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Old June 29, 2012, 09:31 PM   #26
jmortimer
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This article, one of the best ever, from the American Handgunner March-April 2002 by Massad Ayoob follows right along with this discussion and Lance Thomas is one of the United States' all-time heroes in my book.
http://findarticles.com/p/articles/m...6/ai_82533205/
Started with a J-Frame and "evolved" from there.
"It is not lost on him that he has expended 60 percent of his ammunition to neutralize 50 percent of his antagonists."I still like five shot 38's as a general matter. I lived in Los Angeles Conunty at the time Mr Thomas was doing his fine work, and could not believe the politically correct cry-babies at the Los Angeles Times.
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Old June 30, 2012, 02:52 AM   #27
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I think the math crystallizes something I have had notions about for a time.

When I carried a 1911, it was on the assumption that the most likely scenario for its use was against the lone mugger or other threat.

But as time progressed I began to see that the miscreants in my city not only travel together in bands of four or more in public, they often appear together in the crime section of the newspaper for committing robberies and assaults in such numbers too.

That, and a while back I started shooting my handgun at rolling clays and realized instant incapacitation through shot placement on a dynamic target was going to be difficult to rely upon achieving.

So, I "upgunned" to a Beretta PX4 constant that packs 18 147 grain 9mm JHPs. Individually, the rounds are less "potent" on paper by many measures. Collectively, they provide more margin for shooter error than the first 9 .45ACP rounds used to.
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Old June 30, 2012, 03:25 AM   #28
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It's a good mathematical exercise that backs up the old saying, "You can't miss fast enough to win a gunfight."
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Old June 30, 2012, 07:03 AM   #29
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The only time I would take 9 mil over 357 or 45 is if it was coming from a select fire sub machine gun. Its a great carbine round and a pretty mediocre handgun round. I would not say you upped your stopping power by going up in round count and down in effectiveness. Especially in cold weather where I switch to fully jacketed and hardcast rounds as 9 mil just does not cut the mustard. We would switch from MP5s to M4s during the winter months due to penetration issues. I always carried an AK47 some of the guys would carry them in the winter and M14 or AK74 in the summer. High cap does you no good if your shots are not penetrating.

Ps people of varying size and clothing are NOT the same as ballistic gel do not trust any study based on gel penetration. Go shoot a pig it will tell you 10x more.
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Old June 30, 2012, 07:44 AM   #30
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Two factors to consider:

1. What is the second BG doing while you are shooting the first BG? Running away? Attacking? Taking cover? Freezing in place? What do statistics show to be the most likely action taken?

2. How much time does it take to transition from BG to BG? As the number of BGs increases, the time b/t the first BG shot & the last BG shot increases. Will you have enough time to engage all the BGs, regardless of ammo available?

Fights are chaos systems. Predicting chaos systems is slightly less achievable than herding cats.
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Old June 30, 2012, 09:19 AM   #31
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Posted by seeker_two: What is the second BG doing while you are shooting the first BG? Running away? Attacking? Taking cover? Freezing in place?
That's the question, isn't it?

Quote:
What do statistics show to be the most likely action taken?
Stats don't tell us anything.

Quote:
How much time does it take to transition from BG to BG? As the number of BGs increases, the time b/t the first BG shot & the last BG shot increases. Will you have enough time to engage all the BGs, regardless of ammo available?
Some training will tell you that.
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Old June 30, 2012, 10:00 AM   #32
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If you are faced with multiple attackers, start with the highest threat based on, proximity, weapon, aggression, ect. A bandit at 10 feet with a shotgun is more of a threat than the one at 3 feet with a club. Put one into each bandit based on threat, return to those that need more.

Why do most criminals follow that path? Mostly because they lack the drive and motivation to pursue a career in anything else. Crimes are committed based on the motivation level of the criminal, the opportunity. Very few criminals are motivated or loyal enough to stick around when their cohorts start dropping. That being said, it is why they hunt in packs and descend on the victim in packs.

