Interesting observation regarding caliber differences...

[JohnKSa]

Just as you don't need to destroy much of a mountain to blast a tunnel throgh it, you don't need to destroy much of man's tissue to incapacitate him. But dividing the volumes by the total volume of a man (or the amount of rock displace by the total mass of the mountain) obscures the significant differences between the various calibers/loads (or explosive agents)

It's a bad analogy. In the one case you care nothing about affecting the whole unit--the mountain.

In the other case ALL you care about is affecting the whole unit--the attacker.

Since that is the case, it's relevant to point out just how much damage you can actually expect do to an attacker as a whole. It's very important for a person to realize that simply randomly damaging an attacker with a bullet is pointless in terms of achieving incapacitation--regardless of which of the calibers listed they choose.

And, as a consequence of realizing how small an amount of overall tissue is damaged, it becomes apparent that differences in terminal performance shouldn't be considered as the most important factor in caliber selection. Because no matter which caliber you select, on average, you're still only going to be damaging a fraction of a percentage point of the attacker.

No, not at all. When you're trying to incapacitate an attacker, the fact that you're not damaging *all* of the tissue in their arms and legs isn't relevant. The weight contained in the arms and legs adds to the total mass of the man, but doesn't really affect the efficacy of gunshot wounds (torso wounds, at least.)

It is precisely because there is so much of a person that can be damaged without resulting in incapacitation that it's important to understand how little damage a bullet does.

It's not uncommon to hear people making claims about how even a peripheral hit with "insert favorite caliber here" will automatically end a fight. Next time someone says that to you, instead of just saying it's not true, you'll have some data to show him.

Do you deny that your mathematical process completely obscures the variance of almost 300% in the FBI's wound volume measurements?

First of all, it's hardly accurate to claim that the process of "averaging" is "my mathematical process". It was around centuries before I was born.

Second, the wound volume figures from the FBI are actually averages calculated from the many rounds they fired with each loading they tested. So you could say the same thing about their figures. They're hiding information by only providing averages instead of giving you a penetration measurement for each and every round fired.

Third, I said clearly that the figures were on the internet, so it's a real stretch to imply that I was hiding anything.

But nowhere in your initial post (or in post #46 that I could see) did you actually STATE those volumes (or even link to them).

I downloaded them some time ago and once I had them there was no point in keeping a link.

As far as posting them, the data contains measurements from 80 something loads with two wound volume figures for each. Posting them is hardly feasible.

Finally, no one (including you) asked for the data set.

Your math is correct - no one is arguing that.

I take it that since your other arguments have been answered that now that you're now taking a different approach?

 

[ScottRiqui]

Another problem with bringing total mass into the equation when evaluating the efficiency of a caliber/loading is that when you look at targets of varying size, the total mass of the larger targets increases at a much faster rate than the increase in penetration depth required to reach their "vital bits". So as you move up in target size, the ratio of wound volume to total volume is going to drop off much faster than the actual efficiency of the round drops off.

Here's an example. Take Bill, who is 25% bigger in every dimension than Tom. Even though Bill's vital organs are only hidden behind 25% more flesh & bone than Tom's, Bill weighs twice as much (i.e. 100% more). Organ depth only varies linearly with an increase in size, while total mass varies exponentially (specifically, it's a cubic relation.)

If you're going to try to incorporate a target's size into an efficiency calculation, you should concentrate on organ depth, rather than total mass.

 

[JohnKSa]

I think it goes without saying that if you engage a very small attacker that terminal performance due to caliber selection will make a more significant difference in the outcome than if you are confronted with a very large attacker.

...you should concentrate on organ depth...

All of the calibers listed in the first post will penetrate deeply enough to reach vital organs on an average human from any reasonable shooting angles even when employed with expanding ammunition.

Premium self-defense ammunition in all the calibers listed in the first post is designed to penetrate to a depth that meets FBI penetration minimums and maximums in the interest of insuring exactly that ability.

 

[ScottRiqui]

First of all, it's hardly accurate to claim that the process of "averaging" is "my mathematical process". It was around centuries before I was born.

Don't be coy - it's not the averaging that I was talking about. I specifically said that I was referring to your second step of dividing the wound volumes by the total volume of the target (using density as a necessary conversion factor). THAT'S your mathematical process that completely obscured the wide (about 280%) variance in wound volumes among the various calibers/loadings.

