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Old June 27, 2012, 11:48 PM   #1
Join Date: February 12, 2001
Location: DFW Area
Posts: 19,380
Capacity, Hit Rate, Multiple Assailants and some thoughts...

A thread on another forum got 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 succeed 3 times in 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. A 69% hit rate would give a person with a 5 shot handgun a 50.1% chance of succeeding against two opponents who each require 2 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 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 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.
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