That Little Green Dot

[6Taylor4]

I put together some figures from a self-test of the recticles. ; a comment by eagle74 prompted me to try:

He said, "You can easily compare the accuracy of the two [Remington 7600 and Steyr Monobloc] by aiming them at the same object at 300 m or more with hunter sense on. The size of the hunter sense dot (potential bullet spread) will be smaller on the more accurate rifle, the Monobloc."

That got me curious, so I measured them.
I chose 4 rifles and 5 scopes:

Grampa's Rifle, Remington 1903, Steyr CLII, and Steyr SM12 - (T4, T5, T6 - 2)

[1]Bushnell Elite 3.5 -21x50, [2]Leopold VX-6HL 3-18x44, [3]Leopold VX Freedom 1.5-4x20, [4]Leopold VX-3HD 4.5-14x40, and the [5]Leopold VX Freedom 2-7x33.

That's one of each of the available magnifications for scopes.

I hope this makes sense; what I did was stand in the same spot, aimed at the same dark woods on the other side of a lake, about 400 yds. This afforded the best view of the green bullet circle. I then zoomed each scope to max, and measured the green circle physically on my screen. Then I mixed and matched the 4 guns and 5 scopes until all has been measured with each. So these figures are from my monitor only, but the ratios between the measurements should equate to similar ones on another monitor.
1-x50 2 -x44 3 -x20 4 -x40 5 -x33
Rem 1903 1 1/2" 1 1/4" 1/4" 1" 1/2"
SteyrCLII 1/2" 3/8" 1/8" 5/16" 1/8"
Gramps 1" 1" 3/16" 3/4" 5/16"
Steyr SM12 3/8" 3/8" 1/16" 1/4" 1/8"

Now, what does that all mean? (Note: the scopes are not listed in any order)
I have no idea! I'd like to see what others think of this.

I never stopped to consider the targeting error variations between the combinations of rifle/scope. There's a noticeable spread in the accuracy levels (smaller the dot, higher the accuracy), and I don't understand these relationships, why they would be so variable; same weapon, what is it that differentiate the scopes one from another for accuracy?
Take the Steyr S12 - the two most powerful scopes are the least accurate, while the x20 is impressively accurate, as is the x33.
Please share your comments on this subject of proper scope for each weapon, and maybe help me figure this out.
Thanks!

[VictoriaHuntress]

Funny you should bring this up - I'm doing something similar with the rifles and scopes.

First, accuracy and precision are different concepts in the theory of measurement.
Accuracy refers to how close the average of a group of measurements is to the 'true' value, whereas precision is related to the average spread of those measurements from the group average; thus we have the statistical concepts of the mean and standard deviation, for example.

So, you can be accurate and precise, inaccurate and imprecise, accurate but imprecise, precise but inaccurate.

Accuracy is generally affected by systematic, non-random errors. If you know what the errors are, you can account for them and correct for their effects.

Precision is generally affected by random errors that you can't correct for. The most you can do is to try to understand the potential causes of the errors and estimate the magnitude of each on your measurements - that way you can generate the probable error bounds for the measurements. Perhaps you also redesign the measurement procedures to mitigate the effects of some of them.

In shooting, accuracy is affected by things like improperly mounted scopes (misaligned or canted), incorrect dialing of elevation and windage turrets.
Perhaps there is a manufacturing flaw in the rifle that affects all shots in the same way, like the barrel is not floating properly in the stock.
- perhaps you are resting the barrel on a support, instead of the stock - you'll miss the intended target for sure, and probably get lousy groups (precision) to boot.
- perhaps you are using a second focal plane scope, and the zoom is not set to the specified reticle calibration value - all your estimates of angular dimensions will be off by a constant amount.

For shooting precision:
- perhaps there is too much play in the windage and elevation turrets, so you can't set them reliably each and every time
- it is a known fact that mismatches between firearms tolerances and ammunition tolerances wreck your group sizes. My Browning X-Bolt 7 Rem Mag does not like cartridges loaded with 139 grain bullets - i never get better than about 2MOA groups with those, but if I use 150 grain or higher bullet weights, I get sub-MOA groups all day long - the heavier bullets are longer, and so the cartridge is seated tighter in the chamber.
- not all rifles and ammunition are manufactured to the same tolerance specs, so two rifles chambered for the same cartridge/caliber may produce very different group sizes
- wind, air temperature, humidity, barometric pressure, even rain
- aim sway, your heartbeat, breathing - these you can mitigate but not totally eliminate.