If truly ALL that you're trying to point out is that it doesn't take much tissue damage, percentage-wise, to incapacitate a target, then I agree, and always have. But that observation borders on the trivial, hardly worthy of the effort you've expended.

But the way you've presented your data almost seems designed to obscure the significant relative differences in wound volume between the various calibers/loadings that the FBI tested. That's the only part of your post I have a problem with.

 

[JohnKSa]

Don't be coy - it's not the averaging that I was talking about. I specifically said that I was referring to your second step of dividing the wound volumes by the total volume of the target (using density as a necessary conversion factor). THAT'S your mathematical process that completely obscured the wide (about 280%) variance in wound volumes among the various calibers/loadings.

That's not correct. Dividing by a constant won't do what you claim. You can verify that very simply. Take a group of numbers and divide them all by the same constant. You'll find that if one was 3x larger than another before the division it's still 3x larger than the other after both have been divided by the constant.

But the way you've presented your data almost seems designed to obscure the significant relative differences in wound volume between the various calibers/loadings that the FBI tested. That's the only part of your post I have a problem with.

Post #46 explains why I did the calculation.

The point of the calculation was to determine the amount of a human that one could expect to damage, on average, with a common self-defense caliber. The fact that all the figures turned out so similar that they rounded to the same number was just the way things worked out. I thought that it was an "interesting observation" and that's why I posted it and that's why I titled the thread the way I did.

I figured it would be an unpopular result because it challenged what many people believe to be "common knowledge" and that has turned out to be quite true.

 

[ScottRiqui]

It's a bad analogy. In the one case you care nothing about affecting the whole unit--the mountain.

In the other case ALL you care about is affecting the whole unit--the attacker.

But you don't need to incapacitate the arms and legs via direct damage - in fact, that's not even the preferred method.

Doubling the mass of a person doesn't make incapacitating them doubly difficult - nowhere near that, in fact. So bringing total mass into a calculation designed to express the efficacy of a handgun bullet isn't really scientifically valid.

 

[JohnKSa]

But you don't need to incapacitate the arms and legs via direct damage - in fact, that's not even the preferred method.

I agree. It's precisely because there is so much of a person that can be damaged without achieving incapacitation that it's important to get the big picture.

Doubling the mass of a person doesn't make incapacitating them doubly difficult - nowhere near that, in fact.

I agree. And I haven't made any such claim.

So bringing total mass into a calculation designed to express the efficacy of a handgun bullet isn't really scientifically valid.

That doesn't follow.

The fact that there's not a linear relationship between mass and incapacitation difficulty doesn't mean that looking at the amount of damage as a percentage of the whole is unscientific. It just means that we shouldn't expect there to be a linear relationship between the percentage and the difficulty of incapacitation.

 

[ScottRiqui]

That's not correct. Dividing by a constant won't do what you claim. You can verify that very simply. Take a group of numbers and divide them all by the same constant. You'll find that if one was 3x larger than another before the division it's still 3x larger after the division.

Well then, the differences were obscured by the fact that you rounded to one significant figure. 0.10% and 0.14% both round to 0.1%, even though the larger number represents a 40% increase over the smaller number. Perhaps you wouldn't have rounded to a single significant figure if the numbers hadn't ended up being so small after dividing by the target weight?

Why don't you post the six average wound volumes you used? The FBI data was given to three significant figures. If the FBI averages for the six calibers aren't the same to the first significant figure, then there's no doubt that your calculations have obscured differences in the original data.

 

[ScottRiqui]

The fact that there's not a linear relationship between mass and incapacitation difficulty doesn't mean that looking at the amount of damage as a percentage of the whole is unscientific. It just means that we shouldn't expect there to be a linear relationship between the percentage and the difficulty of incapacitation.

So we at least agree that the percentage of total tissue that's damaged isn't a reliable indicatior of a bullet's ability to incapacitate.

If your only intention from the beginning was to point out how little tissue damage is required for incapacitation, then I have no problems with any of your methods. But if you're also trying to imply that incapacitation efficacy is essentially the same between all six calibers you listed, then I certainly have a problem with your methods. If you're trying to make some comment on the efficacy of various rounds, you're better off sticking with absolute wound volumes for that purpose, rather that expressing wound volumes as a percentage of total target volume.

If you weren't trying to make a comparative assessment of the efficacies of the various calibers, a direct statement to that effect in your first post would have made this thread much shorter.

 

[JohnKSa]

I stated up front that I rounded the numbers and also to what precision.

