Well, owning both a K31 and a Springfield and having shot both out to 600 yards, my feeling is that the K31 with GP11 ammo is the better of the two.
YMMV

Very interesting and well done video for educational purpose, with all indispensable details. It tells a lot about de possibilities of a medium rifle caliber.
The maximum distance I shot with a rifle was 880 yards with a Steyr Mannlicher SSG 69 (military sniper version), which is one the most accurate modern sniper rifles in medium caliber in the world at this time (my target was a square meter sized paperboard).

At such distances, one must be knowledgeable about a particular ballistic phenomenon which is the drift owing to the pitch of the barrel’s grooves. A rifle’s bullet is spinning at a very high speed (that why bullet quality matters much). For example, the bullet of a M16 rifle is spinning at the muzzle at about 3000 rounds per second (since the goove’s pitch of a M16 barrel [or a 360° revolution] is in the surrounding of 12 inches). An air bubble in the lead under the jacket will make a bad bullet.
So, the physical effect I’m talking about is that the bullet literally rolls on the ambient air, which is very hard at a speed of 2250 to 2850 fps.
And as it is rolling it drifts naturally in the same direction as the barrel’s grooves. If the grooves turn clockwise, the bullet will slightly move to the right.

This drift is not important for shooters who never shoot at distances such as 200 to 400 yards, as it happens most frequently. But one must count with it from, say, 800 yards on.

For example with a bullet of a 308 NATO rifle, the drift owing to the pitch of the grooves is in the surroundings of 2 feet, which is an important variation when setting a riflescope (so we could surmise that it must go over 4 feet at 2000 yards [inertia in the drift must add to the drift effect, which sould theoretically decrease as the spin is progressively slowing]). As a matter of fact, this phenomenon explains the presence of a curved line associated to the crosshair with certain military riflescopes (case of the Russian Dragunov semi auto sniper rifle in 7.62x54R, for example).
Of course, the problem when shooting at such very long ranges is that the drift owing to the wind is interfering with the drift owing to the pitch of the grooves. That problem is often blurring drift estimates or calculations.

That’s why one must do a great deal of shooting tests at various ranges and take notes in order to write a range table indicating the right number of clicks for a given riflescope at various distances from 100 yards to 100 yards.

Unfortunately, such tables would be of little help, if ever, when using an open sight.

The shooter in this video is using Sierra Match type boat tail shaped bullets, which are the best since long to my knowledge. No other shapes of bullets are as good as boat tail for long distances, and Sierra is the best manufacturer.
So I’m not surprised he found them as the fittest during his shooting tests.

About the Swiss rifle he is using, I believe that he would enjoy a significantly greater accuracy with the sniper version of this rifle, that is the Schmidt Rubin ZfK55 with a 25.65 inches barrel and a 3.5x military riflescope. This is a rare a searched gun, of course, which is currently sold in Switzerland for the equivalent of $5000 to $6000 (about $600 for the same rifle in the video).
Swiss Schmidt Rubin infantry and sniper rifles were conceived for shooting at long ranges in mountains, more especially. And, as anyone may guess it, Swiss quality is in all of those rifles as in any etter known Sig P210 pistol (I call it “civilian Lüger quality”), at the exact opposite of other guns of the same category such as Carcano and Mosin-Nagant.

You can probably hit 4 out of 83 with your eyes closed.

You should try a few shots at 2240 yards.

I would like to add something more to our interesting subject, and also a remark to what Jeff said, even though he was half joking as I surmise.

Of course, at such distance with a middle caliber, even if the shooter had completely locked his rifle in a good heavy shooting bench, there would be a significant dispersal of the bullets. A totally random dispersion, actually.
For multiple factors affect each and every bullet’s trajectories. To name some: the slight deviation of the longitudinal angle of the bullet at the moment the powder ignites and push it through the “throat” of the barrel (this short part located between the “freebore area” just after the chamber, and the bore). A very small variation of this angle when getting stuck in it will make the bullet spinning around a center of rotation that is not aligned with its real physical center.
We also must take into account several small variables such as how the powder ignite from one shot to another, and how much pressure it delivers exactly at each of them. Slight differences are inescapable. We also can take into account the effects of contraction/expansion of the barrel’ steel, and of the way it vibes (a wave phenomenon of the whole barrel, actually [almost like a snakes does] whose detrimental existing justifies heavy barrels on sport and good sniper rifles). The best would be a heavy barrel (made by craftsmen and small companies such as Hart, Shilen or Douglas, for example) freely vibrating. That is to say, not in contact in any way with the wood of the rifle (but some glue it with Loctite on the wood, on the contrary [one call this alternate technique “bedding”]). So, the Schmidt Rubin Swiss ordnance rifle is as badly made as any other ordnance rifle with regard to this. That was for “interior ballistics”.

Then we get some other factors pertaining to the realm of “exterior ballistics”. The wind, of course, which is constantly changing (even if slightly) along the bullet trajectory from 100 yards to 100 yards. I could add air density, changing with atmospheric pressure, and another peculiar factor called “magnus effect” if I wanted to splits hairs.