So, for ballistics calculations, the best you can do is to identify the possible sources of random errors, estimate their magnitudes, and if you can, work out mathematically how they would affect a ballistic firing solution to get an estimate of the probable impact points at the target - that is our scope's projection of the firing solution - the central dot represents the area of most probable impact (where 90% (as an example) of the shots would land, on average), and the concentric ring around it is where the remaining 10% might land, on average.
When you are not holding your breath, the solution has much more uncertainty and so the image is so much fuzzier - more imprecise.
Because the precision errors are random, you can determine what the expected distribution would look like ( see https://en.wikipedia.org/wiki/Multivariate_normal_distribution) and project that on the plane of the scope reticle

I think the precision (the size of the estimated POI error ellipse and the focused dot representing the most probable POI during breath-hold) depends on the rifle more than the scope - put the same scope on different rifles and you'll see the difference. The Bushnell Elite Tactical is the best scope to use since it seems to be calibrated in milliradians and it is now the only scope I use on centerfire rifles (once you have it calibrated for each rifle, you can do away with the HunterSense ballistics calculator and estimate the windage and elevation holdovers from the calibration table).

I don't know that I'd rely on a measurement taken on the monitor image - the game is the source of truth in this virtual world.

In general, the size of the dot relative to the cross-hairs hash marks on the axes is what determines the precision of the aiming solution - you can't really do much better than +/- 1/2 the dot's diameter.

What I've been doing is going out to the airstrip in Aurora Shores, driving over to one end of the runway and using one of the concrete barriers at the other end as an aiming point.
One can aim from a prone position (the most stable, least aim sway and therefore error), so that the shooting angle (relative to the vertical-gravity direction) is 0 degs.
I set up at the following distances: 0m (well, maybe 2 or 3m, just to get the muzzle energy), 25m, 50m, 75m, 100m, 125m, 150m, 175m, 200m, 250m, 300m, 350m, 400m, 450m, 500m, 550m, 600m, 650m (I'll have to find another straight and level expanse to go out to 1000m, though). To make the cross-hair hash marks clearly visible, I set the magnification to 21x - this also helps with aiming at longer ranges.
For each distance, (as confirmed by the ballistics calculator range-finder), I use the ballistics solution dot to estimate the come-up (elevation holdover) at each zero setting of the scope (50, 100, 150, 200,... 1000).

I'm assuming that the tactical scope is truly calibrated in milliradians (you can find it on Bushnell's store site -looks like the G4P reticle)
For the Steyr SSG M1 (6.5 Creedmoor NOTE; the real rifle isn't chambered in 6.5mm Creedmoor LOL), the angular diameter of the dot is about 0.125 milliradians, so the precision of the measurement would be about +/- 0.0625 mrads.

For the Steyr SM12 in .300 Win Mag, the dot looks to be almost 0.25 mrads in the tactical scope - same scope, different rifle/ammunition.

For the Steyr CL II in .338 Lapua Magnum, the dot is even larger, at least a full 0.25 mrads in diameter, perhaps 0.275 mrads, as it overlaps both the 0.25 and 0.50 mrad subtensions when centered between them.

Now, just to complicate matters, the SSG M1 (see Steyr's store site - I want one! ) has an integrated 30 MOA Picatinny Rail for mounting the optics (that introduces an extra down-angle inclination of 30 MOA for extra elevation adjustments at really long ranges). I had not noticed the rail inclination before, so I was puzzled by the seemingly small holdovers even at really long ranges when I first measured them, but now I know why, presuming that the game takes this into account.

I'm still refining the method to get more reliable holdover estimates.

[eagle74]

6Taylor4, The HS dot gets magnified by the scope power setting. That is the reason that the dot will appear bigger on the more powerful scopes. It does not mean that the more powerful scope is less accurate. It does not alter the inherent accuracy of the rifle. Equip the 21x scope on a rifle & aim at a target 300 m or more using both the 10x & 20x settings. The HS dot will be roughly twice as big at the 20x setting.

Now, use that same rifle & equip the 4 different scopes (don't use the 4x one) & aim at the same target with all scopes set to 7X. The HS dot should be about the same size in all cases. The big assumption here is that the scopes are properly calibrated & all actually give you 7x. I have not measured this & IDK if this is the case.

