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

[481]

After reading the OP's exercise in stats- and most of the rest of the thread- I came away with a headache and the belief (which is now greater than ever) that such exercises are little more than mental gymnastics. Too many factors are left unaccounted for and the nifty little graphs seem to suggest that if you can just send enough lead down range you'll hit the bad guy.

That is a questionable message at best since there are no guarantees in a gun fight.

[MLeake]

Funny, I didn't get that impression. I just got the impression that hit rates aren't quite up there with those from the range; that some people require more good hits to stop than do others (physically tough; mentally tough; chemically imbalanced); that there are decent odds of multiple attackers; and that more capacity could be a good thing due to all those factors.

I don't recall anybody advocating spray and pray.

[OldMarksman]

Posted by 481: After reading the OP's exercise in stats- and most of the rest of the thread- I came away with a headache and the belief (which is now greater than ever) that such exercises are little more than mental gymnastics. Too many factors are left unaccounted for....

What factors are left unaccounted for?

Yes, there are some assumptions that may not be realistic; John lists them. One is that one will stop shooting after hitting the target twice; another is that the defender will not be shot or stabbed before landing two shots. If you do not like those, change the assumptions and do the math your self.

... and the nifty little graphs seem to suggest that if you can just send enough lead down range you'll hit the bad guy.

I think you are looking at them wrong. The message is, you are not as likely to land two shots or four shots (take your pick) with fewer rounds than you are with more. That 's an obvious conclusion, but John quantifies it for us.

[pete2]

Practice, practice, practice. You will do what you're trained to do. Being an old timer I'm not nearly as fast as the young guys. IDPA is a game loosely based on defensive handgun. Last match I shot I was much more accurate than one of the young men I shot against, but he gave me a whupping on the score sheet.
In a real world situation The more accurate shooter might prevail. Lady Luck unfortunately plays a big part. If the BG gets off 10 shots while I'm shooting 1 and he hits with only 2 of them, I'm screwed. Practice shooting so that you can shoot fast and accurately, 3, 5, and 7 yards you should be able to make good hits every shot. If you have to make a head shot, you'll have to slow a little, even aim at the 7 yd mark. You should be able to make good hits by pointing the gun except for the head shot at 7. We shoot service pistols and revolvers, if you switch to a 2" 38 or an LCP the odds will go down greatly.
This does not mean you will prevail in a gun fight, but it may give you a chance.

[481]

Originally Posted by OldMarksman:

What factors are left unaccounted for?

Oldmarksman,

More than I have time to list. The effect upon one's ability to shoot accurately while under fire, after being hit, that bad guys move when being shot at, the ability to see and identify one's threat (lighting), etc, etc.

You list more here-

Originally Posted by Oldmarksman:

Yes, there are some assumptions that may not be realistic; John lists them. One is that one will stop shooting after hitting the target twice; another is that the defender will not be shot or stabbed before landing two shots.

Originally Posted by Oldmarksman:

If you do not like those, change the assumptions and do the math your self.

The approach presented is far too simplistic and ignores the majority of factors that influence a gunfight. In short, it is a pointless exercise in mathematical "what-if" that suggests that just sending more lead down-range, ala "spray&pray", is the answer to "the problem" of surviving a gunfight. There's more to this issue than that and I am not silly enough to waste my time chasing this "wild goose" any further.

If you like this kind of stuff, that's fine , but it is in no way an accurate portrayal of reality and no valid conclusions can be drawn from such a highly speculative exercise.

[MLeake]

481, in what version of reality is having less ammunition an advantage?

So far, you are the only one calling for spray and pray. Nice straw man.

[JohnKSa]

Too many factors are left unaccounted for and the nifty little graphs seem to suggest that if you can just send enough lead down range you'll hit the bad guy.

There are many factors left unaccounted for because the graphs are ONLY to tell you what the odds of making a certain number of hits with a certain number of shots given a fixed probability of connecting with each shot.

The graphs do tend to imply that if you can just send enough lead downrange you'll hit the bad guy because that's true (assuming a huge number of rounds available). However, if you read some of my posts you'll see that I make a point of saying that just having more shots won't help you because in the real world, you won't get a chance to stand there shooting at the guy all day and missing until you finally connect--one of the bullets coming back your way will eventually cause you some problems. That and the fact that you don't have unlimited shots.

In reality, there needs to be a balance. Too few shots, and it's very hard to make the hits no matter how well you can shoot. Too poor a hit rate and it's very hard to make the hits even with a high-capacity firearm. You need to find a balance of a good hit rate and enough rounds on tap to get the job done. Balance.

In short, it is a pointless exercise in mathematical "what-if" that suggests that just sending more lead down-range, ala "spray&pray", is the answer to "the problem" of surviving a gunfight.

You're looking at it from exactly the wrong angle. What it really does is demonstrate how hard it is to get a certain number of hits with realistic hit rate probabilities if you only have a few rounds available to make those hits.

It's not telling you how to succeed, nearly as much as it's showing how HARD it is to succeed if you handicap yourself with too few shots or too low a hit rate probability.

