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Thoughts on Multiple Assailants, Hit Rate & Capacity

Discussion in 'Handguns: General Discussion' started by JohnKSa, Jun 29, 2012.

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  1. JohnKSa

    JohnKSa Member

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    This is a compilation of a couple of posts made on another forum. The content may be thought-provoking to some.

    Something I read recently started me thinking about the probability of making a certain number of hits within a certain number of shots given a fixed probability of hitting the target with any given shot. I set up a spreadsheet to do the calculations and thought some of the results might be interesting to other shooters.

    To present the data in some sort of reasonable fashion, I've assumed that an assailant will require 2 or more HITS from a handgun to be neutralized/incapacitated. It's fairly common to assume that it will take more than one hit to neutralize an assailant and since double-tapping is ubiquitous, I figured 2 was a reasonable starting assumption.

    I've assumed a hit rate probability of 30% for the listings below since that is an often quoted figure for the hit rate probability of law enforcement officers involved in gunfights.

    For a single assailant and a 30% hit rate probability.
    # of Shots : Probability of achieving 2 or more hits.
    5 : 47.2%
    6 : 58%
    7 : 67.1%
    8 : 74.5%
    9 : 80.4%
    10: 85.1%
    11: 88.7%
    12: 91.5%

    For two assailants and a 30% hit rate probability.
    # of Shots : Probability of 4 or more hits (i.e. 2 on each assailant).
    5 : 3.1%
    6 : 7.1%
    7 : 12.6%
    8 : 19.4%
    9 : 27%
    10: 35%
    11: 43%
    12: 50.8%

    There are some other assumptions inherent in trying to apply these probabilities practically. For one thing, the two assailant case assumes that the defender is able to tell how many hits have been made on the first assailant and then immediately switch to shooting at the second assailant after making 2 hits on the first--wasting no additional shots on an already neutralized opponent.

    Both cases assume that the defender is able to empty his/her weapon in the course of the gunfight--he/she is not incapacitated before that can take place. Basically, these are sort of "best case" scenarios. The point is to get a rough idea of the best that a gunfight could turn out if you need 2 hits per assailant and you have a given number of shots to pull it off.

    I was surprised at how tough it was to neutralize 2 assailants given a 30% hit rate and 5 shots. Basically one can expect to fail 97 times out of 100 attempts.

    To improve those odds to EVEN odds (roughly a 50/50 chance of success) when using a 5 shot handgun, one would need to shoot well enough to achieve a 69% hit rate during a gunfight. That would give a person with a 5 shot handgun a 50.1% chance of succeeding against two opponents who each require 2 or more hits to be neutralized.

    From a practical standpoint, the probabilities involved suggest that someone armed with a typical small carry pistol (11 rounds or less) and achieving a hit rate of about 30% per shot has better than even odds of failing to neutralize 2 determined opponents before their gun is emptied. Under the same conditions, someone armed with a true pocket pistol (7 rounds or less) is likely to fail to neutralize 2 determined assailants about 90% of the time or more.

    Even with only a single assailant, a pocket pistol will run dry somewhere between 1/3 and 1/2 of the time before a 30% hit rate achieves 2 hits.

    Lance Thomas realized after winning his first gunfight with a 5 shot pistol that he had expended 3 of his 5 rounds neutralizing one opponent--fortunately the other one ran. The realization caused him to change his tactics to include multiple guns in his defense plan, hidden behind the counter in various locations around his gun shop. That's one fairly practical response.

    However, I'm not really suggesting we all need to carry multiple guns or upgrade to high-capacity carry guns. The major "takeaway" from the calculations is to understand the limitations of the weapon system that is the combination of you and your carry gun.

    Taking on 2 determined attackers with a typical compact pistol is a pretty grim mission, if you look at the numbers. If one or both assailants don't cut and run when the lead starts flying, the odds are slim to none of success. If success (survival) is the goal, it might be wise to consider other options. Drawing and shooting it out isn't going to be a wise course of action unless you're sure they'll give up easily or unless there is no other reasonable course of action available.

    Someone will probably point out that real-world results seem to contradict the calculated probabilities. The reason for that is that defenders with low-capacity handguns who prevail against multiple attackers are NOT doing so by shooting all their attackers to the ground by making multiple solid hits on each one.

