Here is a hunting/shooting "math challenge":

What is the calculated change in point of impact for your rifle (given its MOA accuracy), its scope (given the width of its reticle), your ammunition (the bullets BC and the extreme spread of velocity variance between shots) at your typical altitude, temperature, and humidity; when the following occurs...


You believe:

the distance is 600 yards but it is actually 610 and you believe the full value wind is 4 mph but it is actually 6 mph and you have 1 crosshair width of holding error.

Here is an example when you “stack the tolerances” in the same direction:

For a ½ moa rifle, 18 fps extreme spread, 2975 avg fps, 308 190 ABLR G7 BC of .325, width of crosshair is .33 moa, 6000 ft of elevation, 40% humidity, and 30 degree air temperature:

1) +10 yards in range, -9 fps in velocity = 3.0 inches low
2) + 2 mph in wind from 4 to 6 mph = 3.5 inches (will assume to the left)
3) Inherent inaccuracy of a ½ moa rifle @ 610 yards 1.59 inches (assume POI is low and left at 45 degrees)
4) 1 crosshair’s width of holding error 2.1 inches (assume error is low and left at 45 degrees)

When sketched out, I get a total change in impact ~8.3125 inches low and left.

So - tell me what's wrong with the analysis?

That's why 600-yd shots are 300 - 400 yds too far for me.

Me too Delloro.

what's wrong is your getting better ballistics than I do with my 30-06 bullets going 2800 fps.

i'll stick to my self imposed 300yd limit.

quote:

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What's wrong, I can't hit it at that distance, cut the distance in half, then do the math.

What's wrong with the whole situation is your still guessing at the range.

That's what they make lasers for.

P dog shooter,

Your assumption that this is not based on using a laser range finder is incorrect. I don't know of any human alive that believes any other human can accurately estimate range within 1.7% at any any distance let a lone even 10% at typical rifle hunting distances.

Your statement is also inconsistent with practicality/reality in my experience for a couple of reasons that immediately come to mind that could easily lead to a 10 yard difference in actual range at 600 yards relative to measured range with the use of a laser ranger finder which I have used for the last 15 years or so.

1) When using a laser range finder (I have used 3 or 4 different brands), you actually don't know the exact range because you don't know (given the "reticle" in the LRF) did the laser actually reflect off the animal or did it reflect off the ground just in front of the animal or on the ground behind the animal because the beam went just over the animal's back. This is especially true if an animal is at 600 yards. LRFs are usually used offhand, maybe steadied on some sort of rest or sitting. Not very often with the same technique as a prone shooting position with pack etc. The ability to have the LRF "aiming reticle" exactly on target at 600 yards is in many cases worse than a rifle scope reticle and best case not much different than being able to hold a scope reticle exactly on target under similar conditions.

2) Even if you take 3 or 4 measurements, and even if you are "exactly on target" with your LRF, during the transition from LRF to behind the gun, an animal holding still, and a solid hold, the animal can easily move 10 yards further or closer. So what is the hunter to do? re-range and then go back to the the rifle which the transition then starts over and the animal could easily move again. Animals mill about in the same area all the time. So "dialing in" or setting up for a 600 yard shot and having the animal actually be at 610 is a very realistic scenario and does not imply some sort of incompetence or poor process by the shooter in my opinion.

The point of the OP is really about how minor differences can stack-up and the calculation to understand the cumulative effect. You could change the distances to 500 vs 505, the shot to shot velocity variance to 20 fps, and a more typical G7 of .200 and the 8+ inches becomes just over ~7.125 and you still have a likely wounded animal assuming 10 inch vitals. I doubt you are implying that somebody is going to re-range their target for a perceived 5 yard change.

only thing missing is the animal takes a step forward and you got a gut shot animal

Butch,

Excellent point. Thank you. Time of flight in the example above is just shy of .7 seconds.

I don’t like long shots on animals.

To me, 200 yards is a long shot.

But, I have taken a few very long shots - for me - of around 400-500 yards.

I don’t use a range finder - we do once the truck is back, but not while hunting.

And the few times I have done it, I have killed the animal - or at least managed to catch up with him with 100 yards of first shot.

Rifles used were 270/404
30/404 and 375/404.

And I am the first to admit of being so surprised of my hits.

Saw an eland in the mountains in South Africa.

No one wanted to shoot it, they said he was too far.

