Capacity, Hit Rate, Multiple Assailants and some thoughts...

[MLeake]

Frankly, my response was tempered, relative to your posts that preceded it.

And you've said at least once before that you are done with this thread. I suspect you'll say it another time or two.

 

[j3ffr0]

Just a couple of thoughts:
-No one has produced a better analysis than the OP. While it's just a model, it's a darn good one that is based on the mean of some real world data. The model can be adjusted, and anyone no liking the original model is free to make those adjustments.

-The nature of these forms is "what if". The thing we train for is "what if", and there is nothing wrong with discussing "what if".

-Spray and pray can be a valid technique for some situations. It's even taught in the military from my understanding. It's called suppressive fire. One needs to look no further than post #99 for a real world example. "Gramins let loose with a barrage of rounds hoping that what he might lose in accuracy would be compensated for by its suppressive nature. " I hope I never have to use it. It won't be very good option for us folks who don't carry higher capacity pistols.

 

[481]

Posted by 481: I can vary my assumptions all that I want and that still tells me nothing about a gunfight until it occurs.

It does tell you what you might reaonably expect.

No, it gives me the sum or the product of the values that I've just punched into the calculator. Nothing more.

You can press calculator buttons 'til the numbers wear off of them, but you are still playing "what if" based off of assumed and arbitrary numbers and it doesn't mean anymore than it did without those numbers. Playing "what if" with numbers is still playing "what if".

First, the assumtions can be reaaonably assessed within ranges uisng empirical data, and as Bart pointed out, the hit rate assumption need not be arbitrary.

But it is still assumed and just as pointless. You will, cannot, know what your "hit rate" will be until you're an actual participant in a gunfight. You can punch the calculator buttons that you want to punch, but they are still the calculator buttons that you want to punch.

Second, all forecasting, estimation, simulation, and prediction excercises, whether they involve weather, combat, financial returns, medical prognosis, reliability, servce life--you name it--constitute " playing 'what if' ", to use your characterization of the term.

OK, you've stated the obvious. What's the point. They are what they are.

I can assume a "hit rate" of 90% or 9%, but it is still just an assumption. I can assume one bad guy or two, but it is still just an assumption.

What is your point?

You just read it.

I can assume that I have "X" number of bullets, but that is just an assumption.

No. That's a known fact.

No, it is an assumption. I can change that number on a whim. It is made up, pulled from thin air. It is an assumption.

No one needs an exercise in math to tell them that-

-if you run out of bullets, you'll be unable to shoot back
-no matter how good a shot you are, some of your shots will miss their mark due to the stress of a gunfight
-it is harder to shoot two bad guys with guns as opposed to one guy with one gun
-if you are a lousy shot and use up all of your bullets before stopping the bad guys, they'll most likely shoot you
-launching more bullets might produce more hits

Of course not. We all understood all of those things, logically and intuitively.

What John's exercise does for us is provide a reasonable quantification of the likelihood with different round counts.

You may have had an appreciation for the difference, but I did not, John says that he did not, and I seriously doubt that we are alone.

Great, then there is no need for such mathematical masturbation.

You run out of bullets, you can't shoot back anymore; some of your bullets might not find their mark due to the stress of the event; neutralizing two guys is more difficult than one guy; if you don't stop the threat before you run out of bullets, you're going to be seriously hurt/killed; more bullets launched might mean more hits.

The math is superfluous.

I've never seen a calculator laying around at a gunfight. (and I've borne witness to that type of mindless carnage too many times to have missed such a ridiculous thing)

What is the point of that comment?

Happy to spell it out for you-

There is no point in this game of "what if". The numbers that you generate are of your choosing and ultimately tell you nothing except the self-selected product of those numbers. The calculator tells you what you want it to tell you. A times B equals C, X plus Y equals Z. You are selecting the inputs which means that you are also, ultimately, selecting the outputs.

When it occurs, the fight will be as it is, not as you "calculated" it to be.

I can tell you what I've experienced as a police officer working in large metropolitan jurisdiction (if you wish to accept it- I expect that the very existence of my career will be called into question given the tenor of this discussion), but none of the incidents that I've been in adhered to any imaginable mathematical model, no one had a calculator-

Officer#1 (shaking his head): "Ah, guys? Hold on just a sec, OK? I just hit the wrong key an' I gotta start all over.