    Clearly, what's happening is that one or more of the attackers is chosing to run rather than stand and fight. The Lance Thomas incident is a perfect example. Mr. Thomas, armed with a 5 shot handgun, prevailed against two attackers--but not because he skillfully applied 2 solid hits each before running out of ammunition. He won because the second attacker ran when the shooting started.

    So, does that mean that capacity is meaningless? Not at all. It was simply the luck of the draw that the second man ran. Had he stood and fought like his accomplice, Mr. Thomas would likely have not prevailed given that it took him 3 shots to neutralize his first opponent, leaving him only 2 to deal with the second.

    Clearly there needs to be a balance. Moving up in capacity obviously improves your odds, but you can't get carried away in that direction because it's not terribly likely that you'll be able to take advantage of a huge round count in the few seconds a gunfight typically lasts.

    Improving the hit rate probability (sharpening shooting skills) clearly helps, but only if you have the capacity available to take advantage of it. For example, even a very impressive 70% hit rate only gives you a 53% chance of scoring 2 or more hits on each of 2 opponents if you're armed with a 5 shot handgun. On the other hand, if you can achieve just a 50% hit rate with a 9 shot handgun, your odds of succeeding in making the 4 hits are 75%.

    As with many things, it's a tradeoff--a balance needs to be found.

    These calculations don't tell the whole story. They only provide limited insight into certain aspects of a gunfight. That insight needs to be combined with other information before the big picture can start to take shape. But without this insight, a person can have a very mistaken impression about their chances against more than one determined attacker.

    Here are some plots that lay things out in a reasonably easy format.

    In this plot, each line traces out the probability of success with a given hit rate. So if you take the bottom line (10% hit rate) and trace across to where the bottom axis label reads 9 (# of shots), the height of the line will give you the probability of making 4 hits with 9 shots if your hit rate is 10%. It's a very small number...
    attachment.jpg
    In the plot below, each line traces out the probability of success with a given number of shots. So, if you take the bottom line (5 shot line) and trace across to where the bottom axis label (hit rate) reads 50%, the height of the line (about 20%) tells the probability of making 4 hits with 5 shots and a hit rate of 50%.
    attachment.jpg
     
  2. Kleanbore

    Kleanbore Moderator

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    That's a real eye opener. One can vary the assumptions however one pleases, but the probability of success is undoubtedly a lot lower than many people may have assumed. Excellent contribution.
     
  3. trickyasafox

    trickyasafox Member

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    interesting post- wish I could have seen the graphs, but they didn't load for me in any of my browsers.
     
  4. coalman

    coalman Member

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    The natural tendency is to focus on the most immediate threat. That will/may change with circumstances and the actions of all parties. Basically, all unknowns. Much action will be reactive for most. Point shooting likely at best. It will be a general melee. Taking on 3+ active, armed, advancing aggressors in CQB will very likely be a losing battle. Two on target would be great. One can do the job. The idea it will be a cool, controlled Tom Cruise Collateral moment is a pipe dream IMO. Regardless, the belief that 500 rounds a year on paper will get you there is part of the same dream. But, we all like to dream and the smaller caliber, higher capacity camp loves this type of data/stuff. Practice helps us all. Few in either camp put as much thought into all this. Thanks for sharing.
     
  5. Lawdawg45

    Lawdawg45 Member

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    "You can't get us all.......That's a fact, but you're first and he's second, do you care what happens after that?" Tom Selleck.....Last stand at Saber River:D

    LD
     
  6. JohnKSa

    JohnKSa Member

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    If you watch the scene in slow motion, it's clear that the second gunman has to bobble his draw to give Cruise's character time enough to make the scene work.
    Right, I guess I had assumed all along that going up against 3 or 4 determined opponents was essentially suicide. I will admit I was pretty surprised to see how bad the odds were against just 2 determined opponents with a typical concealed carry gun and a typical LE gunfight hit rate.

    If you'd told me a month ago that a person who was capable of a 30% hit rate in a gunfight and was armed with a 5 shot handgun would only be able to score 2 hits on each of 2 opponents 3% of the time before the handgun ran dry, I'd have been very skeptical.