To compare the accuracy of two different rifles, just use the same scope at the same magnification at the same target. Choosing one of the more powerful scopes fulled zoomed is best bc the differences will be more pronounced & easier to detect.

[VictoriaHuntress]

Originally posted by eagle74:

6Taylor4, The HS dot gets magnified by the scope power setting. That is the reason that the dot will appear bigger on the more powerful scopes. It does not mean that the more powerful scope is less accurate. It does not alter the inherent accuracy of the rifle. Equip the 21x scope on a rifle & aim at a target 300 m or more using both the 10x & 20x settings. The HS dot will be roughly twice as big at the 20x setting.

Now, use that same rifle & equip the 4 different scopes (don't use the 4x one) & aim at the same target with all scopes set to 7X. The HS dot should be about the same size in all cases. The big assumption here is that the scopes are properly calibrated & all actually give you 7x. I have not measured this & IDK if this is the case.

To compare the accuracy of two different rifles, just use the same scope at the same magnification at the same target. Choosing one of the more powerful scopes fulled zoomed is best bc the differences will be more pronounced & easier to detect.

Oh, I missed the part where 6Taylor4 said he used the maximum magnification of each scope in the comparison of the linear diameter of the on-screen dot.

You can't compare the linear sizes directly this way.

The proper way to do this is to consider how a riflescope ( or telescope or binoculars) zoom in:

First, consider the actual angular diameter of an object at a distance:
This is given by:

tan (theta/2) = H / (2*D), where H is a linear dimension of the target (in units of linear length), D is the distance to the target (in the same units of linear length as H), and theta is the angle subtended by the target as seen by you, in radians ( recall that Pi (radians) = 180 (degrees))

So, the angle is
theta (radians) = 2 * arctan(H/(2*D)) , and multiply by 180/Pi to get the angle in degrees.

Now, what a scope does is to magnify the image by a factor of 'M", so the apparent angular diameter of the target gets magnified by that same amount:

alpha = 2 * M * arctan(H/(2*D)),

Then

alpha/(2*M) = arctan(H/(2*D))
or
tan( alpha/(2*M)) = H/(2*D)

Now, for really small values of alpha (in radians), to a very good approximation

tan(alpha/(2*M)) = alpha/ (2*M)

so alpha / (2*M) = H/(2*D) => alpha = M * H / D = H / (D/M))
That is, you perceive the target image as being a distance D/M away.
You can do the full optical calculation with no small angle approximations for the lens system of the scope, and come to the same conclusion about how zooming works.

So, you'd have to convert the linear diameter of the dot as measured in monitor space to pixels in screen space to in-game linear dimensions in Image FOV space to get the apparent linear dimensions of the dot, and use the above formula to calculate the true angular diameter represented by the dot.


The best way to measure this is to use a calibrated riflescope, since it is specifically designed to measure angular dimensions ( in radians ( 1 MRAD = 1/1000 radian) or degrees ( 1 MOA = 1/60 degrees)).

For a first focal plane scope, like the Bushnell Tactical, the reticle magnifies with the zoom, so the subtensions always represent the true angular diameter.
For a second focal plane scope. like the Bushnell Engage, the reticle does not change size, so the subtensions represent the true angular diameter at only one magnification, usually the largest.

[6Taylor4]

Originally posted by eagle74:

6Taylor4, The HS dot gets magnified by the scope power setting. That is the reason that the dot will appear bigger on the more powerful scopes. It does not mean that the more powerful scope is less accurate. It does not alter the inherent accuracy of the rifle. Equip the 21x scope on a rifle & aim at a target 300 m or more using both the 10x & 20x settings. The HS dot will be roughly twice as big at the 20x setting.

Now, use that same rifle & equip the 4 different scopes (don't use the 4x one) & aim at the same target with all scopes set to 7X. The HS dot should be about the same size in all cases. The big assumption here is that the scopes are properly calibrated & all actually give you 7x. I have not measured this & IDK if this is the case.

To compare the accuracy of two different rifles, just use the same scope at the same magnification at the same target. Choosing one of the more powerful scopes fulled zoomed is best bc the differences will be more pronounced & easier to detect.