Officer #2 (looking very frustrated): Aw, c'mon, man! Not again! That's the third time this month!

Thug (looking astounded, lowers gun): Whaaa? Hey, man...

Officer #2 (glares angrily at Thug): Cool your jets, pal, we're gettin' this straightened out.

Officer #1 (relieved, looks at both Thug and Officer #2): OK, yeah, there we go, that's it. Alrighty now, who has fired shots and how many did y'all fire?

Thug (absolutely confused, gun hanging loosely in his hand at his side): What the fuh...?

Officer #2 (beginning to look panicked): Geez, man, hurry up! C,mon! This guy ain't gonna stand here much longer.

Officer #1(smiling assuredly and nodding) : OK, just a minute now....and were ready...Now!"


-and no one was worrying about what some statistical exercise said they were supposed to do.

 

[481]

And you've said at least once before that you are done with this thread.

Nope. Just with you.

 

[481]

-Spray and pray can be a valid technique for some situations. It's even taught in the military from my understanding. It's called suppressive fire. One needs to look no further than post #99 for a real world example. "Gramins let loose with a barrage of rounds hoping that what he might lose in accuracy would be compensated for by its suppressive nature. " I hope I never have to use it. It won't be very good option for us folks who don't carry higher capacity pistols.

That's great if you are "in theatre". Not so great if you are in a self-defense situation (esp. in a populated area) where you will be held accountable for each and every round that you send off into the "wild blue".

Let just one of those little pills find an innocent down range and you will be sued 'til there's nothing left but lint in your pockets. Think because it was ruled as "justifiable" by the DA's Office, that the aggreived won't come after you for everything you've got? Think again. As a bonus, you get to live forever with the fact that you've seriously injured/killed another person.

 

[Crow Hunter]

481

So

You are saying that because a mathematical model can't be used to predict ever single variable that might happen in a gun fight that it is useless?

So, since the mathematical models that were used to send men to the Moon or the Curiosity Rover to Mars couldn't possibly account for every single variable, that they shouldn't be used and we should just "wing it"?

Understand what a mathematical model is for. It allows a method for calculating the statistical outcome of a certain set of variables. While it can't account for reality, it can point someone in the general direction of thought processes and either back up, or dash certain "common sense".

There are A LOT of people out there that carry a gun on a daily basis with 5 shots with no reload who believe that they adequately armed for any situation and don't need any "high cap tacticool crap" to defend themselves.

What this model demonstrates is potential fallacies with this line of thinking. If someone can perform at an increased performance level than the inputs into this model, under these circumstances, they may be perfectly right. It might actually be like the saloon scene in Unforgiven.

To be perfectly honest, the likelihood of sucess of a single person in a gun battle with 2 determined attackers is probably even less than what John posted unless there are some other factors involved. Like someone runs away, they shoot worse than you, you have cover, weapon malfunctions, etc. Most of the time, just the presence of the weapon will be enough to end hostilities, but that isn't something that I would want to count on.

I think it is a wonderful tool for getting people to look at their circumstances and possibly "try this at home" with their shooting practice. Set up a couple of targets, draw and fire after having done 15 pushups or running to a table. Then try it one handed or with their off hand, or from the ground as though they had been actually attacked 1st.

They may find that they need a different plan or they my get great comfort in their newfound abilities.

To Poo Poo statistical modeling because it doesn't fit reality is short sighted and demonstrates a basic misunderstanding of how it is used and how results should be interpreted.

 

[481]

481

So

You are saying that because a mathematical model can't be used to predict ever single variable that might happen in a gun fight that it is useless?

In this case, yes. It is all just guesswork. Statistical guesswork.

So, since the mathematical models that were used to send men to the Moon or the Curiosity Rover to Mars couldn't possibly account for every single variable, that they shouldn't be used and we should just "wing it"?

The models used to calculate such landings are based upon physical law- gravitational acceleration & decceleration, momentum, the amount of impulse a propellant/rocket motor can produce, they produce real results confirmable through trial and error. The statistical model being offered here is a probabalistic model- it, at best, offers what might happen if some variable(s) happens to be in place at the right time and the right place. There is much more uncertainty there than in the orbital mechanics equations you allude to. It's a common error.

While it can't account for reality, it can point someone in the general direction of thought processes and either back up, or dash certain "common sense".