While not all inclusive by any means I think the NRA's Armed Citizen is the only data base at all that tracks civilian defensive use.
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Old June 30, 2012, 10:31 AM   #33
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The data doesn't take into consideration the fact that most people will hesitate to shoot another human being so if the BGs are sociopaths you are playing catch up already. With a little training you can put hits on multiple assailants in seconds. A good rule of thumb is to shoot them all high or in the head once, then go back and finish whatever is still a threat. If you start first there will be a 1.5 second lag before someone starts shooting back. If they start first you're in big trouble if they can shoot. If there is cover, run to it if it's close and you have a chance. It takes a high skill level to hit a moving target, you will be able to move 10 to 15 feet before they shoot and most gunshot wounds are not fatal. Better yet don't get into a gunfight.
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Old June 30, 2012, 10:43 AM   #34
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The only time I would take 9 mil over 357 or 45 is if it was coming from a select fire sub machine gun. Its a great carbine round and a pretty mediocre handgun round. I would not say you upped your stopping power by going up in round count and down in effectiveness. Especially in cold weather where I switch to fully jacketed and hardcast rounds as 9 mil just does not cut the mustard. We would switch from MP5s to M4s during the winter months due to penetration issues. I always carried an AK47 some of the guys would carry them in the winter and M14 or AK74 in the summer. High cap does you no good if your shots are not penetrating.

Ps people of varying size and clothing are NOT the same as ballistic gel do not trust any study based on gel penetration. Go shoot a pig it will tell you 10x more.
All handgun rounds are marginal stoppers. 9mm FMJ is more penetrative than is .45ACP FMJ. Each handgun round runs from potentially lethal to potentially ineffective. Given the true effectiveness of handgun rounds I'd rather have more at my disposal than less.
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Old June 30, 2012, 11:21 AM   #35
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Posted by rgrundy: The data doesn't take into consideration the fact that most people will hesitate to shoot another human being so if the BGs are sociopaths you are playing catch up already.
We are not discussing "data". John has presented some statistical calculations based on some assumptions

Quote:
With a little training you can put hits on multiple assailants in seconds.
Good defensive pistol training does address the skills necessary to put multiple hits on multiple targets in seconds--very few seconds. Whether one can do that on a moving target in a stessful situation is another question.

Quote:
A good rule of thumb is to shoot them all high or in the head once, then go back and finish whatever is still a threat.
I've never heard of any qualified instructor who recommends head shots.

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If you start first there will be a 1.5 second lag before someone starts shooting back.
What? How does one "start first" and justify it?

A more realistic scenario is someone running at you, giving you perhaps 1.5 seconds to draw and shoot. And of course, it would be foolish to count on that first shot to keep you from getting cut.

Quote:
If there is cover, run to it if it's close and you have a chance.
OK

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It takes a high skill level to hit a moving target, you will be able to move 10 to 15 feet before they shoot and most gunshot wounds are not fatal.
Let's turn that one around. Your target is moving, perhaps from 25 feet away. Can you run backward faster than he can run forward?

You have to draw, fire, hit several times, and get out of his way in maybe one or two seconds.
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Old June 30, 2012, 02:21 PM   #36
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The data doesn't take into consideration the fact that most people will hesitate to shoot another human being so if the BGs are sociopaths you are playing catch up already.
Correct. There are any number of reasons why the probabilities listed might actually turn out to make success (success=2 or more hits on each opponent) seem MORE likely than it really is.
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The only time I would take 9 mil over 357 or 45...
The calculations do not take caliber into account at all. They only assume the following:

1. Only a certain number of shots available.
2. A hit rate probability.
3. Success = 2 or more hits per opponent.
4. The defender uses his rounds to maximum effect (e.g. doesn't shoot all of his rounds at the first opponent if he hit him with the first two.)
5. The defender is able to shoot all his rounds in the encounter.
Quote:
If you are faced with multiple attackers, start with the highest threat based on, proximity, weapon, aggression, ect. A bandit at 10 feet with a shotgun is more of a threat than the one at 3 feet with a club. Put one into each bandit based on threat, return to those that need more.
That's good advice. The calculations don't take that into account. They assume that if you make 2 hits on an opponent that he's neutralized regardless of what order or strategy you use to distribute those hits. It is simplistic, but that's because the results are not intended to be a high-fidelity simulation of a gunfight--it would be impossible to provide that kind of information with a simple probability calculation.