You didn't say that in your original post about the green dot size; after reading the Huntress, I'm leaving the math to you guys. I am more confused than ever: tan(confusion*x)+arctan(greendot/FOV)= SHOOT!
I appreciate the technical explanation; there's not a calibrated riflescope in-game, I'm kinda lost on this green dot stuff.
You can make all the RL explanations you want, and they are helpful, but in terms of playing the game, I'd like a clearer in-game method of determining the right equipment for the task.
Do we need all this technical information, or is there a simpler way to match items?
Has anyone done this? Are the rifle/scope combinations covered anywhere?
I've read individual choices, I'm still confused, and haven't "got it" yet.
Thanks. I'm going to search this more.

[eagle74]

I'm sorry if my original post was not clear. As far as matching equipment goes, I like both the Bushnell 21x & the Overgaard 15x for the reticles. These are the only ones I use for centerfire rifles in the game. You cannot go wrong with either. And don't worry about all the technical stuff & calculations. Just use the HS dot & the game does the math for you.

[VictoriaHuntress]

Originally posted by 6Taylor4:

You didn't say that in your original post about the green dot size; after reading the Huntress, I'm leaving the math to you guys. I am more confused than ever: tan(confusion*x)+arctan(greendot/FOV)= SHOOT!
I appreciate the technical explanation; there's not a calibrated riflescope in-game, I'm kinda lost on this green dot stuff.
You can make all the RL explanations you want, and they are helpful, but in terms of playing the game, I'd like a clearer in-game method of determining the right equipment for the task.
Do we need all this technical information, or is there a simpler way to match items?
Has anyone done this? Are the rifle/scope combinations covered anywhere?
I've read individual choices, I'm still confused, and haven't "got it" yet.
Thanks. I'm going to search this more.

Well, the Bushnell Elite Tactical is 'calibrated', as it uses the G4P reticle, so we can at least assign a numerical value to the position of the targeting dot relative to the center of the crosshairs. Based on my first run with the Steyr SSG M1 it does appear that they are using true MRAD values.
The Bushnell Engage uses the Deploy MOA reticle, so minor tick marks are 0.25 MOA, and the major tick marks are 1 MOA. It's a SFP scope, so we'd have to use the highest magnification setting to get the true MOA holdovers, and then calibrate the apparent holdovers at lower magnifications against that.
Also, we can compare results with the gold standard - the Bushnell Tactical.


There is no 'best' combination of rifle and scope - as long as you have the HunterSense ballistics firing solution turned on, you paint the target with that, and shoot.

There are some general guidelines:
- use low-to-medium powered scopes for hunting in forests, as you are not likely to be shooting beyond 150m
- if you are not using HunterSense, and you don't know the actual holdovers for your rifle and zero range settings, 'dial the elevation turret' to set the zero range value closest to the actual range to target - then holding the crosshairs-center on the target vital area will most likely result in a kill shot.
Otherwise, you'd have to know the actual trajectory to determine the bullet drop and wind drift

If I have to choose for Ranger Mode, I'd pick the Bushnell Elite Tactical and the Bushnell Engage 4-16x44mm, as they both have usable reticles.

[dbond1]

Originally posted by VictoriaHuntress:

If you are not using that, then you need to know the actual trajectory of the bullet to get the bullet drop and holdovers for elevation and windage.

Exactly, and this is one of the reasons why the .270 is such a fine hunting round. And why it was so popular before range finding became mainstream. The flatter trajectory is more resistant to range error than other cartridges. And if you play WOTH with no range information I'd say it is the best caliber to shoot (within proper energy limits, of course).

In that thread I had also brought up the impact dot, using this to determine accuracy. I'm interested if anything can be decisively proven, and this assumption that the Monobloc is more accurate can be confirmed or put to rest. But at the same time it feels a bit like a snipe hunt. If there is any deviation between the two rifles, it must be so small as to be practically meaningless.

If you're shooting at very long range it becomes significant I guess, but for normal shot range, say 150-250 yards, this difference, if it exists, will be too small to notice.

[VictoriaHuntress]

Originally posted by dbond1:

Originally posted by VictoriaHuntress:

If you are not using that, then you need to know the actual trajectory of the bullet to get the bullet drop and holdovers for elevation and windage.

Exactly, and this is one of the reasons why the .270 is such a fine hunting round. And why it was so popular before range finding became mainstream. The flatter trajectory is more resistant to range error than other cartridges. And if you play WOTH with no range information I'd say it is the best caliber to shoot (within proper energy limits, of course).