I fired a shot - 270/404 with Jensen 150 grain bullets.

He jumped at the shot. Ran a few yards and stopped.

I fired another shot at him and he took a couple of steps and dropped.

Both my shots were within 4 inches of each other on his shoulders.

One went completely through and the other we recovered under the skin on the other side.

There is no way in I could have guessed where to aim to get the bullets so close.

Just used Kentucky windage!

Last years West Texas aoudad is a perfect example.

The guide had an LRF, another guy had an LRF and I had mine.

The guide told me the range, and got excited when I told him give me a minute I wanted to check my own.

The variance between LRF's can be 1-30 yards. And brand doesn't really seem to matter.

For your own LRF, take a 100 yard measuring tape, or a 36 foot one and stretch it out multiple times to check your LRF's actual range accuracy.

I have really good luck with the Leupold LRX 1800, there is a new 2800 model and I'll get one of those when they come back in stock in January or February of next year.

Mike, were you shooting uphill/downhill? Most of the current LRF's give you the linear distance, after they use the pre-programmed calculation and onboard inclinometer to create a "dial too distance". But if you don't turn it on, or screw with the settings and forget to change it back that can bite you on uphill/downhill shots.

I have also noticed that just because I have a calculation from Hornady or Brian Litz's ballistic solvers, and I have a reading from a chronograph doesn't mean that it will be 100% on. It might be 1-4% off. You MUST true your data. I do this by shooting a big 36x36 inch target at 100, 300, 600. At the same point.

http://panhandleprecision.com/...n-ten-steps-success/

https://www.snipershide.com/pr...ith-weaponized-math/

You also have the issue of scope adjustments not being 100% on. 3 MOA might be 3.1 MOA or 2.7 MOA depending on your scope.

https://www.snipershide.com/pr...g-test-results-2020/

This is all kind of pillow talk, because based on what you have written I think you already are working on all of these work flows.

So many factors affect bullet flight:

1. BC of the bullet
2. Air density
3. Temperature
4. Spin Drift
5. Rotation of the earth
6. Humidity
7. Wind
8. Wind
9. Wind
10.Wind

Yes I understand that when shooting conditions vary.

If one doesn't feel comfortable taking a shot at any distance.

One should not take the shot.

What I don't understand is the preaching to others.

About what they or they should not do.

Unless you have personnel knowledge of a persons skill level. Then add into the other factors at the very time of the shot.

You really have no business telling others what they can or they can not do at any given time.

What might be a shot that can be easy shot one day might not be unmakeable shot another day.

I have seen days so bad that making hits on Pdogs was almost impossible at a 100 yard. Gusting winds over 30 mph.

Other days calling 1st rounds hits to 500 was regularly done.

10's of thousands of rounds down range in the field and on then range can give one a very good indication.

If a shot can or can not be made.

Again if you uncomfortable in making a shot. For what ever reason Don't shoot.

quote:

Just used Kentucky windage!

This is an acquired skill and for me it took years to acquire it.

Rangefinders are not always accurate.
On my last pronghorn hunt in the Texas Panhandle, there were plenty of healthy 14 + inch bucks. An assistant guide with a range finder told me to shoot at some that he said were only 225-250 yards away. But they looked to me to be beyond my self established 300 yard range. He told me it was 250 yards (that is an easy shot with my 308) on two occasions when the game just looked out of range. To humor him, I took a good rest and aimed where the bullet would hit the shoulder at 250 yards; the shot was low and dust flew up about 200 yards beyond. He could not believe his range finder was off, so I told him that next time an antelope was within range I would call the range and call the shot and then we would step off the distance to the dead buck.

That afternoon, a buck that I had been watching circled us and stopped within my range. I called a chest/shoulder shot and fired and the buck went down with a shattered right shoulder. Three of us stepped it off and it was 235 yards!

Back at the camp, we learned that the same guide had similar range estimation problems with two other hunters.


AS Pdog said "Again if you uncomfortable in making a shot. For what ever reason Don't shoot."

quote:

Originally posted by Mike_Dettorre:
Here is a hunting/shooting "math challenge":

What is the calculated change in point of impact for your rifle (given its MOA accuracy), its scope (given the width of its reticle), your ammunition (the bullets BC and the extreme spread of velocity variance between shots) at your typical altitude, temperature, and humidity; when the following occurs...