DING DING DING DING DING DING

We have a winner! Why should I accept such a thing if it can't account for reality?

If someone lacks the common sense to make these realizations, no amount of math is going to help them and they probably shouldn't be carrying a gun in the first place. No amount of math can fix stupid.

There are A LOT of people out there that carry a gun on a daily basis with 5 shots with no reload who believe that they adequately armed for any situation and don't need any "high cap tacticool crap" to defend themselves.

What this model demonstrates is potential fallacies with this line of thinking. If someone can perform at an increased performance level than the inputs into this model, under these circumstances, they may be perfectly right. It might actually be like the saloon scene in Unforgiven.

To be perfectly honest, the likelihood of sucess of a single person in a gun battle with 2 determined attackers is probably even less than what John posted unless there are some other factors involved. Like someone runs away, they shoot worse than you, you have cover, weapon malfunctions, etc. Most of the time, just the presence of the weapon will be enough to end hostilities, but that isn't something that I would want to count on.

Look at that. You did that all without needing to resort to a probabalistic model. Why resort to all sorts of fuzzy math, when you can just apply common sense?

I think it is a wonderful tool for getting people to look at their circumstances and possibly "try this at home" with their shooting practice. Set up a couple of targets, draw and fire after having done 15 pushups or running to a table. Then try it one handed or with their off hand, or from the ground as though they had been actually attacked 1st.

None of that requires a model or a calculator. Done that sorta stuff several times, very useful.

They may find that they need a different plan or they my get great comfort in their newfound abilities.

To Poo Poo statistical modeling because it doesn't fit reality is short sighted and demonstrates a basic misunderstanding of how it is used and how results should be interpreted.

You've already said that such a model cannot account for reality.

While it can't account for reality...

There is no point in using it if it cannot account for reality and I am not silly enough to waste my time trying to make it stick.

 

[Crow Hunter]

In this case, yes. It is all just guesswork. Statistical guesswork.

All statistic predictions are guesswork. The difference is that there is a framework that is utilized that approximates a result based on the inputs used. If done correctly, those results will approximate reality within the confidence interval used.

The models used to calculate such landings are based upon physical law- gravitational acceleration & decceleration, momentum, the amount of impulse a propellant/rocket motor can produce, they produce real results confirmable through trial and error. The statistical model being offered here is a probabalistic model- it, at best, offers what might happen if some variable(s) happens to be in place at the right time and the right place. There is much more uncertainty there than in the orbital mechanics equations you allude to. It's a common error.

Yes, it is a probabalistic model, all models are. There is no way to account for an infinite number of variable in any calculation. So you look at the variables that are statistically probable and discount the others as negligable either in likelihood or magnitude. Since it is impossible have a working model of Mars or the Moon here on earth, they had to make "assumptions" based on statistics and model them as part of their calculations.

Look at that. You did that all without needing to resort to a probabalistic model. Why resort to all sorts of fuzzy math, when you can just apply common sense?

Because "common sense" isn't really all that common. I can guarantee you that at least 75% of the CCW carriers (probably more than that based on the cross section of posters I have seen reading on this forum) in the US have never even thought about what they would do if they had to shoot one handed due to injury or other circumstances and firmly believe that they will do "just as good" in real life as they do on a static range AND most of them probably CAN'T shoot as good as your average police officer.

Therefore, if you take the average hit percentage of police officers and apply it statistically only taking into account the factors of the number of rounds and hit percentage and see that it is statistically nearly impossible to prevail with only 5 shots, maybe someone will take that to heart and decide to practice realistically, and arm themselves realistically and use tactics best suited to their weapon of choice.

I don't see why anyone would have issue with this. It isn't supposed to be reality. But if it makes just one single person do something to improve their chances in real life, it wasn't a waste of time.

 

[481]

Yes, it is a probabalistic model, all models are. There is no way to account for an infinite number of variable in any calculation. So you look at the variables that are statistically probable and discount the others as negligable either in likelihood or magnitude. Since it is impossible have a working model of Mars or the Moon here on earth, they had to make "assumptions" based on statistics and model them as part of their calculations.

Looks like NASA's model works well enough. The proposed one under discussion and unproven as it stands, not so much.