    Basically the probabilities show that if one or both of the attackers don't cut and run when the gun makes its appearance, the defender with a 5-6 shot handgun is in serious trouble unless he's able to achieve a gunfight hit rate probability that borders on superhuman. To have a one in 10 chance of success (success = making 2 hits on each of 2 attackers) with a 5 shot handgun, one would need to have a hit rate of almost 90% for each shot and for a 6 shot handgun, a hit probability of 80% would be required.
     
  7. Kleanbore

    Kleanbore Moderator

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    One might do the job--if it just happens to hit something vital.

    Consider this: if someone with an edged weapon is charging at close range at something like three yards per second, one has to ask who in his right mind would fire one shot--or two--and wait to assess the impact. I would be more inclined to fire three or four as rapidly as possible.

    Yes, that of the assumptions is to stop firing after a second hit--but if it doesn't work out that way, more rounds will be needed.

    The number of hits necessary to effectively stop an attacker quickly enough to save the day is an unknown; two were selected here for purposes of illustration. There is absolutely no guarantee that two will suffice.

    I, for one, do not like to dream about this kind of thing.

    I should think that these calculations--which do not constitute data at all, but which show something about probabilities given several quite plausible assumptions--would cause some among those who are not in "the maller caliber, higher capacity camp" to question their preconceived notions.

    They sure cause me to better realize the limitations of the J-Frame that I often carry.
     
  8. Lawdawg45

    Lawdawg45 Member

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    Half of my career was in the wheel gun era, and the other in Glockamerica, and I can honestly say that our wheel gun training also stressed the importance of cover and speed reloads. Statistically, after the first shot or two multiple aggressors will scatter and usually run, but in the event they don't, finding immediate cover is the key to survival.
     
  9. buck460XVR

    buck460XVR Member

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    Anyone with even a slight grasp on reality and any knowledge at all of their own skills and limitations should already know this. Those that don't, probably won't believe it anyway. One must realize tho, for a civilian, that the odds of ever using your gun for SD is miniscule. The odds of ever facing "2 determined attackers" with the intent to either kill you or die is even less. Folks that continuously hang out in areas with high crime, put themselves at risk by hangin' with the wrong folks or allow themselves to be sucked into compromising situations are the exception.

    While it's cool to sit and dream about theoretical scenarios where we pop multiple assailants in the head while saving the damsel in distress, it's just that.....a dream. Truth is the majority of us, regardless of weapon would have the same chance of a snowball in damnation against well armed determined multiple assailants. All we can hope for is to take one or two with us and give our loved ones a chance to escape.
     
  10. SaxonPig

    SaxonPig Member

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    I'm sorry, but I didn't read the entire original post because it was way too long and complicated. Let me make a couple of observations.

    1. There is absolutely no way to accurately predict what the reaction of any particular individual will be to a gunshot wound. If you research gunfights this is something that jumps out at you. Big, strong men have been felled and incapacitated by a minor wound to the arm while slightly build individuals have absorbed numerous hits from large caliber weapons with no apparent immediate effect. Trying to speculate how many rounds will be needed to "stop" an attacker is a useless exercise. Too many variable including drug use which skews any attempt at scientific predictions.

    2. Civilians coming under gang attack are very rare. Average citizens very rarely need to worry about engaging multiple opponents. The typical criminal attack will involve a single perpetrator, maybe two. Not that multiple person attacks never happen, but they are few and far between.

    When a gang does attack, they are cowards. If they were courageous they wouldn't feel the need to operate as a group. I suspect that in 99.9% of such cases a single gunshot, Hell, simply displaying a weapon will scatter the attackers. The only way you will shoot more than one or two gang members is if you can hit them in the back as they run (which is a bad idea from a legal standpoint).
     
    Last edited: Jun 30, 2012
  11. Lawdawg45

    Lawdawg45 Member

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    My professional observation here locally differs a bit. Indianapolis has seen a huge increase in home invasions involving multiple armed suspects, and the theory of "not hanging around bad parts of town" doesn't float since criminals would rather invade a $500,000 house than a run down ghetto shack.;)

    LD
     
  12. CDW4ME

    CDW4ME Member

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    I've always felt more comfortable with the 9 or 10 + 1 round capacity of a subcompact Glock (versus anything with less) and this speculative data supports my preference.
     