You believe:

the distance is 600 yards but it is actually 610 and you believe the full value wind is 4 mph but it is actually 6 mph and you have 1 crosshair width of holding error.

Here is an example when you “stack the tolerances” in the same direction:

For a ½ moa rifle, 18 fps extreme spread, 2975 avg fps, 308 190 ABLR G7 BC of .325, width of crosshair is .33 moa, 6000 ft of elevation, 40% humidity, and 30 degree air temperature:

1) +10 yards in range, -9 fps in velocity = 3.0 inches low
2) + 2 mph in wind from 4 to 6 mph = 3.5 inches (will assume to the left)
3) Inherent inaccuracy of a ½ moa rifle @ 610 yards 1.59 inches (assume POI is low and left at 45 degrees)
4) 1 crosshair’s width of holding error 2.1 inches (assume error is low and left at 45 degrees)

When sketched out, I get a total change in impact ~8.3125 inches low and left.

So - tell me what's wrong with the analysis?

Well, for one thing, the "odds" of a bullet hitting at the extreme outside point of its grouping ability is not likely. It can happen, but let's assume the odds are 20% that it hits where you say it does. The odds of your wind error being left or right is 50%. Same for the hold error. So multiply those and you have a 5% change of those errors stacking in the manner you describe.

I just got done taking a shot at 910 yards. The wind was blowing from behind at 7 oclock at 5 mph from my shooting position. The mirage was to the right about 5 mph. But when I focused my parallax so the mirage was in focus, it was blowing only slightly right (changed from my spotting scope look). No vegetation was blowing hard at the target. I put the right end of my 1 MOA crosshair on the right side of my 2.75" aiming square and touched it off. Shot was 2" low 3" right. MV was 2840. Rifle is a Stiller Predator, Brux 30" bbl, McM stock, Jewell trigger, and NF ATACR 5.5-25X scope.

I would say these are the biggest issues on a LR shot:
1. Steady position
2. Wind
3. No definite aiming point (animals don't have 2.75 inch red squares on their lungs)

I will honestly say I can hit my 10x12 inch gong at 504 yards every time in just about any condition. 715 is not difficult unless my wind hold is 2 MOA or more, in which case it is likely gusting. At 910, I don't hardly miss if the wind is 5 mph or less, or if the mirage is can be seen clearly. If the wind is strong, my odds drop big time.

I keep a log of all my shots when practicing. I don't shoot LR with anything that doesn't launch a high BC bullet relatively fast. I define a hit as within 5" of my point of aim.

Here a my results since Jun 8 (my other log is in AZ) for the my "super accurate rifles" (28N, .338 Lapua, .338 Edge). I also practice with a 300 RUM that is relatively lightweight, but not including the results of it or my Savage Lapua, which is really accurate, but MV is not up there with the Edge or other Lapua. BTW, I have a LabRadar and record the MV of every shot.

For my last ten shots at 500, I am 10/10 in all wind conditions (true with the Savage and RUM as well).

For mild or no wind (zero to <1 MOA wind call):
715: 8 of 8
910: 9 of 10 (the miss was a bad wind call - I thought it as to the right but it was actually to the left, as I found with a subsequent shot)

Moderate (1 to 1.5 MOA wind call):
715: 6 of 6
910: 9 of 10 (one wind I called moderate was apparently not)

Strong (>2 MOA wind call):
715: 5 of 7
910: 4 of 10 (strong winds are often gusty and can change during the TOF; mirage washes out so you are basically taking an educated guess)

All of the above shots are first round shots; I wait at least one hour between shots, usually more.

910 yards is far more difficult than 715; you have to account for spin drift and aerodynamic jump (the later can change your vertical impact +/- 1 click). You need a rangefinder that takes these into consideration as well as the obvious changes in altitude and temp (altitude being the big one).

I would also say it is very important to practice in different places; you get to recognize conditions based experience with that place. The wind at my CO place is much more gusty than in the desert in AZ, and constantly switching direction, esp in the summer afternoons when the thunderstorms roll in. And if your only experience is shooting on flat fields in the Midwest, you are going to be in for a surprise the first cross-canyon or cross-valley shot that you take.

I will say with constant practice you can get reasonably good as long as the wind isn't excessive and the range extreme. I can shoot out the back door of my CO place, which is a luxury I take full advantage of. IF I had one of my LR rifles and IF I had a steady shooting position, I would not hesitate to shoot an animal at 600. I did kill an elk at 643 with a .338 WM from a not so steady rest, but it wasn't DRT. I hope it was my last LR shot at an animal. Hell, by the time I study the wind for a LR shot, I could have gotten 200 yards closer!