Because "common sense" isn't really all that common. I can guarantee you that at least 75% of the CCW carriers (probably more than that based on the cross section of posters I have seen reading on this forum) in the US have never even thought about what they would do if they had to shoot one handed due to injury or other circumstances and firmly believe that they will do "just as good" in real life as they do on a static range AND most of them probably CAN'T shoot as good as your average police officer.

You don't need a model for that. If I am disabled (to some varying extent), by something then my abilities suffer. To what extent is an unknown. The model has no way to account for a condition like this unless you make an assumption as to how much you will be disabled. More guesswork.

Therefore, if you take the average hit percentage of police officers and apply it statistically only taking into account the factors of the number of rounds and hit percentage and see that it is statistically nearly impossible to prevail with only 5 shots, maybe someone will take that to heart and decide to practice realistically, and arm themselves realistically and use tactics best suited to their weapon of choice.

I don't see why anyone would have issue with this. It isn't supposed to be reality. But if it makes just one single person do something to improve their chances in real life, it wasn't a waste of time.

I am sure the figures, whatever one enters, will always work out. The sum or product of two given numbers will always be the same. It's the numerous, and often dubious, underlying assumptions that make this particular specimen a loser.

 

[Bartholomew Roberts]

By your own admission, you make several assumptions (probability of making a hit, etc) that may or may not hold true under all conditions and then proceed to explore hypothetical situations using those as a basis for that work.

Well, I am convinced. No more making any assumption that doesn't hold true under all conditions. I mean, I had always assumed I would not need a .375 H&H to kill a charging elephant; but clearly, there are conditions where that was necessary for others. So because my assumption failed to hold true for all conditions, it must be an invalid or useless assumption, yes?

The models used to calculate such landings are based upon physical law- gravitational acceleration & decceleration, momentum, the amount of impulse a propellant/rocket motor can produce, they produce real results confirmable through trial and error.

So those models produce real results confirmable through trial and error; but the number of rounds you will have in your firearm during a gunfight is an arbitrary and unknown number over which we have no control?

 

[481]

Well, I am convinced. No more making any assumption that doesn't hold true under all conditions. I mean, I had always assumed I would not need a .375 H&H to kill a charging elephant; but clearly, there are conditions where that was necessary for others. So because my assumption failed to hold true for all conditions, it must be an invalid or useless assumption, yes?

If you want to be silly, I guess so.

I said "may or may not hold true" not "won't hold true under all conditions". Using what I said within an incorrect context is a faulty argument device.

So much for rational debate, huh?

So those models produce real results confirmable through trial and error; but the number of rounds you will have in your firearm during a gunfight is an arbitrary and unknown number over which we have no control?

Sure. There's uncertainty everywhere.

 

[Crow Hunter]

You don't need a model for that. If I am disabled (to some varying extent), by something then my abilities suffer. To what extent is an unknown. The model has no way to account for a condition like this unless you make an assumption as to how much you will be disabled. More guesswork.

No you absolutely don't need a model for that. But people don't always think about it until someone does something like what John has done.

He laid it out and demonstrated statistically just 5 rounds with no reload might not be enough with the assumptions/inputs he stated.

Now if someone looks at that and says, "Wow. I actually can't hit the bullseye with all N# shots in my XXXX gun with a 2 handed hold on a square range 100% of the time on demand with only 1 target. Maybe I should seek competent training and/or practice more, or choose a different weapon than what I use today." That is a good thing.

In reality if you don't "Go stupid places, with stupid people and do stupid stuff" you probably won't need a gun at all, and the times that you do, just having it and maybe firing a shot or 2 will be enough to end a confrontation.

But "reality" isn't what this is about. It is statistical probablities given a specific set of variables.

I hope people look at it and it prompts them to think about what it actually means without getting to far into the probabilities of those specific variables happening and use it to evaluate their own Mindset, Tactics, Skill and Gear.

 

[MLeake]

481, you keep making comments like "so much for rational debate..."

You accuse others of emotionalism, or of attacks...

But you keep using words like "silly," "foolish," "loser," etc.

You also don't give straight answers. In an earlier post, you claimed you had only said you were through responding to me; however, after reviewing earlier posts of yours, you had said you were through with "this silly wild goose chase," and other such things before I had joined the conversation.

And, of course, after specifically (so you claim) saying you meant you were no longer going to respond to me, you responded to me. Color me surprised.