I've made the point repeatedly that there needs to be a balance. If you read the second post I made on this thread, I think you'll find that addresses many of your concerns.

...no valid conclusions can be drawn from such a highly speculative exercise.

Sure they can. If you assume a given hit rate and a given number of rounds, you can draw a valid conclusion about the probability of making a certain number of hits (4 in the graphs) before running out of ammunition.

The real eye-opener is running the numbers with very high hit-rates and an available round count of only 5 or 6. If the probability of making the required number of hits is low with that round count, even with very high hit rates for each single shot assumed, one can draw the valid conclusion that it's hard to make the required number of hits with an available round count of 5 or 6.

It's a mistake to look at the calculations and assume that they're giving you a realistic calculation of your success rate. They're really sort of a best case scenario in one sense. There are many issues that might make things turn out much worse than the calculations suggest.

The real story the calculations tell is how hard it is to succeed even with very high hit rates if you don't have sufficient rounds on tap.

[OldMarksman]

Posted by 481: ....The effect upon one's ability to shoot accurately while under fire, after being hit, that bad guys move when being shot at, the ability to see and identify one's threat (lighting), etc, etc.

Every one of those issues (along with several other things) enters into the "hit rate", which is something that one assumes for the purpose of analysis.

The approach presented is far too simplistic and ignores the majority of factors that influence a gunfight.

It provides an estimate of how many shots one would have to fire to score a given number of hits on the attacker, based on an assumed hit rate. That assumed rate, which is a direct input to the calculation, must, of course, take into account all kinds of things.

In my view, the most significant error in the estimate is introduced by the assumption that the defender would stop shooing after scoring two hits. If under attack by a charging assailant starting from "Tueller distance", most of us would fire several rounds at the first attacker. That means that the estimate is probably low.

One could change that assumption and do the math oneself, but I don't need to. I'm already convinced. I have retired the J-frame from primary carry.

In short, it is a pointless exercise in mathematical "what-if" that suggests that just sending more lead down-range, ala "spray&pray", is the answer to "the problem" of surviving a gunfight.

Again, you are looking into the instrument from the wrong end. It "suggests", or rather it shows rather persuasively, that, given an assumed hit rate (you choose it), one's likelihood of scoring two, or four, hits when limited to five shots is quite a bit lower than one might have thought; that one's chances improve more than most people might have guessed with six shots; and it shows how much seven might help, if the defender is still in a position to keep shooting.

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

I will not try to assess the accuracy, but the calculations are highly illustrative. And the conclusion that five shots are likely to prove inadequate for scoring four hits, or even two, under adverse conditions, is quite valid.

[481]

Originally Posted by MLeake:

481, in what version of reality is having less ammunition an advantage?

So far, you are the only one calling for spray and pray. Nice straw man.

Calm down. There is no need for such rudeness.

I never said that having less ammo was an advantage. Those are your words, not mine.

[481]

Originally Posted by John KSa:

There are many factors left unaccounted for because the graphs are ONLY to tell you what the odds of making a certain number of hits with a certain number of shots given a fixed probability of connecting with each shot.

The graphs do tend to imply that if you can just send enough lead downrange you'll hit the bad guy because that's true (assuming a huge number of rounds available). However, if you read some of my posts you'll see that I make a point of saying that just having more shots won't help you because in the real world, you won't get a chance to stand there shooting at the guy all day and missing until you finally connect--one of the bullets coming back your way will eventually cause you some problems. That and the fact that you don't have unlimited shots.

In reality, there needs to be a balance. Too few shots, and it's very hard to make the hits no matter how well you can shoot. Too poor a hit rate and it's very hard to make the hits even with a high-capacity firearm. You need to find a balance of a good hit rate and enough rounds on tap to get the job done. Balance.

You're looking at it from exactly the wrong angle. What it really does is demonstrate how hard it is to get a certain number of hits with realistic hit rate probabilities if you only have a few rounds available to make those hits.

It's not telling you how to succeed, nearly as much as it's showing how HARD it is to succeed if you handicap yourself with too few shots or too low a hit rate probability.

I've made the point repeatedly that there needs to be a balance. If you read the second post I made on this thread, I think you'll find that addresses many of your concerns.

Sure they can. If you assume a given hit rate and a given number of rounds, you can draw a valid conclusion about the probability of making a certain number of hits (4 in the graphs) before running out of ammunition.

The real eye-opener is running the numbers with very high hit-rates and an available round count of only 5 or 6. If the probability of making the required number of hits is low with that round count, even with very high hit rates for each single shot assumed, one can draw the valid conclusion that it's hard to make the required number of hits with an available round count of 5 or 6.

It's a mistake to look at the calculations and assume that they're giving you a realistic calculation of your success rate. They're really sort of a best case scenario in one sense. There are many issues that might make things turn out much worse than the calculations suggest.

The real story the calculations tell is how hard it is to succeed even with very high hit rates if you don't have sufficient rounds on tap.