  13. Kleanbore

    Kleanbore Moderator

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    Since attacks involving multiple assailants are probably as common as those involving only one, I am not willing to resign myself to defeat before trying.

    Absolutely true.

    Of the sixty three actual incidents summarized here, forty seven--75%--involved two or more "bad guys".

    That's a small data sample, to be sure, but it should lead one to consider preparing for more than one possible attacker.

    That's another thing that cannot be predicted.

    In an incident in which a couple of robbers try to take something for the sake of its monetary value, a second perp will likely run after the shooting starts, if he can safely do so, to rob again some other day.

    If he cannot, all bets are off.

    If quickly obtaining a car different from the one they have been driving, or a car with a higher supply of gasoline, or a car that is still able to be driven, is essential to the continued travel and to the escape of the perps(perps of that kind are very common along the highways that go through our area), it would seem very imprudent to count on anyone taking off after the shooting starts.
     
  14. Billy Shears

    Billy Shears Member

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    I'm a cop as well, and mob assaults are pretty rare, at least where I work. (Though there is a recent example, wherein two Virginian Pilot reporters were assaulted by a juvenile gang -- Bill O'Reilly even covered it, since the regular news media, even the reporters' own paper neglected to do so).

    From my own experience, I am convinced that the vast majority of these mobs will scatter like cockroaches when the lights are turned on once their members start taking gunfire. They behave just like every other set of predators in nature: they look for easy prey, and avoid situations where they could get hurt. When they attack in numbers, they are emboldened by the expectation that their victim couldn't effectively fight back against so many, and none of them will be seriously hurt. Let the victim have a gun, and start shooting back, however, and suddenly the instinct for self-preservation will take absolute precedence. A mob would have to be extremely determined to keep pressing an attack on a victim who has just shot one or more of its members, and appears willing and able to keep shooting. No one in that mob would be making the rational calculation "he can't get us all;" the fear of being one of the ones he does get, and the unwillingness to be one of those, would prevent this.

    I'm not saying it couldn't happen that a mob would keep on attacking. I suppose under the right set of circumstances anything is possible. But it would really be an outlier. Most mobs just don't display that kind of determination, cohesion, and discipline.
     
  15. Kleanbore

    Kleanbore Moderator

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    Mob attacks are beyond the range of John's illustrative calculations, and it doesn't take a statistician to conclude that handgun defense would be futile unless all but a couple of them were to run off.

    Possible attacks by one or two assailants are much more relevant to most of us.
     
  16. buck460XVR

    buck460XVR Member

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    Didn't mean to sound like I was tellin' folks to resign to defeat before trying. I certainly am not gonna give up without a fight either. But one must be realistic. If two armed assailants have their guns pointed at you or your loved ones, you will be lucky to get one shot off, much less pull your weapon. Rambo lives only in the movies. Is one better prepared for a attack by multiple assailants if they carry 2 high capacity guns and two mags for each? Sure. But one would also be better prepared against getting struck by lightning by never going outside. Which one do you think affects more average citizens? I always tell folks when it comes to SD, don't do what I do, do what makes you comfortable and what you have the most confidence in. But I myself don't need scientific studies with graphs and charts to tell me I'm in a crapload of trouble if attacked by a squadron of well armed ninjas.:rolleyes:

    As far as the rise of multiple attackers in home invasions, I assume the majority of them are not professional hitmen, coming to do in the owner and his wife. They are there to rob and will avoid a confrontation. Yes, some are there to rape and torture, but even then, they are looking for easy prey. In most cases the availability to hide, along with the owners access to multiple guns and larger quantities of ammo if prepared, makes this a totally different scenario. Add a dog and an alarm system(most $500,000 homes have both) and the playing field is evened out.
     
  17. Kleanbore

    Kleanbore Moderator

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    Yes, that is a little late to start reacting.

    As a matter of fact, one assailant with an edged weapon (and he will not wave around in advance or sound a buzzer for you to draw) would pose a really serious threat.

    I'm not sure what it has to do with the number of rounds one should carry, but the lifetime risk of being victimized by violent crime is more than one thousand times that of the lifetime risk of being struck by lightning.

    Of course not. But John did not provides us with charts of that kind.

    He made up some charts involving one or two attackers. I suggest that a number of people who have been saying that they could handle any contingency with their five shot revolvers might benefit from pondering those charts.

