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

[JohnKSa]

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.

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.

...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.

 

[Lost Sheep]

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?

Lost Sheep

 

[JohnKSa]

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.

 

[Nanuk]

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.

 

[JohnKSa]

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.

...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.

 

[MLeake]

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.

 

[Merad]

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 Chance.xlsx

 

[Neal_G.]

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.

 

[Glenn Dee]

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.

 

[Doc Intrepid]

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.....

 

[Nanuk]

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 really 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.

Very well put, I guess I misunderstood your process at first.

 

[44 AMP]

can't fault the data....

or the calculations as flawed. Given the stated assumptions, it looks pretty good to me.

However, what conclusions we draw from the data can be flawed. Or they can be accurate, and just not applicable to a specific situation we might find ourselves in.

Since a movie was mentioned, lets look at another one....
A "standoff" scene in (I believe) Delta Farce (yes, I know, a comedy but look at the point)

"You think you can shoot ALL of us?"
"No, but I can shoot YOU!"
"oh, I always forget that part....."

I think it is important to realize that the bad guys seldom expect effective armed resistance, and often the reactions of the ones not being shot are not instant attack.

And I don't see any way to figure that into any calculations. Even highly trained soldiers (about as professional as you can get) have differing reactions when the lead flies, especially for the first time. Some follow their training instantly, some don't. And few criminals are as well trained as soldiers.

The data is interesting, and worthy of thought, but any confrontation we will be in is an individual thing, as likely to fall outside the averages as within.

The Armed Citizen column in the American Rifleman (and other NRA publications) is full of situations where, when confronted, many of the bad guys flee. You can't count on it, but you shouldn't discount it, either, IMHO.

 

[JohnKSa]

I think it is important to realize that the bad guys seldom expect effective armed resistance, and often the reactions of the ones not being shot are not instant attack.

And I don't see any way to figure that into any calculations.

Actually, the calculations sort of highlight the point that it's rarely necessary to physically disable attackers--that they tend to run. The probabilities show that if it were actually necessary to shoot all attackers to the ground, the chances of success with a typical carry pistol are miserable. Given that we know that defenders succeed in multiple-attacker scenarios on a fairly regular basis, we can see that something else is happening a lot of the time and that something is attackers often choosing to stop attacking when the shooting starts. That happens a good percentage of the time.

It's not really possible to tailor the calculations for every alternative, the point was not to produce a high-fidelity gunfight simulator, the idea was to provide insight into one particular aspect of a gunfight, namely how hard it is to put multiple hits on multiple opponents with a realistic hit-rate probability and a limited number of shots. Turns out it's a lot harder than I think most people assumed it is--it's harder than I expected it to be.

Does that mean that every gunfight will require putting multiple hits on multiple attackers? No, it doesn't. Clearly some gunfights, even ones with multiple attackers are resolved in favor of the defender without anyone being hit at all, some with one attacker being hit multiple times but the other being hit only once, some with only one attacker being hit multiple times, some with only one attacker being hit once. It can play out many different ways, and the calculation only looks at one type of scenario.

Of course, while it's not uncommon for attackers to give up when the shooting starts, it's not a given that it will happen in any gunfight. It's important to understand that while they're not the norm, there are determined attackers out there who won't automatically turn and run.

 

[Glenn Dee]

Missing an assailent isnt always a total fail. I'd bet that more often even a miss will cause the desired effect from the assailent. I doubt if there is much information regarding the actions of a person once they have been shot at.

 

[OldMarksman]

It's important to understand that while they're not the norm, there are determined attackers out there who won't automatically turn and run.

Are not the following likely to fall into that category?

• The attacker who is already very close to you, who may conclude in the heat of the moment that you will shoot him if he does not stop you first
• The desperate fugitive who has attacked you to get your car because his is known to the authorities, running poorly, or out of fuel, and he cannot escape without it
• Users of methamphetamine or bath salts who do not act like rational persons

 

[btmj]

I wish I could have participated in this thread earlier... I was on vacation for the last week...not a lot of computer time...

I have had a similar thought process as JohnKSa, and I made a similar point about a month ago regarding bear defense rifles. Given some probability of hitting a vital spot, it is always better to put more bullets on target than less.

It is analogous to an aircraft mounted gun. They don't use sniper rifles on aircraft. They use machine guns with a extremely high rate of fire. It does not take hundreds of hits with a 20mm cannon to bring down a fighter or a helo... it only takes one. But the probability of making that one hit goes way up if you can fire a burst of 100 rounds per second.

 

[btmj]

Missing an assailent isnt always a total fail. I'd bet that more often even a miss will cause the desired effect from the assailent. I doubt if there is much information regarding the actions of a person once they have been shot at.

Probably very true. I heard someone say once (Massad Ayoob perhaps?) that a person could get 90% of the benefit of a concealed carry handgun by just carrying a pistol loaded with blanks. The majority of the time, just displaying the weapon ends the situation. If you do need to fire, they won't know you are shooting blanks, all they know is that they are getting shot at, and most of the time they will run. The guy who said it was not advocating carrying blanks, but his point was that the vast majority of successful armed self defense situation end without any blood being spilled.

 

[mes228]

Ferfal

Along the line of this thread on capacity. I suggest that people read Ferfal's blog "Surviving in Argentina". Go back through his posting and search for the shoot out in the Radio Celebrity bedroom. Three bad guys already given all the hostages had ie cash, watches, flat screen televisions etc.etc. Still not enough as the bad guys were going to rape the women. Thinking their all dead the Radio guy feigns a heart attack and falls down. Retrieves a hidden Glock .40 and comes up shooting. The hostage son also gets a hidden a .357 and enters the fight. The end result is one bad guy shot 8 times in the chest and is dead right there. BUT IT TOOK EIGHT ROUNDS (.40 cal.), another BG wounded and flees to hospital for wounds, one runs away un-harmed.

However, the Radio guy shot is up severely, hit 4 times, leg bones protruding from wounds etc. But keeps fighting. Son shot 2-3 in the buttocks/stomach and is critical. The good guys won but both wounded, all the women unharmed. The point of my retelling this is that the good guy's fired well over 20 rounds in that bed room. They had no place to run, no cover apparently. Just "toe to toe" and shoot till you --- or them, are dead.
Capacity may not be everything in a confrontation, but it would seem to be GOOD thing to have in a lot of situations. All this is written from memory so read it for your self on Ferfal's blog. Your mileage may vary.

 

[output]

I have read somewhere that our chances of encountering multiple attackers/assailants are about 50/50. Does anyone know how accurate that number is? I can’t remember where I read it or what it was related to i.e., robberies etc.

I find these calculations fascinating, and it leaves me curious as to what the probability is that a person will encounter multiple attackers (especially in urban environments.)

 

[buckhorn_cortez]

The assumption of 30% seems valid in light of police statistics showing that around 30% is the "average hit rate" - which includes: people, dogs, cats, and automobiles.

What seems skewed in the analysis is that the avererage number of shots fired. I have seen a statistic giving 8 shots as the average amount fired during a shootout for the initial exchange. Shots fire after that seem to end at 13 - 15.

So, given lies, damned lies, and statistics - apparently, if you can survive the first exchange of 8 shots, you may need 5-7 additional shots. What that means is that unless you're carrying a gun with at least a 16 round capacity magazine, you're going to be reloading regardless of whether you are carrying a gun with an 8, 10, 12, or 13 round magazine.