The Shooter Tolerance Stack

Alternate titles:

-Why Having a Precise Zero is Important
-How on Earth Did I Just Miss That Shot?
-Why You Shouldn’t Disregard Everything!

-Why Wearing Underwear as a Hat is a Good Idea (just kidding)

In January I spent a lot of time, ammo, and careful measuring in establishing where my rifle was shooting. In February I shared my results in the form of a cumulative 60 round group comprised of 6 10-shot groups shot with the same zero setting over the course of a month, as measured by On Target TDS. In that last article I promised to explain why I would go to all that trouble. Here’s where I do my best to make good on that promise.

Before even entering into this discussion, I should frame it by asking you to keep a few generalities in mind:

-Exertion decreases precision and accuracy.
-Time stress decreases precision and accuracy.
-Precision and accuracy tend to degrade proportionally with the height of the shooting position from the ground.
-The ability to precisely target internal anatomy is a skill in and of itself.

The basic premise of this series of articles will center on a concept that I think of as the “shooter tolerance, stack”. In machines such as guns, variations in dimension in parts are a reality. Some dimensional variance is expected. The manufacturer will specify a certain acceptable range of variance, called a tolerance, for each part. The idea is that even with the specified tolerance, the parts will be able to be assembled into a machine that will function properly and reliably. As I understand it, a problem can arise when several parts are at the extreme end of the specified tolerance. This is called a tolerance stack.

Shooter tolerance stacking as I define it occurs when more than one process or condition involved in placing a round on a target is on the edge of what any one process or condition, by itself, would still be acceptable to facilitate a hit on the desired target.  Because more than one variable is involved in the tolerance stack, what by itself would be insignificant could, in concert with other variables, result in a miss.  I think that this is most likely to be a problem in practical shooting situations that don’t allow a high degree of control on the part of the shooter. This would likely be an uncommon occurrence, but as they say, “stuff happens”.

The smart shooter, especially when working with a target or vital zone of a known and relatively fixed dimension, will adjust his sight to allow for a maximum point blank zero that maximizes the potential of his round’s trajectory. This is a great strategy, and to some degree will usually allow the shooter to fire a shot without having to compensate for distance or atmospheric conditions. I believe that although this is a sound strategy, if only understood at a surface level it can lull the shooter to completely disregard trajectory and wind.

Problem #1

Most shooters think of zeroing as a matter of aligning point of aim and point of impact. The point of aim, especially in a rifle scope, appears as a finite point that is easy to see. It’s so easy to forget that the next shot that comes out of the barrel is part of a potential group (the group that would appear if you just kept firing round after round of a particular ammo using a particular sight setting). Unlike your point of aim, the rifle’s point of impact is not exactly a finite point, and could be more accurately called a “zone of impact”.

Something that exacerbates the shooter’s tendency to disregard the potential shot group is that group sizes in gun magazines tend to be evaluated in terms of 3 or 5 shot groups. Groups have this strange tendency to get larger as more rounds are fired, and 3 or 5 shots will not be indicative of what your rifle will actually do.  In practical terms, this means that the 0.75 MOA capability, as defined by a typical gun magazine, might actually mean that the 3 groups that formed that group are actually part of a larger potential group that is probably closer to 1.5 or 2 MOA, and you don’t know where the three round sample fits into the bigger picture of the rifle’s potential group. If you’ve found yourself adjusting your zero on successive range trips you may be using too small a sample size to set your zero (assuming quality components, which is a huge assumption). Groups on the internet are often made up of a larger number of rounds, but are almost always cherry picked examples shot under perfect alignment of celestial bodies (mine excepted of course). In short, many of us have unrealistic expectations from our rifles.

Cumulative Group
An accurate representation of a 60 round group made up of 6 10-round groups shot over a month with the same sight setting, as measured by On Target TDS. Notice the frequency of shots in various locations in the group. Pick any three shots that seem statistically reasonable to you. Now ask yourself a.) whether the size of that 3-round group is indicative of the size of the rifle’s “bigger picture” group, and b.), whether the center of those three shots coincides with that of the 60 round group. Also consider whether five rounds is going to show you much more.

I’ll continue this next time. Hopefully it won’t be a month before then.

6 thoughts on “The Shooter Tolerance Stack

  1. Excellent stuff brother….also Brian Litz’s book has a great discussion on this….the two types of variables….deterministic and non deterministic….he goes into ammo dispersion as well.

    • I have the 1st edition of his book, which I bought right as the 2nd edition came out. I’m waiting for the 3rd edition to come out so I don’t get burned like that again. I’ll give it a re-read and see if it causes any new mental breakthroughs.

      • Vol. 2 of Litz’s work has enough new stuff that it is worth getting. Both work together well, and are not just a rehash of each other. 2 is actually better reading as well.

  2. You are light years ahead of me for sure in methodology ,but empirical data brought me to the conclusion that if you had zeroed rifle that would strike within inch any direction of the mark and it had a good trigger,you better hang on to that stick

  3. Good post. And thanks for the illustration. In this case it proves that a picture is indeed worth a thousand words. It proves your point quite well.

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