    I agree.

    The greater danger lies in the risk of attacks out of doors. The attackers are most likely not professional hitmen either, but they do not avoid confrontations.
     
  18. Billy Shears

    Billy Shears Member

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    Well, to play devil's advocate... That may not be so unrealistic in the context of the scene. What you have is a couple of lowlifes with piss poor gun handling (longhaired thug holds his weapon sideways, gangsta style, because he thinks it makes him look more badass and intimidating), who are used to dealing with cowed, unarmed subjects. Then, in an eyeblink, the dude they thought was harmless draws quickly and pumps a rounds into the one holding the gun. If that's not a "HOLY S#&%" moment, I don't know what would be. It would be very natural and understandable, in that circumstance, for the second thug to be caught by surprise, and a little slow on the draw, or to fumble his draw because he's hurrying too much.

    Now whether the average joe who carries could do this is still doubtful. The ability to take down two bad guys like we see in that seen presupposes a level of skill and of coolness in a crisis that Cruise's character -- a cold-blooded, professional killer -- was supposed to have, and that some real life gunfighters like Wild Bill Hickok, Wes Hardin, Jelly Bryce, et. al, really did have. But I do think the average civilian with a concealed weapon permit would most likely not be capable of doing what we see in that scene.
     
  19. barnbwt

    barnbwt Member

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    The only way I can see someone (singular) prevailing against multiple gunmen would be if he suprised them (i.e. home invasion defense). In such a scenario, panic among the attackers would be nearly guaranteed, and at least one of them would be down before they could return fire. Otherwise, the defender would be mobbed by bullets or bodies before he can accomplish much to remedy the situation (unless you're Sam Fisher, of course ;))

    But for the shootout postulated, If 12 shots are required for two guys, how long does it take you to fire 12 semi-aimed shots? How many shots could they throw back in that time, at the same "30% hit-rate" as yourself? Can you then get 12 shots out in the first place? Odds (at any point) of the attacker(s) or yourself panicking, being injured, or running away? It's more a "Game Theory" question than a Statistics question because of all the human factors involved, and tiny dataset. I'd be willing to bet though, that it basically hashes out as "the side that gets shot first, loses" nearly every time. (Although, there are shootings where both sides empty their (sideways) pistols without harming anyone :p...)

    The shopkeeper mentioned earlier "won", I believe, because he was well trained, and consistently underestimated by his attackers. He also had a plan (any plan) for what to do when a goon came knocking. The first time, they probably assumed he was unarmed, and the subsequent times (that guy must've loved gunfights to stick around as long as he did :rolleyes:) ill-trained goons botched the operations and weren't prepared for rapid, mulitple "New York Reloads" (I think I read the play-by-play on Ayoob's site, or something). Survival was attributable to luck, a plan (any plan), practice, and the ability to keep fighting after being shot (also luck, IMO). But that was such a ridiculously over-the-top scenario that guy was in, that I don't try to apply it to my situation. Now if you're planning on man-to-man siege-warfare, by all means. But plan for Molotov Cocktails and machine guns, too. That guy eventually wised up and got the hell outta there, but not after being shot (5 times?!).

    TCB

    *geek voice* Dude, that was just a movie... :D
     
  20. coalman

    coalman Member

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    Agreed. I explained myself poorly I guess. In contect of my whole post, my point was that a predictable, consistent double tap is not likely. Nor, IMO, controlled fire of any kind for that matter for almost all shooters. What's more likely is to point fire upon the first threat then move to the second once you feel/think it more a threat, then the third and so on. That could be 1 round, 2, 3 or whatever. This was the context of my "one may be enough" comment because that might be all you get.

    More "training" (i.e. practice) helps, but few will achieve the needed round count annually, or get proper "training", to develope or maintain those Tom Cruise Collateral "skills". I'm a realist, and I've never been a lower capacity (e.g. 5 shot snubby) disciple to begin with.

    The "what ifs" and "yeah, buts" go on forever because it's all imagination until it's not. And, when it not, you do the best with whatcha got.
     
    Last edited: Jun 30, 2012
  21. Kleanbore

    Kleanbore Moderator

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    By far the best way to handle home invaders is to shoot from a defensive position as they step into your field of fire--if they are so unfortunate as to have failed to heed your warnings.