The calculations results provide insight into how hard it is to make multiple hits on multiple opponents given a certain number of shots and a given hit rate probability. Period.
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That, and a while back I started shooting my handgun at rolling clays and realized instant incapacitation through shot placement on a dynamic target was going to be difficult to rely upon achieving.
Exactly. Introducing motion into the target is one of the reasons that people don't hit the target as often in a gunfight as they do standing in front of a stationary target at the range. Another is that during a gunfight there's someone shooting at them. Another is that during a gunfight they may be moving themselves to avoid being shot. Another is that they may have to adopt unorthodox shooting positions to take advantage of cover. I'm sure there are others.

It's important for people to understand that the fact that they can stand still in front of a stationary paper target and put 5 rounds into it with 100% consistency doesn't translate to being able to make the same hit rate during an event as dynamic and stressful as a gunfight.
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Old June 30, 2012, 03:04 PM   #37
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If I ever get into a shooting, I'll very quickly go over the charts, graphs, and numbers. Then remembering all the Massad Ayoob articals, and taking into consideration the Marshal-Sanow study I'll draw my firearm and deftly perform a mozambique drill....
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Old June 30, 2012, 03:25 PM   #38
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Sorry,I believe I was trained in the wrong venue. Head shots were okay if there was a possibilty of the attackers wearing vests. Moving targets are definitely hard to hit so I would suggest some Bianchi (48 shots at a mover that approximates how fast a man can run) practice at the very least.
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Old June 30, 2012, 04:22 PM   #39
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Rats can't remember the Tom Cruise movie where he is the hit man cruising around in a taxi in LA and gets into a confrontation in a subway at o-dark thirty with two muggers attempting to rob him? That scene in the movie about 3 seconds worth of gun fire is some of the most awesome visuals on handling a multi BG attack I have ever seen..... Yes I know its a movie but the gun handling against multi BG.s covers some of the debate here. Granted its a visual on a really CQB situation but I remember being trained to respond just that way...
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Old June 30, 2012, 06:42 PM   #40
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Basing this theory of effectiveness on a mathematical formula based on statistics and assumptions is all fantasy warrior-ship.
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The formula/calculations have no bearing on effectiveness in the sense of predicting a person's success in an actual gunfight.
No, it isn't a fantasy warrior-ship and such exercises do not readily relate to any sort of predictive realities for any one given situation. Simply put, it is unreasonable to assume that based on historic data of autonomous events (which is basically what is being assumed by the summary hit rate considerations) that whatever pattern they show in the past will necessarily predict the outcome of a given autonomous incident occurring now or in the future, but can be accurate in predicting a pattern for such events in the future. Looked at another way using medical information, if a given type of cancer has a 50% mortality rate, just because you get it doesn't mean you have a 50% chance of dying from it, though people may continue to die from it at a rate of 50%. It very well may be that when discovered quickly, historically folks recover 99% of the time and when discovered late that they die 99% of the time from it. So while the average death rate for the particular cancer may be 50% for the entire population, the entire population trend indicated isn't really even a reasonable predictor of the rate at which an individual may die from it. We actually went through something like this with my dad and his doctors. In his case, the cancer kills folks in the first year after discovery 90% of the time. As it turned out, about 85% of the time when discovered, the patients were already terminal. Pop's was discovered very early, within a 3 month window and he got the correct treatment. So while the 90% fatality rate in the first year and 98% fatality within 5 years sounded horrible, it is just the trend of the overall population and not indiviually specific.

Trend analyses provide you information about trends more so than about individual specific events. It may look like that for a given event there is X% likelihood of occurring and that would be correct for a trend perspective, but not necessarily correct from a specific event perspective.