You aren't attempting a rational debate. You aren't trying to contribute to discussion. You are poo-pooing a basic statistical model, for its being a basic statistical model. You are behaving in an obnoxious manner, and accusing others of behaving obnoxiously.

It is pointless for anybody to argue with you, as your argument will change each time.

By the way, my first post, which you found rude, etc, was based on your previous arguments, and your signature line about being in "a state of reality." In other words, it was derived from your inputs - so your reaction to it was interesting.

I am no longer going to argue with you in this thread, because other than this recent sidetrack (aka 481), it has been a good discussion and I would prefer not to derail it, by feeding your standup routine.

 

[481]

He laid it out and demonstrated statistically just 5 rounds with no reload might not be enough with the assumptions/inputs he stated.

We can arrive at the same conclusion just as easily without punching calculator buttons.

And by mere fiat, one can change those assumptions/inputs to justify that that very same arrangement will be enough.

This is just another example of paralysis via over-analysis. You can make even the simplest decisions far more intricate than they need to be. The return for all of the extra effort isn't there.

But "reality" isn't what this is about.

Yep. So that'd be fantasy?

 

[Bartholomew Roberts]

I said "may or may not hold true". Using what I said within an incorrect context is a faulty argument device.

1. Well, the context of your comments is here for everyone to read, so I did not feel a need to quote everything you had said in order to establish context. I find that brevity helps keep conversations focused and less likely to be emotional or nonsensical.

2. As I understood your arguments, the context was correct. Throughout the thread, you have made comments such as:

"it is in no way an accurate portrayal of reality and no valid conclusions can be drawn from such a highly speculative exercise."

"I can vary my assumptions all that I want and that still tells me nothing about a gunfight until it occurs. You can press calculator buttons 'til the numbers wear off of them, but you are still playing "what if" based off of assumed and arbitrary numbers and it doesn't mean anymore than it did without those numbers. Playing "what if" with numbers is still playing "what if".

"But it is still assumed and just as pointless. You will, cannot, know what your "hit rate" will be until you're an actual participant in a gunfight."

"In this case, yes. It is all just guesswork. Statistical guesswork."

My reading of these comments is that you feel that any assumption that is not always valid is a useless assumption? If I have misunderstood your context, I welcome the chance to better understand what point you were trying to make.

Sure. There's uncertainty everywhere.

Again, this comment is perfectly in line with how I understood your earlier comment. You seem to be insisting on absolute certainty/always valid assumptions. On the one hand, you accuse me of taking your comments out of context and not seeking rational debate, on the other hand, when I ask how it is possible you cannot accurately predict how much ammo you choose to carry on a given day, you respond that the number is arbitrary and there is no way I can know with certainty how much ammo I am going to be carrying?

So which is it - are you saying that I cannot control the amount of ammunition I carry with a high enough certainty to make it practical for the purposes of our discussion or were you being pedantic and insisting on absolute, unshakeable certainty in the amount of ammo I choose to carry while simultaneously complaining about a lack of rational debate and taking things out of context?

 

[481]

Bart,

This comment, offered up by CrowHunter, is reflective of the problem that I have with using a statistical model to quantify the highly variable tangibles (and intangibles) that are involved in a gun fight.

To Poo Poo statistical modeling because it doesn't fit reality is short sighted and demonstrates a basic misunderstanding of how it is used and how results should be interpreted.

If it doesn't "fit reality", what's the point? Why bother?

Sure, it's fun to play with numbers and calculators, but the only answers that matter are the ones that actually occur.

I am not saying that you cannot play "what if" 'til your heart's content, but to think that you are going to get real answers from numerical fantasizing is a "fool's errand".

You seem to be insisting on absolute certainty/always valid assumptions.

Yep. Invalid assumptions produce invalid results/conclusions. If I assume that I have a greater "hit rate" then I actually have (an invalid assumption) and draw the conclusion that I need only "x" number of rounds to successfully handle "y" number of attackers (an invalid conclusion) when in fact I'll need more, I am gonna have a really bad day when I come across "y" number of attackers.

 

[481]

Of course, all of this presumes that we can predict our "hit rates" under the duress of a gun fight to a reasonable degree of precision and certainty. I, for one, cannot.

 

[Bartholomew Roberts]

If it doesn't "fit reality", what's the point? Why bother?