I guess after 20 years on AR I should not be amazed by members reading way more into a post than there is.

The OP is not about who should shoot at what distances or not. It is about understanding and accounting for accumulation of variables (or stacking of errors) and inherent or likely inaccuracy.

If the OP stated:

"I have a Rem 740 in 30-06 that shoots 3.25 inch groups at 100 yards do you think I can use it on deer out to 500 yards?"

I suspect advice would have been "bad idea" because that rifle is likely shooting around 16.25 inches at 500 yards and half of that is 8.125. So assuming even a generous 12" vital zone (6 inch margin of error in any direction), you could have a "perfect" hold and your bullet could strike 7+ inches from the point of aim and only wound the animal.

But instead in my OP I bring in more factors, and ask about accounting for the stacking of errors. I also use a more accurate rifle and small variances at longer distances and say "Hey, this is the calculation I get." What's wrong with the analysis?

The varying responses to the OP and the question speak for themselves.

quote:

Originally posted by Mike_Dettorre:
I guess after 20 years on AR I should not be amazed by members reading way more into a post than there is.

The OP is not about who should shoot at what distances or not. It is about understanding and accounting for accumulation of variables (or stacking of errors) and inherent or likely inaccuracy.

If the OP stated:

"I have a Rem 740 in 30-06 that shoots 3.25 inch groups at 100 yards do you think I can use it on deer out to 500 yards?"

I suspect advice would have been "bad idea" because that rifle is likely shooting around 16.25 inches at 500 yards and half of that is 8.125. So assuming even a generous 12" vital zone (6 inch margin of error in any direction), you could have a "perfect" hold and your bullet could strike 6 inches from the point of aim and wound the animal.

But instead in my OP I bring in more factors, and ask about accounting for the stacking of errors. I also use a more accurate rifle and small variances at longer distances and say "Hey, this is the calculation I get." What's wrong with the analysis?

The varying responses to the OP and the question speak for themselves.

Mike:

I certainly agree that at some point you can prove a shot is too long; I just don't think that limit is 600. I see guys claiming to shoot animals at 1400 yards (and used to see it quite a bit on TV a few years ago). Your 1/2 MOA rifle is grouping 7 inches at that range, meaning you have only 3 inches of wind drift error. The TOF is 2 seconds, which is plenty of time for your perfect wind call to be imperfect. When the wind is blowing here in CO, at least in the summer time, it changes enough in two seconds to cause a miss at that range. To be sure, it is likely different at your target, but just as likely to be as variable there as your shooting site - in fact, since you are generally not on top of ridge or hill when taking a shot, it is likely even more variable.

AAZW,

600 yards is/was an arbitrary distance that was simply used as an example.

Tony,

I guess I am still surprised that instead of a response of "go get chicken", some of the responses are - "you have no business telling anybody where to eat".

Mike,
I truly appreciate the humor that you often bring to this site, but you should learn that many members just do not give a damn about long range shooting or even talking about it, much less calculating about it!

When I saw your post, I should have just passed it by and will try to do better next time.

CR,

I see nothing inappropriate about your posts.

quote:

I certainly agree that at some point you can prove a shot is too long; I just don't think that limit is 600.

True what is a long shot for one is not for another.

All kinds of factors make some shots possible or not possible.

Range is only one of those factors.

A good hunter knows his limits.

Over 50 years ago I stated stretching the ranges I shot at.

I thought hitting milk jug at 300 was a miracle. I got better rifles and scopes

Then I started hitting them all the time.

Then it was clay pigeons then smaller targets.

Then I had access to a 700 yard range and I stretched by range further.

Then I started making multiple trips a year to shoot PDogs.

Shooting many thousands of rounds a year in practice and shooting Pdogs. 10's of thousands of rounds over the decades.

I know perfectly well what it takes to make a shot with in my limitations.

Unlike some here some of us really do know how to shoot at the ranges we shoot at.

I can make or break any shot on paper at any distance if I can set then requirements and conditions of that shot.

But it doesn't make it right or wrong. Right or wrong is a totally different subject then shooting.