In that thread I had also brought up the impact dot, using this to determine accuracy. I'm interested if anything can be decisively proven, and this assumption that the Monobloc is more accurate can be confirmed or put to rest. But at the same time it feels a bit like a snipe hunt. If there is any deviation between the two rifles, it must be so small as to be practically meaningless.

If you're shooting at very long range it becomes significant I guess, but for normal shot range, say 150-250 yards, this difference, if it exists, will be too small to notice.

That's one reason why I'm working on holdovers for elevation and windage tables for each rifle - these are independent of the scope, and of course, the elevation holdovers depend on the zero range setting. Then I can turn off the ballistics firing solution dot for most hunting scenarios. This makes it more like typical IRL hunting, when one doesn't have a ballistics-enabled rangefinding scope LOL.

[6Taylor4]

Well best of luck with that, and I hope eventually it will become understandable, however your technical expertise is a bit beyond me as I have no idea what this means: "and of course, the elevation holdovers depend on the zero range setting"
Not looking for an explanation of that phrase, just saying I admire all of you being able to discuss this at such great detail; don't stop, my ignorance never stopped me from learning, so I'll try to keep up.
Do RL hunters understand and use this technological data in their hunts? The few hunters I know just grab their rifle and go; but I never pressed them for technical info. Anyone have an idea of how much this ballistic science is understood and used by hunters?

[dbond1]

If you are shooting at a target at 500 yards with a zero of 100, you have to hold over more than if your scope were zeroed at 300 for example. In game it has some use as well, since there is a 50m gap between each zero, so you can fill in that gap with hold overs/unders. This becomes more significant at long range, with bigger gaps in the zeroes.

To answer the question... in my experience we didn't do any technical data, but spent time at our range to zero our rifles in for a particular distance. 150 yards was typical. Before hunting season we would recon where we were planning to hunt. I would choose my spot(s) and do a sort of pre-plan, not unlike an artillery crew pre-registering target reference points. You get the various ranges around you and then zero your rifle to the optimum setting to engage targets within that framework. If the field I was hunting had max 100 yard view range, then no reason to sight it in at 200, as one example.

When a deer entered this space you knew from your recon roughly how far away it is, you know your zero, and then you hold over (or under) as the situation requires, using the mils on the reticle, each of which subtends a certain amount of deviation at various ranges (3 inches at 100 yards, 7 inches at 200 yards, 10 inches at 300 yards and so on). My scopes do not have variable range, like you have in this game. I cannot redial my zero with a flick of the cursor key. So you have to make up for range deltas with hold overs and unders to shoot accurately.

You can mimic this in game by playing with a fixed zero, say 150m/164y. Then you learn to use the scope to adjust for estimated range.

[6Taylor4]

Excellent, thank you. As I read it, you did your science in the real world on the range. When you say "hold over or under" you mean "aim", yes? I do notice, when using a scope to survey an area that the green dot moves above center and below center, and on windy days moves horizontally off-center - I play on hiker - most of my WOTH hunts have been short range shots, so the green dot wasn't much of an issue, as I'm using the crosshairs' nexus as my aim. Now that I'm beginning to learn about the science of it, thanks to all, I may try higher levels with more precision required.
The terms and all the acronyms are still confusing but I enjoy reading these discussions. It's given me a lot to think about.

[dbond1]

Hold over means that you essentially aim higher. If you are zeroed at 200 yards as an example and you place the reticle dot on a target at 200 yards it will hit on the aim point. Zero.

But if you are zeroed at 200 and the target is 400, and you place the dot on your target, your shot will fall well short. In this case you need to aim higher to allow for the drop over the increased distance. Each little line on your scope reticle is there to allow you to do this, those tick marks are designed to compensate for range above and below your zero.

[6Taylor4]

Originally posted by dbond1:

Hold over means that you essentially aim higher. If you are zeroed at 200 yards as an example and you place the reticle dot on a target at 200 yards it will hit on the aim point. Zero.

But if you are zeroed at 200 and the target is 400, and you place the dot on your target, your shot will fall well short. In this case you need to aim higher to allow for the drop over the increased distance. Each little line on your scope recticle is there to allow you to do this, those tick marks are designed to compensate for range above and below your zero.

