingly bought into the ‘gun magazine’ reality that five shots (or three shots) is all that is needed and pretty much avoided them. In fact, I can’t remember the last time I fired anything like a ten shot group.

    And then, of course, my shooting interests in recent years have revolved more around ‘practical’ field shooting (a la Cooper’s ‘Art of the Rifle’) where I am more concerned with getting into the best position I could and doing the best I can with that first shot and maybe a follow-up.

    In short, you’ve got me thinking that there could be some learning to be gained by having a bit of a go myself at something similar to what you’ve done here over January.

    Anyway, best wishes.

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