Well, all the aforesaid factors and variables mix together to make what I called a “random effect”, absolutely impossible to put into equation, like in weather forecast. One bullet will go slightly to the right, and the next less slightly to the right, and the next only God knows why to the left downside… (but we know why too, to some extent; we just cannot predict when it’s going to happen, and to which direction it is going to affect the bullet’s trajectory)

However, we always find in the random distribution of the bullet’s impacts a pattern, which we call (rather in the field of artillery) “Gaussian dispersion”. For if you could shoot a picture of all impacts from a shooting series (of about 80 shots in our example), then sketch a perfect circle containing them, you would notice an increasingly great concentration of them as you get to the circle center inward. You can graphically express this concentration as a bell shaped curve, or “Gaussian curve” (or “Gaussian dispersion”). Artillerymen take this Gaussian dispersion into account when they aim at a target far away (say a tenth of miles and often much more in their case). So those gunmen know that they won’t hit the target with the first shell, nor with the second, and even probably not too with the third. They shoot as enough shells as necessary until they hit the target, so “by chance” Jeff would rightly say.

But by chance to some extent only since our gunners took into account a good deal of parameters before they shot their first shell. So, “eyes closed”? Certainly not, as suggests JDZ. But I explained all this to say that what Jeff said is not entirely false however.

P.S.: in my previous comment, in the line “For example with a bullet of a 308 NATO rifle, the drift owing to the pitch of the grooves is in the surroundings of 2 feet”, I missed to add “at 1000 yards”.

P.S. II: the shooter in the video is talking about another phenomenon he doesn’t understand, seemingly, when his bullets shift from supersonic speed to subsonic. Actually, the cause of it lies in the shape of the bullet. It will fail to appear with boat tail shaped bullets, because it pertains to the realm (one more) of aerodynamics.

I think this is a more interesting story about long range shooting:
http://www.americanrifleman.org/articles/2011/6/15/one-for-the-record-books-camp-perry-1921/
Regarding the K31 vs. Springfield, I’ll be shooting both at the CMP Games matches at Perry this year (as well as the Garand). IMHO, the Springfield is the more consistent shooter because of its sights. The K31 is very accurate indeed, but the sights are crap.

Thank you, but I do feel that there is some clarification required. I’ve heard comments from individuals regarding the number of shots taken at this event, to state that x number of shots were fired and x number hits were made is not an accurate representation of what occurred.
We rented this range two months in advance, and obviously having no control over the weather. It rained for nearly two weeks prior to the event. We set up and took 25 shots; it started raining again forcing us to stop the event. Because of the wet soil, of these 25 shots, roughly only 4-5 impacts were observed. When the rain stopped, then I threw 25 more shots. Again, because the dirt damp, well over 80% of all 50 shots fired were undetectable.
We were using 7 very experienced spotters, positioned at the shooting bench, and additional spotters positioned at 1500 yards. We also used three live feed cameras set up on/near the target. The impacts into the wet dirt created an impact plume of approximately one-foot, nearly impossible to spot from 1.27 miles. Not until we paused a third time, to allow the second storm to pass. At this time I took a 25-shot string with 4 hits. It began raining (Storming) again and we were forced at that time to stop. Thanksgiving I shot this same target under reasonable weather conditions and achieved 7 hits out of 26 shots, same rifle & same setup.
A second thing occurred I’d like to point out that made this event very unique, and resulted in an atmospheric condition that I had never dealt with before. It was fascinating and I would like to share.
At the start of the third 25-shot string, I noted that the storm was not one large mass of black clouds, but that it included numerous very small dark rain clouds which would pass through the bullets trajectory. The third string, in which I acquired the four hits, was the first time the small clouds caught my attention. I am very accustomed to long range shooting and thought I had a decent grasp on all the variables, but I had observed that the bullets (Once impacts were observed) were stringing vertically, and I couldn’t initially understand why. I realized that the small dark clouds passing through the bullet trajectory, were causing small high pressure areas beneath and slightly behind each cloud, and these small high pressure zones beneath the clouds were causing the vertical string effect. The 25-shot string was thrown as one of these small clouds passed and another was approaching. I noted that bullets passing under, or through the tail, of one of these passing rain clouds appeared to decelerate and the impact would fall short. And as the cloud passed, the vertical impacts would again significantly rise. It should be noted that these clouds were dark, and passing over 1,500 yard group of spotters, and that they were not dropping rain as they passed overhead.
My conclusion was that the high pressure zone directly beneath the cloud was the cause of the bullet drop. It was a very strange, and very noticeable, effect. I’m not a meteorologist, but I am curious if my suspicion about the bullet drop was a result of the cloud density?

Good shooting Mr. Jimenez. Too much fun.

Thank you sir, it is a great obsession indeed!

Thank you, it is the greatest obsession possible! :-)