If assumptions always fit reality, they would not be assumptions. However, many of the assumptions we make will fit reality - for example, even without the day ending, I still feel good about not running across any charging elephants. That assumption, while not always valid for all people in all conditions, has a high probability to be a good assumption for planning my day. I also feel safe about assuming that if I start the day with 10 rounds in my pistol, I'll have 10 rounds in it when a gunfight starts. That won't fit reality perfectly; but it will fit it often enough that planning that way makes more sense than not planning that way.

I am not saying that you cannot play "what if" 'til your heart's content, but to think that you are going to get real answers from numerical fantasizing is a "fool's errand".

Like a lot of your statements in this thread, that one strikes me as being so obvious I am not sure why you said it. Were you under the impression that I, or some other poster, was convinced that the original framework here was for the purpose of predicting gunfights and that we could do away with all that training and just carry a really big magazine?

If I assume that I have a greater "hit rate" then I actually have (an invalid assumption) and draw the conclusion that I need only "x" number of rounds to successfully handle "y" number of attackers (an invalid conclusion) when in fact I'll need more, I am gonna have a really bad day when I come across "y" number of attackers.

This is the same as GIGO (Garbage In, Garbage Out). If you input bad data into a model, you'll get results that don't reflect reality. You write as though you have a problem with the model; but all of your substantial complaints seem to revolve around the data rather than the model. Specifically, I understand you as saying that none of that data (hit rate, amount of ammo available to you, number of attackers, number of hits necessary to stop attackers) can be known with absolute certainty.

I found the framework here to be quite useful for planning purposes despite the uncertainty around the numbers. For example, if you shoot as well as the average big city police officer and have two attackers (the most common assault scenario), 12 rounds will give you a ~50% chance. 10 rounds will give you a ~36% chance. If you happen to be someone carrying a compact Glock with no spare, that is an illuminating difference spelled out a lot more clearly in math than it can be in words.

I think in terms of a rough analysis of how much ammo is enough, the model presented here makes a good planning tool. And like most planning tools, it is easy enough to hedge uncertainty by lowering your expectations if you don't like the assumptions used here.

Of course, all of this presumes that we can predict our "hit rates" under the duress of a gun fight to a reasonable degree of precision and certainty.

No; but we can look at what the mean hit rates of people who have been in gun fights as a rough guide to what to expect from similarly trained shooters. If we want to be especially cautious we can even halve those numbers.

And the numbers really need not be precise; because unlike the Price is Right, we don't have to be the closest to the actual number. We just need to not go over it.

 

[Crow Hunter]

If it doesn't "fit reality", what's the point? Why bother?

Just because something doesn't model reality exactly, doesn't mean it doesn't have merit. You can't know that the temperature tomorrow is going to be vastly lower than it is today. But that doesn't mean that you won't know enough to not walk outside wearing a parka in 95F heat. What John did is say if given X then B is your chances of success. I don't think it is or should be construed to be the end all and be all of gunfight analysis.

And by mere fiat, one can change those assumptions/inputs to justify that that very same arrangement will be enough.

Yes you can. But your inputs might be looked upon as suspect. 100% hit rate is not something that is likely to occur. While a 30-40% hit rate is what has been demonstrated by police officers in many regions of the country.

That is part of the power of statistics. It allows you to model different inputs quickly and easily once the model is built. It allows you to get a good indication of how things probably will happen given the initial assumptions. But that doesn't mean it reflects reality exactly, it doesn't need to for what it does.

So, your argument, in a nutshell, is that it is a waste of time trying to model what could happen in a situation where you had to defend yourself against 2 assailants becaue it is obvious that a person shouldn't be carrying a 5 shot revolver with no reload.

Why shouldn't they?

 

[481]

So, your argument, in a nutshell, is that it is a waste of time trying to model what could happen in a situation where you had to defend yourself against 2 assailants becaue it is obvious that a person shouldn't be carrying a 5 shot revolver with no reload.

Yes.

That carrying a 5 shot revolver with no reload is a bad idea no matter the number of assailants I meet requires no model to ascertain.

Why make the process more complicated than it need be?

Yes you can. But your inputs might be looked upon as suspect. 100% hit rate is not something that is likely to occur. While a 30-40% hit rate is what has been demonstrated by police officers in many regions of the country.

That 30-40% hit rate average is not a guarantee. I'll bet that within that study you'll find at least one poor guy who couldn't get a shot off for whatever reason. So much for the average.