Mike, good post. I like this kind of math. You arbitrarily picked a good distance for this example. It seems 600 yards is where the miscalculations become substantial changes in impact.
Scott

I have an American flag on a pole near my house. Maybe 40 feet away I have another flag at my mail box. A neighbor caddy cornered from me has a flag maybe 150 feet away. It is very common to see these 3 flags doing completely different from the other two. One might be still , one waving left and another waving right. What the wind is doing from where you shoot and at the target 600 yards away can be vastly different. So to be safe, buy an inflatable 600 yard wind tunnel and put bait at one end and wait for the animal to go to the bait. Now we know exact range and what the wind is doing. Allow extra time if you are inflating the wind tunnel by mouth. Then allow more extra time for your heart rate to settle down. Allow plenty of extra time locating a 600 yard wind tunnel.

Mike,

I'll look at your calculations later and comment on the "error stacking". I'm sure it CAN happen. there's also a chance of a bullet that lacks concentricity so the stacking even at 300 yards might be too much. Nothing's perfect all the time.

For my bro and me, we feel like 600 yards is a chip-shot *IF we have plenty of time and if we don't have time, we have no shot. Simple>

900 yards is 3x more tricky than 600 although it's only half again more. (our range only goes out to 900 so I refer to that often).

Now where should I eat today?

I've scene these video shots even past 1,100 yards and all the animal has to do is move a little bit and you've got trouble.

I have made a few long shots when the deer, elk or whatever zigged when he should have zagged..I the last few years most of my shots have been under 200 yards, and the fabled long shot animals like pronghorn antelope and desert sheep were all shot under 200 and most at around 100 yards..Long shots are for the youth of this world, or so it was in my day..

quote:

Originally posted by 376 steyr:
I've scene these video shots even past 1,100 yards and all the animal has to do is move a little bit and you've got trouble.

Same at the shorter ranges.

If one is so afraid that one might wound a animal.

Then one should give up hunting because it will happen.

quote:

Originally posted by p dog shooter:

quote:

Originally posted by 376 steyr:
I've scene these video shots even past 1,100 yards and all the animal has to do is move a little bit and you've got trouble.

Same at the shorter ranges.

If one is so afraid that one might wound a animal.

Then one should give up hunting because it will happen.

Not in the same magnitude. The amount of distance a moving animal covers from trigger break to impact is much greater at 1,100 yards than it is at 100 yards. Why is that even debatable?

One could also say "if one is not willing do everything in your power to assure a clean kill, including getting as close as you can, then one should give up hunting"

quote:

Not in the same magnitude. The amount of distance a moving animal covers from trigger break to impact is much greater at 1,100 yards than it is at 100 yards. Why is that even debatable?

I see no debate a wounded animal is wounded no matter the range.

A dead animal is a dead animal no matter the range.

I never had a critter tell me the difference.

More importantly is, the people who go hunting and cannot shoot worth a damn!!

I met a German hunter in Zimbabwe.

He had a custom 416 Rigby, the rifle was so heavy.

He had one box of ammo.

He wanted to shoot a lion!

He never fired the gun.

His gunsmith installed the scope on it, and never shot it.

He fired a few shots to sight it in.

He could not hit the target box!

He went to shoot a kudu cow for bait.

He missed it, and killed a young kudu bull a couple of yards to the side.

As you can guess, he never got a lion.

And his PH told him he was fully booked in the next few years, when he asked to come back!

Your limits are your limits.

Some of these responses remind me of the famous quote by Thomas Sowell.

“The reason so many people misunderstand so many issues is not that these issues are so complex, but that people do not want a factual or analytical explanation that leaves them emotionally unsatisfied. They want villains to hate and heroes to cheer - and they don't want explanations that fail to give them that.”

Mike,
Your calculations are correct.

If we're assuming;
Let's assume you're shooting southerly so you'll have some coriolis and spin drift which will correct about 2.5" and let's remove the unusually fat crosshair width from the equation for most shooters who shoot at those ranges will have about 1/8 minute hair.
IF everything stacks against you it COULD be more or less 4" on a bad day.

BUT, if you increase the range error, misread the wind by a greater margin, have a .5 minute crosshair, have a 1.5 minute rifle, 50 foot extreme spread in fps, you might not hit my 4' x 4' white plastic corrugated board with a shoot-n-see target in the middle.

Here's my villain to hate: Jerk the trigger at 100 yards (many do) and the shot is wild also.

Just might be there's no right or wrong answer to "should we be shooting deer at 600 yards?"