And all that math and formulation results in an accurate understanding of the distance that each tiny line on the crosshairs are equal to; that's why there's small horizontal ticks on the vertical line, but under the horizontal line; you're much more likely to need to adjust to a target moving away from you, than one moving toward you, yes?

In real life, just snapping in a scope has no chance of being zeroed in, I assume; that's why you go and sight it in. In WOTH, it's different, as you can swap scopes at anytime and it's properly sighted in - correct? In real hunting, you can't do that, can you?
So I see that through the use of some impressive math, you can be precise in your distance adjustments, that's comes down to each tick is X feet. Crucial to know this value, and the math is needed to verify it, or define the distance.
Seems that then there is not a transfer of that info directly from one scope to another; if I know what the x33 tick-measurement is (for lack of a term) does it transfer to the x44? Or is there a separate calculation for each scope on the same rifle? I've never thought about this, just gabbed the highest power and went. One thing I have noticed, is the hunting experience for me is different when looking through the x20 than it is through the x50: the x20 feels like it's helping a little but the accuracy is my responsibility, whereas the x50 makes me feel like I'm doing something wrong, with those obvious measuring lines everywhere.
I have to take this in small bits. This is great. Thank you!

[VictoriaHuntress]

Originally posted by 6Taylor4:

Excellent, thank you. As I read it, you did your science in the real world on the range. When you say "hold over or under" you mean "aim", yes? I do notice, when using a scope to survey an area that the green dot moves above center and below center, and on windy days moves horizontally off-center - I play on hiker - most of my WOTH hunts have been short range shots, so the green dot wasn't much of an issue, as I'm using the crosshairs' nexus as my aim. Now that I'm beginning to learn about the science of it, thanks to all, I may try higher levels with more precision required.
The terms and all the acronyms are still confusing but I enjoy reading these discussions. It's given me a lot to think about.

Well, so did I LOL - I actually took a marksmanship course offered by a husband-wife team - he is a retired Canadian Forces officer who taught shooting skills and marksmanship to our soldiers and snipers, and she is a championship competitive long range shooter for Canada (although I think she retired from competition to focus on teaching and mentoring).

Now they teach shooting skills to military and law enforcement personnel, competition shooters, and hunters.

Plus, being a physicist, I find the whole subject of ballistics extremely interesting, and the advanced math is all in my wheelhouse LOL.

You can see this for yourself if you go to an ammunition manufacturer's web site and use their ballistics calculator. I like Hornady's site (use the Standard Calculator for basic estimates, and their 4DOF if you need more aerodynamically realistic calculations, but don't use Metric Units - ironically their conversion from U.S. units to metric units is wrong LOL). It's pretty decent otherwise, and you can print out a 'cheat sheet' that lists the elevation and windage holdovers for the distance range and step size and relevant ballistics parameters you selected.
There is also the JBM Ballistics Calculator, and the Applied Ballistics site (this is pretty much the Gold Standard for shooters)

[6Taylor4]

I went back and did a quick test. First of all, I apologize for referring to scopes by their objective lens diameter, that's not a good way to refer to them, I guess.

(I pretty much understand now what's happening inside my aging brain; it's degraded its ability to remember things in the short term, it's slower, and is losing more and more information; for instance, in high school I was in advanced math; by sophomore year, we had completed algebra, trig, plane and solid geometry; junior year we started on Calculus and Differentials; Senior year we learned the "New Math" from Harvard; I could use a slide ruler; I took a graduate course on Einstein's E=M(C*C), one semester of theory, one semester of math. Point being that here now, all that knowledge is barely accessible. Decline is inevitable, but I'm still a student and now I have more empty files to fill, is how I see it.
So that's another reason I'm interested in this, it keeps my brain challenged, as does WOTH!)

I used the Remington 700 and the Steyr CLII; I used six different scopes on each rifle at x7, zeroed to 109yds, from a prone position at the same object, a fence-post about 100 yds away.
The Steyr had a 5mm green dot on all scopes set to the same target and zoom - no variance at all.
The Remington was less consistent, varying from 8-10mm, so not much.
I'm not sure what that confirms or disproves or illustrates, as scope choice seemed to have no effect on the rifle.
My conclusion at this point is to use the scope that gives you the most info and the best chance of an accurate shot; but since the test was extremely narrow in the results, I'm unclear as to how to select the proper one; right now I think the Bushnell 3.5-21x50 has the most info in the scope.
Thanks!