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As long-range shooters, we tend to obsess over every little detail. We think everything is important! After all, we’re trying to hit relatively small targets that are so far you may not even be able to see them with the naked eye. While you can get away with a lot of minor mistakes and still ring steel at short and medium ranges, as you extend the range small mistakes or tiny inconsistencies are magnified. So, most things are important … but to differing degrees.

So if we have a limited amount of time and money, where would we get the biggest return on investment? In other words, there are lots of things I could focus on (more precise rifle, better scope, more consistent handloads, more practice, etc.), but where should I spend my time and money to get the biggest improvement in the probability of getting a hit at long range? How do I recognize when I’ve hit that point of diminishing returns? Tough questions.

There are so many variables that it’s easy to get lost, and most of us end up doing our best to spread our finite energy and resources in every direction. Is there a data-driven approach to help guide us toward the most important factors to increased hits at long-range?

I’m glad you asked! Bryan Litz created the WEZ (Weapon Employment Zone) analysis tool to gain some insight into this dilemma. So I dropped $200 for the Applied Ballistics Analytics Software Package, which allows you to run your own WEZ analysis. This gives you the ability to systematically study how different field variables in real-world shooting affect the probability of hitting long-range targets. Here is his summary of this software package:

“The Applied Ballistics Analytics software tool is a full-featured ballistics solver that includes the capability to compute expected probability of hit using the same Weapon Employment Zone (WEZ) method described in Bryan Litz’s book Accuracy and Precision for Long Range Shooting. This tool allows a shooter to see how his rifle can be expected to perform under a wide range of conditions, and how errors contribute in causing a bullet to miss its target.”

The WEZ tool appears to be doing what’s called a Monte Carlo simulation, which is a good way to model scenarios that have a certain level of uncertainty in the inputs. Monte Carlo simulations essentially play out hundreds or thousands of possible outcomes based on your inputs. The variables in each scenario are randomly populated within the ranges you set and according to a probability distribution. For example, if you indicated your rifle was capable of holding a 0.5 MOA extreme spread, then it might play out one scenario where it drilled the exact point of aim, another where it hit 0.2 MOA high, another where it hit 0.25 MOA low, another that hit 0.12 MOA to the right, etc. Those shots would all still be within a 0.5 MOA group. It does that same thing for each of the variables in every scenario (muzzle velocity, wind call, range estimation, etc.), then it plays out each scenario, and plots where that shot would land. After it’s ran 1,000 different scenarios, it looks at the results of all of those and calculates your probability of hitting the target based on the variables and uncertainties you defined. Here is a screenshot of this part of the program, and I highlighted some of the key variables you can tweak.

I’d already read Bryan’s book on this topic, but in his examples he really only used 308 Win and 300 Win Mag ballistics. I wanted to run similar analysis on some of the more popular precision rifle cartridges. After playing around with the WEZ tool a lot, I can say it was very enlightening! It challenged a lot of my long-held assumptions about how important different aspects were. As Bryan Litz said in his book, “Looking at each variable separately teaches us how to assess the uncertainties of any shot and determine how critical each variable is to hitting the target.”

Over the next couple posts, we’ll dive into a few specific pieces to the puzzle that we as handloaders tend to fixate on. We’ll start with a big one:

How much does group size matter?

Virtually every rifle shooter loves to print a tiny group on a target. There aren’t many things more satisfying than sending multiple shots into one ragged hole. But, is there a point of diminishing returns in terms of how tiny groups relate to your probability of hitting targets at long-range?

The chart below shows how your odds of hitting a target increase as you shrink the size of your group. All the other variables are fixed, and only the extreme spread of the rifle/ammo combination is changing. I’ve graphed two different scenarios, a 10” circle target at 700 yards, and a 20” circle target at 1,000 yards.