    As discussed here, multiple assailants are not uncommon; thus, the defender really owes it to himself or herself to develop the skills necessary to prevail against them, starting with avoidance and fast threat identification and including successful tactics and effective shooting.

    Not long at all.

    Watching this part of the same recent episode of The Best Defense should prove to be a very worthwhile way to invest a little less than nine minutes of your time.

    You will note that the host, Mike Seeklander, fires four shots at the first target and four at the second, each engagement occurring in about a second. In the second demonstration, he fires three at the first and five at the second, again taking about a second for each target.

    I would pay less attention to that than to the tactical discussion.

    I agree--that is the right way to do it if possible; however, if someone is rushing with an edged weapon at close range, it may be more prudent to fire several shots very quickly while trying to get out of the way..

    John had to select a simple set of assumptions in order to come up with a set of charts that can be readily understood.
     
  22. NG VI

    NG VI Member

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    He did a great job.

    I would assume that at any reasonably close distance, once you start making hits on a person your chance to hit again would go up quite substantially. That assumes that you are even moderately proficient, a box or two a year shooter may not have the same ingrained skills as far as landing shots repeatably.

    I think that for a combination of reasons, not least that the hardest shot to get off accurately is likely going to be the first one, and that the attacker will hopefully show at least some reaction to being hit, even if it's a very slight reduction in speed of movement and violence of action.

    Sorry I didn't complete that sentence before I posted earlier.
     
    Last edited: Jun 30, 2012
  23. JohnKSa

    JohnKSa Member

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    That is absolutely correct, and explaining that these calculations make no attempt to do any such thing is a part of why the initial post is "long and complicated". ;)
    There is no speculation as to what is required to stop an attacker. For the purposes of the calculations an assumption is made. However, the assumption can be modified and the calculations rerun with different assumptions. In order to get a data set that allowed a reasonable comparison between different hit rates and capacities, there must be some assumption, so I made one.

    There is absolutely no attempt on my part to imply that 2 hits on an attacker will always be required to, or will always suffice to neutralize an attacker, it's just a number used to allow the calculations and comparisons.
    I tend to agree. That's why I ran the numbers first for a single perpetrator, and then again for two. The plots show data for two perpetrator scenarios.
    I think that given your obvious interest in the topic, you might find the OP a worthwhile read. At the least, it would certainly allow you to craft responses that are more applicable to the data presented in the OP.
     
  24. bds
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    bds Member

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    Oops, duplicate post.
     
    Last edited: Jul 1, 2012
  25. bds
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    bds Member

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    Depends on where you live. Home invasion robberies do occur more frequently in metropolitan cities. Appreciate the OP/thread for the "reality" of possibly engaging multiple attackers for a given HD shooting. When your targets move fast and shoot back, it is a very different situation than shooting stationary paper/cardboard targets at the range.

    Review of home invasion robberies in my city/county revealed that increasing number of invasions occur with organized gang "teams" comprised of spotters and well armed intruders who follow a scripted routine (monitor a house/neighborhood for several days/weeks, enter through back patio/kitchen door, tie up the family members, systematically search the house for valuables, rape/execute family members despite being cooperative, etc.). It is the armed gang members who are determined, cocky and confident instead of the home owners. PD/SD officers I shoot with on occasion caution that these gang members are likely to engage in a gun fight rather than to run/scatter with a single gunshot.

    Read this excerpt from 2011 FBI report on gangs on changing trends - http://www.fbi.gov/stats-services/publications/2011-national-gang-threat-assessment/
    As OP posted, I rather factor in "worst case scenario" and be better prepared/armed/practiced than be saying, "Oh crap." Are you prepared to defend against several attackers who rush in through the back door with AK47s? Yup, your prized safe queens and range toys in the gun safe won't help you when that happens. Yes, we do carry INSIDE the house. ;)

    If you live in a city/state where home invasion robberies don't occur, good for you but have sympathy for the rest of us and help us with more realistic/practical discussion on engaging multiple attackers because that's our sad reality.
    2010 DOJ report on California gangs - http://www.google.com/url?sa=t&rct=...sg=AFQjCNHOPdqilnWwq4uGgSjkTBZzk0v-Qw&cad=rja
     
    Last edited: Jul 1, 2012
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