But, for those who didn't realize what that meant, the range of numbers, given to 3 significant digits that will round to 0.1% is as follows:

0.149% to 0.050%

The larger number is 3.04 times larger than the small one.

By the way, the ratio of the largest figure to the smallest in the actual data was only 1.55

So we at least agree that the percentage of total tissue that's damaged isn't a reliable indicatior of a bullet's ability to incapacitate.

If you believe that then why are you so bent out of shape that I didn't present the percentages to three significant digits?

Quick review.

I'm the one who says that the percentage of total tissue damaged is so small that trying to determine the effectiveness of the bullet via that number is ridiculous.

You're the one who's been trying to prove that I'm hiding data by not carrying more significant digits. Meaning, of course, that if you and others could see the differences in the percentages of total tissue damaged listed to 3 significant figures it would prove that some calibers are better than others.

 

[ScottRiqui]

So why did you round to only one significant figure? The FBI data is given to three significant figures, and you're justified in using at least two for the average weight of an adult human male, if not three.

When you're dealing with numbers as small as the percentages you got after dividing by the average weight, you can't afford to toss away any justifiable digits.

As your example shows, rounding to only one significant figure when your original data has three significant figures can obscure a relatively huge difference between the numbers.

The fact that you announced what you were doing doesn't change this, especially since we didn't have the six average volumes, which would have immediately many any variances obvious.

 

[JohnKSa]

So why did you round to only one significant figure?

They say that the third time's the charm.

From post #85

"Post #46 explains why I did the calculation.

The point of the calculation was to determine the amount of a human that one could expect to damage, on average, with a common self-defense caliber. The fact that all the figures turned out so similar that they rounded to the same number was just the way things worked out. I thought that it was an "interesting observation" and that's why I posted it and that's why I titled the thread the way I did."

As your example shows, rounding to only one significant figure when your original data has three significant figures can obscure a relatively huge difference between the numbers.

Honestly it never crossed my mind that an example would be necessary or helpful. I just assumed that the concept of rounding numbers was common knowledge.

 

[ScottRiqui]

You're the one who's been trying to prove that I'm hiding data by not carrying more significant digits. Meaning, of course, that if you and others could see the differences in the percentages of total tissue damaged listed to 3 significant figures it would prove that some calibers are better than others.

No, I'm saying that the way you presented your data in your initial post (six different calibers with identical percentages next to all of them) has led several people in this thread to infer that you're trying to say that there aren't significant differences in the incapacitating abilities of the six different calibers.

If you had listed the six average wound volumes the way the FBI presented them (three significant figures) rather than just jumping right to the truncated-precision percentages, I believe that fewer people would have misunderstood the point you were trying to make.

And *no one* has ever tried to argue that the percentage of total tissue damaged is some kind of measure of efficacy. In fact, you're the first person that I've ever seen that's even performed such calculations.

 

[ScottRiqui]

"Post #46 explains why I did the calculation.

The point of the calculation was to determine the amount of a human that one could expect to damage, on average, with a common self-defense caliber. The fact that all the figures turned out so similar that they rounded to the same number was just the way things worked out. I thought that it was an "interesting observation" and that's why I posted it and that's why I titled the thread the way I did."

That's not a valid reason for throwing away one or two digits of precision that you would have been justified in using. Had you preserved the level of precision that you were entitled to, I think you would have found that the values were not "so similar", relative to one another. As you've already shown, chopping off two digits can hide a three-fold variance within the numbers.

Had you not arbitrarily rounded the numbers the way you did, your initial post could have very well been an observation that the .357 damages three times as much tissue as the 9 mm (to pick two calibers at random). But because of the level of (im)precision you chose to use, we'll never know.

 

[JohnKSa]

That's not a valid reason for throwing away two or three digits of precision that you would have been justified in using.

Ok, here comes try number 4.

Had you not arbitrarily rounded the numbers the way you did...

The rounding was not arbitrary. The rounding was done in an attempt to get a representative figure for the percentage of tissue destroyed on average by typical self-defense rounds.

You can't just keep arbitrarily rounding or you end up with all zero results. The point that all of the numbers rounded to identical NON-ZERO results was exactly what was interesting.

No, I'm saying that the way you presented your data in your initial post (six different calibers with identical percentages next to all of them) has led several people in this thread to infer that you're trying to say that there aren't significant differences in the incapacitating abilities of the six different calibers.