Essentially, what the chart is saying is if you were firing at a 10” circle at 700 yards with a rifle capable of 1 MOA, you’d have an 69.7% chance of hitting the target. But if your rifle capable of 0.5 MOA, that would jump to a 78.3% chance of hitting that same target. So by tightening our groups to 0.5 MOA, we’ve increased our chances of hitting the target by almost 8.6%. If we continue to refine that load, and can get to 0.3 MOA then that boosts our chances to 79.9%. So there is only a 1.6% gain there, and if you’re able to go from a 0.3 MOA group all the way down to a tiny 0.1 MOA group, your odds only increase by 0.8%. Here is a look at what the shot simulations looks like for those scenarios:

Did it surprise anyone to see that there was only a 2.4% increase in hit percentage from a 0.5 MOA group to a 0.1 MOA group? What about just a 0.8% increase from a 0.3 MOA group to a 0.1 MOA group? I’ll be honest, it surprised me.

The blue line on the chart above represents the 20” circle at 1,000 yards, and you can see the effect of tighter groups on hit probability is far more minor for it. The reason is at longer ranges most misses are due to wind, not vertical dispersion. Litz reminds us “Wind is usually the greatest uncertainty in long range shooting, and the cause of most misses. Improving ballistic performance can increase hit percentage at long range, but even high performance rounds are highly susceptible to wind uncertainty.” These simulations were ran with the ability to call the wind within +/- 2.5 mph, which is what Bryan Litz says is what a good shooter is able to do in scenarios he framed as medium difficulty. He says a novice shooter is typically closer to +/- 4mph, an average shooter is usually +/- 3mph, and elite shooter is +/- 2mph. These simluations were programed so that the shooter would be able to call the wind within 2.5 mph 95% of the time, and most of the time (68%) they’d be able to call within 1.25 mph.

Did you notice that? There is only a 5% difference in hit probability in a 1 MOA rifle and a 0.1 MOA rifle when you’re trying to hit a 20” circle at 1,000 yards! You can see that there aren’t many misses above or below the target. The dispersion is virtually all on the horizontal axis from wind uncertainty. So tightening groups on that size of target at 1000 yards, simply doesn’t have a significant impact. You may get more hits that were centered vertically on the target, but if you’re just looking at hit or no hit … there isn’t much of a difference in this scenario. Honestly, that surprised me, and I bet it did some of you guys too. As Litz explains in his Accuracy and Precision book:

“At long range, the environmental uncertainties play a much greater role in dispersion. But at short range, the environmental uncertainties are less important and so hit percentage is more driven by raw precision capability.”

This model helps illustrate the point of diminishing returns, and reminds us that when you reach a certain level of precision it takes an exorbitant amount of effort and money for relatively small improvements in performance. There are no right or wrong answers here! Of course, tighter groups are always better … but it’s up to each shooter to decide how far they’ll chase small improvements in performance. The benchrest guys take it to the extreme, but it’s up to each of us to strike the right balance for our specific circumstances. Hopefully this gives you a more objective perspective on how all that stuff contributes to the probability of getting a hit at long-range, and where the point of diminishing returns lies for one of the items we tend to fixate on the most.

One last point to keep in mind, is that all of this analysis assumes you have centered groups. That means they represent the best case scenario for hit percentage, since your odds only decrease if groups come off center. If you’re scope isn’t zeroed, or your rifle is canted slightly to one side, or your scope’s clicks aren’t calibrated correctly, or you pull the shot … then your hit probability can decrease dramatically. But these simulations assume we have all that stuff squared away.

Other Posts In This Series

This post was one of a series of posts that takes a data-driven look at what impact different elements have on getting hits at long-range. Here are some others posts in this series:

If you want to dig more into this subject or explore some of these elements for your specific rifle, ammo, and ballistics, I’d encourage you to buy the Applied Ballistics Analytics Package to run these kinds of analysis yourself. You could also pick up Bryan’s Accuracy and Precision for Long-Range Shooting book, which has a ton of great info on these topics and other aspects of shooting.

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