"There are no facts, only interpretations." Nietzsche (With that cryptic prelude, this is going to be a rather philosophical post, but will be airgun-related)
How accurate is the (insert x here)?
Sooo very many of the threads we see on the forums all boil down to whether or not a specific rifle/barrel/pellet/slug/brand/etc/etc/etc/combo of the above is accurate. Do airgunners even have a clear definition of what "accuracy" means to us? There was a recent discussion about the phrase, "hole in hole." The premise of that conversation was chasing at the heels of the matter of defining accuracy. For some of us, it means being able to hit a soup can at x yards. For some, it means being able to hit a grey or fox squirrel in the head out to x yards. Some will define it as x # of shots under a (insert dime, quarter, penny, nickel here) at x yards. For others, it means MOA accuracy out to x yards. There's the benchrest crowd, who want a gun that is capable of 250s. And the field target guys who want to shoot a match without a miss. There are so many possible qualifiers: how many shots make a group? was the wind blowing? benchrested? bipod? cherrypicked, or average? were there any witnesses? were the pellets/slugs sorted and weighed, or straight outa the tin? and on and on.
Accuracy is almost like the terms "expensive" and "cheap." It's all relative to the individual, subject to that individual's experiences and opinions. We've also got the fisherman among us, whose cherry-picked group sizes likely decrease with each recounting of the event, the way a fish gets bigger every time the story of how it was caught gets retold.
The funny thing about all this ambiguity, is that most of us know accuracy when we see it, and all of the above descriptors are simply our way of trying to convey to others, what we ourselves perceive as "accurate."
I'd like to suggest that an actual discipline exists that very effectively summarizes the concepts behind all of the above questions regarding "accuracy." That discipline is statistics. Terms like standard deviation are pretty familiar to us, but there's many more from the world of statistics that could be applied: cluster sample (cherry-picked), continuous variable (wind or variation in pellets), confidence interval (how often we do or don't get flyers), distribution (extreme spreads, both in fps or group size), probability, controls, mean, mode, Poisson distribution (the bad tin of JSB 25.39 that has a couple low striking pellets out of every 5 or 6 shots), then there's alphas and p values and power, and on and on and on. And that isn't even touching on the role the trigger-puller plays. We could analyze the concept of randomness that the human factor imparts into the equation. An increase in the application of statistical principles to our hobby could really be quite exhausting, but much more precisely describe accuracy. A simple google search for something like, "confidence intervals for shooting group sizes," can lead you on a pretty deep (and interesting!) dive into statistics and how they apply to our shooting hobby.
Being as this is a review of the Red Wolf, let's get back to that. Is the Red Wolf that I have been reviewing "accurate"? With this idea of some of the concepts of statistics in mind, I decided to analyze a recent shooting session with the gun. I took a bunch of statistics classes, but that was a decade ago and I’m pretty rusty, especially because the focus wasn't analysis of shooting results at the time. So, due to my lack of statistical analysis practice, I'll be stretching some of the concepts a bit here.
“Accuracy” in this little experiment is viewed as the ability to place the pellet on a dime-sized target. A dime measures 0.705 inches. A .22 pellet is usually somewhere around 0.217inches in diameter and makes a slightly smaller than that hole. For this analysis, I’m going to define accuracy as the ability to place a pellet within 0.461inches of where I want it to go. This visual might help illustrate my thoughts:
0.705 (diameter of dime) + 0.217 (diameter of pellet) = 0.922 / 2 = 0.461inches from center of dime, 360 degrees from the theoretical desired perfect shot/aim point).
I initially was hoping to keep them all WITHIN the confines of the edge of the dime, but I'm just not that good of a shot so had to settle for basically anything within or touching the dime. I believe the big long range benchrest comps like EBR are scored this way, cut the line and get the higher score.
The shots were taken on LOW with JSB 18.13, straight from the tin, about 29fpe. At 53 yards. Benched. The starting pressure was 244 bar and ending was 134. 160 consecutive shots, no sighters were taken at any time during the 160 shots. The shots were divided into 16, ten shot groups. Minimal winds: 5-7mph, right to left.
Aim points were the photocopied dimes target I made a few weeks back.
Here it is.
So much to potentially look at here.
Back to that subjective aspect of how we perceive accuracy, for me, there is a strong theme of consistency in an accurate gun. And by that, I mean that a gun needs to be able to consistently place pellets where I want them. So, the primary endpoint here was whether or not the RW could shoot 160 shots at this power setting, with these pellets, with me at the helm, without having any outliers (flyers). Basically, what is the confidence interval (CI) of the guns accuracy? First off, the CI in statistics is based on the sample size. The larger the sample size, the stronger the likelihood that the observed results were not due to chance. In other words, the robustness of the data grows with sample size. 160 consecutive shots seemed like a large enough number for flyers to rear their ugly heads.
To be able to properly calculate a confidence interval, I would need a measurement of all the impact points, starting at 0 inches (dead center of dime) all the way up to 0.461 inches (outer edge of the point the pellet could hit and still cut the outer edge of the dime). That would allow me to calculate the confidence interval, which is really a measure of the dispersion within a data set. Think of it as a bell curve and envision sorted pellets. This was shared here on AGN (not by me) about 5 years ago and gives a good visual:
What we see there is essentially a bell curve. Whoever weighed those likely chose a window of what they considered "good" or rather, consistent pellets, which is the purpose of weighing, to exclude the outliers. The outliers residing in the outer edges of the curve, like this:
That diagram starts to get into using the confidence intervals to determine a confidence level, but that's another rabbit hole.......
Back to the 160 shots on that target above. I'm seeing somewhere between 15 and 25 shots that did not at least cut the outer edge of the dime. That bottom dime in the 3rd column messed up my data. I had been holding for wind and it got late enough in the evening the wind quit on me, so hold-off was no longer needed. It just took my stubborn self a full 10 shots to realize the wind had let up. Let's assume that group was centered on the dime and I've got 15/160 shots not touching the outer edge of the dime, ie within 0.461 inches from dead center of the dime. Let's call it 16 to make the math easier. 10% of the shots did not fit into my defined parameters of "accuracy." (If I throw that bottom dime in third column out completely, same result, 15 of 150 shots = 10% were outliers). Back to the pellet comparison. 10% of a 500 count tin of pellets would be 50 pellets. So, comparing this data to a sorted tin of pellets, only 50 of the pellets did not make the cut for "consis
tent", 450 did. Considering there was a human pulling that trigger for all of the 160 shots, really incredible show of accuracy from the Red Wolf. The outliers were shooter-induced.
This is not a cluster sample (cherry-picked). I didn't repeat this 160 shot experiment a bunch of times and pick the best one. I took these 160 shots ONE time and this is the result. No cluster sample, best the gun can do, out of 10 tries here. I simply shot 160 shots, one time, and these are the results.
Although I would like to take a closer look at a cluster sample within the data set. This is a close up of the third dime down, second column. Ten shots into that little group. Best 10 shot group of the 16, 10 shot groups right there.
My Nietzsche-like interpretation of all that...............pretty good evidence that the Red Wolf platform is capable of consistent "accuracy," however you like to define it.
(I mentioned it once already in the review, but this is a gun that I would really like to strap/clamp into some sort of vice and do a bunch of high-volume, long-range shooting. I think the results of what it can do with the shooter taken out of the equation would be unbelievable, unless you happened to be right there watching it happen. )