Assuming the data are 100% accurate of real life, missing from the equation is also the speed of incapacitation. Over the years, we have discussed several events where mortally wounded people still managed to kill other people before dying. I will see if I can find it, but I seem to recall a midwest cop who was victorious, but killed in a gunfight with multiple bad guys (2, I think). One badguy was killed and the other seriously wounded and handcuffed by the cop. This was pre-ballistic vest and it was winter. He did not realize he had been shot, thought he was fine, had told people he was unharmed, and collapsed while talking with late arriving officers about the event. So he was incapacitated and incapacitated by 2 wounds which were inflicted early in the fight and after suffering the wounds, killed one guy, wounded and handcuffed the other, and then stood around talking about the event.

It is for reasons such as that that the Secret Service trains its protection detail to run their hands over the President after a shooting as the person shot (such as Reagan) doesn't always know it. Of course in Reagan's case, the hand inspection missed the wound the first time which delayed Reagan getting to the hospital. Reagan did feel pain, but thought was from being essentially dogpiled into the limo with him on bottom.

Anyway, so time to incapacitation is also significant and extremely difficult to model for things other than shots producing immediate and significant high CNS damage.
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Old June 30, 2012, 08:30 PM   #41
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If I ever get into a shooting, I'll very quickly go over the charts, graphs, and numbers.
I know you're being sarcastic, but I'll answer seriously anyway. The point isn't that you should think about these graphs during a deadly force encounter. The point is that you can think about them NOW and hopefully make some constructive decisions based on your assessment of your own performance/risk and other personal requirements.
Quote:
Rats can't remember the Tom Cruise movie where he is the hit man cruising around in a taxi in LA and gets into a confrontation in a subway at o-dark thirty with two muggers attempting to rob him?
The movie is Collateral. The scenario takes place in an alley where two men steal his briefcase out of the taxi where he left it. Watch the scene again in slow motion and focus on the second BG. You'll see that he has to bobble his draw in order to give Cruise's character time to get the job done.
Quote:
...missing from the equation is also the speed of incapacitation.
That is correct. If one really thinks hard about the assumptions and results, one can come up with a number of reasons why the calculated results actually paint a rosier picture than is likely in a real life encounter facing 2 determined attackers.

Realistically even if the defender has a 100% hit rate, it's absolutely possible that he might expend all the rounds from a high-capacity pistol and still fail to incapacitate just one attacker given the difficulty of using a tiny bit of lead at medium velocities to destroy a 180lb creature.

Basically what the calculations are going to provide is some basic insight into how hard it is to make multiple solid hits on multiple attackers before running out of ammunition.
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Old June 30, 2012, 08:30 PM   #42
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Flawed data?

Flawed data? No. Not in the least.

It is not data at all.

As stated in the OP, it was an exercise in theoretical statistics. Its applicability to real-world situations is limited to to the clearly stated goals of that exercise.

It is eye-opening and I thank JohnKSa for posting it. It has wide and valid applications to the planning of tactics and weapons choices if one stays aware of the limitations of simulations. Don't try to make it what it isn't. If you use it for what it is, it is VERY useful.

JohnKSa, I do think it would be useful as a sticky (with a warning that it is not intended to take into account the psychology of opponents). I would put it into the Tactics and Training forum, though.

Thanks for posting it. Would you be willing to share the formulas?

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Old June 30, 2012, 08:34 PM   #43
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Thanks for posting it. Would you be willing to share the formulas?
I would if I had one.

I didn't take the time to derive a closed form solution, I simply "brute-forced" it with an Excel spreadsheet. The solution is actually a collection of pages (15 tabs in a spreadsheet) some of them containing over 30,000 lines of data. Not that easy to share, unfortunately...

Basically the spreadsheet replicates every possible outcome for each scenario (5 shot, 6 shot, etc.), then calculates the probability of each outcome and sums the probabilities of each outcome that meets the success criterion.