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. Working from assumptions and arbitrary numbers gets you nothing more than more assumptions and arbitrary numbers. You can play “what if” with numbers all day long, but in the end, all you get is more numbers that mean nothing more than the arbitrary numbers that they are based on.

Originally Posted by John KSa:

The real story the calculations tell is how hard it is to succeed even with very high hit rates if you don't have sufficient rounds on tap.

Sure, not having enough bullets can get you killed. Who needs lengthy calculations based on arbitrary numbers to tell them that?

[mayosligo]

Well done. Thanks for the sobering info.

[Bartholomew Roberts]

The number used happens to be square in the middle of the average hit rate NYPD (33%) and LAPD (28%) report for their officer involved shootings. So I would disagree with 481s supposition that the hit rate is arbitrary or not based in reality.

I'd say it also shows that if you do as well as a police officer in these shootings, and face a typical scenario (2 or more attackers) then you have a big challenge ahead.

[OldMarksman]

Posted by 481: Sure, not having enough bullets can get you killed. Who needs lengthy calculations based on arbitrary numbers to tell them that?

No one. That's not the point.

The point is, what are the differences? Vary your assumptions. Try different ones. Look at the calculations, which are based on very basic statistics. And which give best case results, as it happens.

Did you have any idea of how the answers would come out? Were you "comfortable" with five rounds? Are you still comfortable, or are you in denial? Or do you just not understand basic mathematics?

Or did you grasp it all without having had it demonstrated?

[Nanuk]

One other thing that has not come up, IF You are involved in a lethal encounter you are 3 times more likely to have that encounter within 6 feet of an adversary than 6 to 12 feet. How many chances do you want that close?

[481]

Originally Posted by Oldmarksman

No one. That's not the point.

The point is, what are the differences? Vary your assumptions. Try different ones. Look at the calculations, which are based on very basic statistics. And which give best case results, as it happens.

Did you have any idea of how the answers would come out? Were you "comfortable" with five rounds? Are you still comfortable, or are you in denial? Or do you just not understand basic mathematics?

Or did you grasp it all without having had it demonstrated?

Sure, I understand a good bit of math. There is no need to engage in insult. A childish display of such emotionality suggests a rather unhealthy investment in the topic. It also tells me that you feel as if you have nothing to offer in the way of valid debate.

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".

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


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)

[481]

Originally Posted by JohnKSa

The graphs do tend to imply that if you can just send enough lead downrange you'll hit the bad guy because that's true (assuming a huge number of rounds available). However, if you read some of my posts you'll see that I make a point of saying that just having more shots won't help you because in the real world, you won't get a chance to stand there shooting at the guy all day and missing until you finally connect--one of the bullets coming back your way will eventually cause you some problems. That and the fact that you don't have unlimited shots.

Ok, I can buy that. Thanks for being honest about the implications without resorting to insult, too.

Lots of folks react childishly when they are told something that they might not agree with (not just here) and your response is a good example of how a debate ought to be run. Thanks.

[MLeake]

481, you are the poster who has brought up, on multiple occasions, "spray and pray."

You are the one claiming that a straight statistical model has no basis in reality; you say you are "not silly enough" to pursue JohnKSA's wild goose chase.

So, basically, you spend a significant part of your time in this thread creating a straw man (as JohnKSA never advocated, nor have any of us advocated, "spray and pray"), using exaggerations and hyperbole...

... and then you accuse OldMarksman and me of being overly emotional, or of behaving childishly?

At this point, I think you are engaging in irony and parody, and waiting for everybody to catch on.

[wayneinFL]

I stopped obsessing over this stuff a long time ago. There are more important things to worry about. More people are killed with lack of a gun altogether or poor tactics than running out of ammunition.

I want a pistol with the capacity of an AR, stopping power of a 12 gauge, the recoil of 9mm, the reliability of a revolver, the sight radius of a rifle, and the size of a Kel-tec 32.

Until they make that, I have to make some kind of a compromise. Today, it's a 6 round 45 pocket pistol. If a mob of 7 people attack me tonight, I'll make all my shots count and get a couple of them to line up.

[OldMarksman]

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.

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.

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.

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?

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

No. That's a known fact.

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.

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?

[481]

Originally Posted by MLeake

481, you are the poster who has brought up, on multiple occasions, "spray and pray."

You are the one claiming that a straight statistical model has no basis in reality; you say you are "not silly enough" to pursue JohnKSA's wild goose chase.

So, basically, you spend a significant part of your time in this thread creating a straw man (as JohnKSA never advocated, nor have any of us advocated, "spray and pray"), using exaggerations and hyperbole...

... and then you accuse OldMarksman and me of being overly emotional, or of behaving childishly?

At this point, I think you are engaging in irony and parody, and waiting for everybody to catch on.

Your response was rude and accusatory and yes, childish. I'll not entertain your behavior further than this repsonse.

[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]

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.

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.

What is your point?

You just read it.

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.

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.

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]

Originally Posted by MLeake

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

Nope. Just with you.

[481]

Originally Posted by j3ffr0

-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.