There's really no need for inferring. My position is not at all unclear and if anyone is still in doubt it's not for lack of my stating it repeatedly on this thread.

For what it's worth, if that's what they're inferring then they got it right.

the .357 damages three times as much tissue as the 9 mm (to pick two calibers at random).

Really bad random choices. The .357Mag and the 9mm gave identical results to 3 significant digits.

 

[ScottRiqui]

The rounding was not arbitrary. The rounding was done in an attempt to get a representative figure for the percentage of tissue destroyed on average by typical self-defense rounds.

Yes, your decision *was* arbitrary, because there's no scientific reason for throwing away that much precision. If you divide an average wound volume expressed to three significant figures by an average weight for an adult human male expressed with two significant figures (since you used 180#), then you're perfectly justified in keeping two significant figures in your result. If you had instead used 185# for the average weight, which I've seen, you could have kept three significant figures in your answer.

There is NO valid need to chop the final answer down to only one significant figure, and by doing so, you've potentially hidden a significant variance between the six averages.

Why not post the average wound volumes for the six calibers from the FBI report, with all three significant figures given in the report?

 

[ScottRiqui]

Really bad random choices. The .357Mag and the 9mm gave identical results to 3 significant digits.

Okay, so bad example. From the FBI report I linked to, the 10 mm rounds averaged 5.17 cubic inches of wound volume (the "clothed + bare gelatin" column), while the .357 Magnum rounds averaged 3.53 cubic inches in the same column.

Using the three significant figures I'm entitled to, the average wound volume for the 10 mm rounds is 46.5% larger than the average volume for the .357 Magnum rounds. Had I rounded my results to one significant figure like you did, the difference would only be 30% (5 cubic inches versus 4 cubic inches, percent difference rounded to one SF). But if the average volume for the .357 Magnum had been just a tiny bit smaller (3.49 cubic inches instead of 3.53), then rounding to one significant figure would show a difference of 70% (5 cubic inches versus 3 cubic inches, percent difference rounded to one SF).

This is why it's important to use as many significant figures as you're justified in keeping. In this case, I was averaging numbers with three significant figures, so I'm justified in keeping three significant figures in the final result.

 

[JohnKSa]

If you had instead used 185# for the average weight, which I've seen, you could have kept three significant figures in your answer.

The fact that I used 180 for my calculation doesn't mean that the weight only has 2 significant digits, it just means that the last digit is zero.

You can have a number that has many trailing zeros and all of them can be significant digits if that is really the precision that you know the number to. Whether you can actually carry them through a calculation to the result depends on the other numbers in the calculation.

Ok, call me skeptical, but at this point I'm getting the feeling that your assessment of my results is based, not on your intimate knowledge of practical mathematics, but rather on the fact that you just don't like the way they turned out.

The figures in your link are the ones I used. My methods are clearly laid out in this thread. I would be happy to have you verify/correct my results and post that information on this thread.

This is why it's important to use as many significant figures as you're justified in keeping.

Are you seriously lecturing me on math at this point after demonstrating on this thread that you don't understand the effects of scaling by a constant, the meaning of significant digits, the effects of averaging and what happens when you round a number?

I gotta say that's pretty impressive.

 

[ScottRiqui]

Think back to your engineering classes. If you're given a three-digit real-number quantity that ends in zero and doesn't have a decimal point, that's two significant figures unless otherwise stated.

Of course, integer "counting" numbers, like "550 buckets", have infinite precision.

Regardless, if you want to assume that 180# is accurate to three significant figures, that's fine with me.

I'll be happy to re-run the numbers from the FBI report tomorrow with an appropriate level of precision and post the results. Just tell me if you were using column #6 (bare gelatin) or column #8 (clothed and bare gelatin).

 

[ScottRiqui]

Are you seriously lecturing me on math at this point after demonstrating on this thread that you don't understand the effects of scaling by a constant, the meaning of significant digits, the effects of averaging and what happens when you round a number?

Okay, I'll freely admit that it wasn't your division by a constant that obscured the information contained in the FBI's data - it was your decision to round to one significant figure when you were entitled to keep three.

And my only use of significant figures that you've complained about was 180 having two significant figures, and I think you'll find I'm right on that point.

Both of us agree that rounding three-digit numbers to one significant figure can hide large variances, as you showed with your example of .149 and .050, so I don't know what part of my understanding of rounding you're faulting. And I don't know what you think I'm missing when it comes to taking the average of numbers - we haven't disagreed on that point as far as I can recall.