Not pretty or elegant, but it works and provides some easy ways to double check to make sure the results make sense.
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Old June 30, 2012, 10:28 PM   #44
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It certainly was a lot of work. It is very valuable, in that, it may make some people think about carrying a reload or two.
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Old July 1, 2012, 03:17 AM   #45
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It took a little bit to get it all running right for the first tab, from there it was a matter of doing a lot of cutting & pasting & adjusting to set up the other capacities. The plots were a pain because each scenario had to be run manually for each hit probability and then the 63 results copied over to be used in the plots.
Quote:
...carrying a reload or two...
I think the key is balance.

You need a reasonable amount of capacity to have a chance of making enough hits before you run dry. But having lots of ammo/capacity is only worthwhile if you have the time to shoot it all. You also need a good hit rate probability. But, again, even a tremendous hit rate probability won't help if you don't have the rounds you need to make the all the hits.

It's all in finding a happy medium. We shouldn't rely exclusively on capacity--we may not have the time or the skill to make use of those extra rounds. We shouldn't rely exclusively on our belief that our hit rate probability will be high in a gunfight. For one thing, it might not be that high, and even if it is, we still need need enough rounds available in order to be effective.

Really, that's the story of self-defense and handguns in a nutshell. You need skill, and you need equipment and you need to find a balance between the emphasis you place on each. You can't substitute skill for equipment/capacity/caliber because if your equipment doesn't work/you don't have enough shots/you pick a caliber that can't do the job then skill can only take you so far. You can't substitute equipment/caliber/capacity for skill because the best equipment in the world won't carry you if you can't shoot well enough and run your equipment well enough to get the job done.

I did the calculations to satisfy my own curiosity. I didn't know how the results would turn out. When I saw how they turned out, I decided to share them so people could use the information to try to find their own balance of capacity and skill based on something a little more concrete than speculation.
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Old July 2, 2012, 11:37 AM   #46
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I like the scene in Collateral, but find at least one flaw in Cruise's character's techique: He moves between the two BG's.

Had Vincent performed the deflection on BG1 while moving to his left (BG1's right) - IE the outside of the pair - he'd have put BG1 between himself and BG2.

That might have made BG2's "bobble" unnecessary.

There are actually tactics one can learn for dealing with multiple adversaries. Will they always work? No. Will they often yield higher survival percentages than would going in full frontal? Most definitely.
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Old July 2, 2012, 01:01 PM   #47
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I'm a bit rusty on statistics, but I think I set this up correctly. Here's a spreadsheet where you can play with values yourself (rounds carried, hits required to stop, number of attackers) and see the graph update immediately:

https://dl.dropbox.com/u/24553495/Defense%20Chance.xlsx
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Old July 2, 2012, 04:02 PM   #48
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Realistically even if the defender has a 100% hit rate, it's absolutely possible that he might expend all the rounds from a high-capacity pistol and still fail to incapacitate just one attacker given the difficulty of using a tiny bit of lead at medium velocities to destroy a 180lb creature.
And there in lies the mystery of trying to figure out, even theoretically, what will happen in any handgun based defensive scenario!

Great thread, thanks for the work you put into it.
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Old July 2, 2012, 04:25 PM   #49
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JohnSKa

Yeah man I was being sarcastic. I meant no harm... GOD forbid any of us get into an actual armed confrontation I'd hope the mind would be on the task at hand and not on some statistics. The goal in a gunfight is not to consider statistics.. The goal in a gunfight is to not become one...

Accepting any thoughts of anything other than being victorious with what ever gun you have, shooting what ever ammo you have at what ever distances it takes place is seeding defeat. All these stats and opinions allow for failure. Failure in a gunfight is NOT an option.
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Old July 2, 2012, 05:04 PM   #50
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Great thread, and the findings are worthy of consideration.


One of the more sobering realizations I take away is that in the area in which I live - in which crime is often conducted by (at least) two umbrella gangs, Nortenos and Surenos, quite frequently when crimes are reported in the press there are more than 2 armed adversaries.

Often 3, occasionally 4, is more the norm. Very seldom (unless its a case of domestic violence) do you hear about only one armed adversary. They tend to run in groups of however many can fit into one car.


Its sort of grim to realize that your surviving an armed encounter depends, at least in part, on the probability that one or more of the group will run away when the shooting starts.....
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