I have no idea if I added too much of my opinion in response to your thread.

Zeke

PS: I'm having lunch on Monday with my Casper buddy and we will discuss what you and I spoke about earlier. I'm on my way to hunt pronghorn in Montana for a couple days. It should be awesome!

Zeke,

Not at all. Opinion that is related to the topic is always welcome. I really appreciate the fact you were willing to "do the math". You even added in some additional relevant points.

My OP was not about 600 yards being good or bad. It was just a distance to use for the calculation that was representative of a "long shot" given today's technology.

I've got a LOT of experience at 600 yards...probably burned out a barrel or two at 600. Highpower Competition.

Simplified but the 10 ring is 2 MOA and the X ring is 1 MOA. I could routinely score 197-198 with 12-14 X counts. Using Open sights and a 1 MOA at best rifle/ammo Shooting prone unsupported BTW with a time limitation--20 shots in 20 minutes.

That means I dropped 2 or 3 bullets into the 9 ring out of 20 and 7 or 8 into the 2 MOA ten ring. 12-14 were in the 1 MOA X ring.

We were shooting out west and it was common to see 10 MPH or more gusting winds and corrections often had to be made based on observed conditions or off actual observed and marked rounds.

In your situation I doubt you could adjust for the difference in 10 yards range difference. My come ups from a 200 yard zero to 600 yards were 8 minutes or clicks +/- a half MOA for light conditions or elevation differences.

3-4 mile an hour wind MIGHT warrant a single click or 1 MOA adjustment or might just call for you to favor one side of the bull depending.

Light conditions and elevation would make a small difference as would temperatures. We shot at ranges at 4,200 feet and 8,000 feet. The elevation changes made a pronounced difference at 1,000 yards less so at 600

In my experience a 100 yard group tells you nothing about the long range potential of your rifle. Only RARELY is accuracy linear in a rifle at longer ranges--meaning a .75 MOA rifle at 100 yards will also be a .75 MOA rifle at 1,000... Some actually get better at extended ranges as bullets have different flight characteristics. A better guide is your 300 yard groups. By then most bullets have settled down in flight and you'll see something closer to what you can expect at longer ranges.

I am not a long range hunter in spite of my extensive experience shooting rifles at a very high level of competition out to 1,000 yards. Its my own ethical limitation I put on my hunting experience and nobody else's. If long range hunting is really your bag have at it.

In my opinion the two biggest factors for success at long range are trigger control (we were using 4.5# triggers by rule) and breath control.

Just be honest with yourself and your perceived capabilities. If you find yourself missing more often than not you might want to dial it down some.

quote:

I am not a long range hunter in spite of my extensive experience shooting rifles at a very high level of competition out to 1,000 yards. Its my own ethical limitation I put on my hunting experience and nobody else's. If long range hunting is really your bag have at it.

What is long range?

No one wants to set the magical number.

That maybe sir is because no one should set a “magic” number. That would just be the BS straw man for the next argument fire. Make your own choice, live with the consequences and let others do the same.

Rifle accuracy is probably the least important part here.

The conditions, and shooter, are ultimately the weakest links.

I have seen friends who out shoot me on targets any day, with smaller calibers.

But, while hunting, they find it very hard to hit anything.

quote:

True what is a long shot for one is not for another.

All kinds of factors make some shots possible or not possible.

Range is only one of those factors.

A good hunter knows his limits.

quote:

Just be honest with yourself and your perceived capabilities.

Yes to all of the above.

I had a younger hunter call me about hunting Africa. He was a self perceived and conceited long range hunter (the type that convinces himself that he really should have been a Navy Seal Sniper-you all know the type). He had shot and killed a bull elk a couple of years back here in Nevada at 1250 yards. Thereafter he deemed himself to be a long range expert and told everyone so. He told me that he only wanted to hunt Africa if he could shoot and kill at long range. I frankly told him that he was not for Africa and Africa was definitely not for him. Fortunately, he's never gone.

Your math looks good, but here's more to the equation.

We have known values, known variables and unknown variables.

I shoot out to 600 on my range regularly and have seen what felt like they should be "solid hit shots" go left, right, up and down. Most can be explained away after the fact by the presence of unknown thermal pockets between the muzzle and the target.

I believe there are more shots on game past 300 yards that have gone right due to skill mixed with a dash of luck then people care to admit.

Luck is hard to factor in.