The most important factors in defensive gun use (DGU) – A mathematical model

The most important factors in defensive gun use (DGU) – A mathematical model

Goal:  Learn what gun owners should focus on to be best prepared for a gunfight using Probabilistic risk assessment including event trees and sensitivity studies.

To read the event tree, you start on the left assuming that an encounter where you need to use your gun is occurring.  The factors analyzed include a timely draw, the chance of a misfire, a level of training variable, and the chance of accurate shot placement (given your training). All of the positive outcomes are branches that are highlighted green (where you stop the threat).  The negative outcomes are red (where you are injured or worse).

Probabilities for each of these factors are then multiplied to get the likely outcomes.  Data was gathered from diverse sources and the range of values for each factor were tested in the model for sensitivity. Putting it all together then, as an example, the probability of neutralizing the threat would be:

P(Neutralizing Threat) = 1 * P(timely draw) * P(reliable weapon and ammo) * P(accurate shots given your level of training)

For example, P(accurate shots given your level of training) was varied from 54% to 99% as other variables were held constant.  Testing different ranges of values for factors in the model, iteratively, and then comparing the magnitude of the adverse outcomes, to each other, gives you a sense of what factors are most significant/sensitive in the universe of possible conclusions.  


The number one thing you can control to ensure you survive a defensive gunfight is having a timely draw. This factor represented 75% of the risk for negative outcomes.  Breaking this down further, this means that you need to be aware of your surroundings, avoid situations where there is the potential for violence, understand how to deescalate potential violence, and be well-trained in drawing your weapon under stress.  You must assume that your attacker has had prior experience in gunfights and can begin firing at you as quickly as 0.25 seconds.

In the second scenario, we assume that you follow all of the above guidance in an attempt to avoid violence yet the aggressor persists and you successfully draw your gun.  The critical factor now is shot placement. Having average or worse accuracy, under stress, represented 93% of the negative outcomes in this scenario.

Average accuracy can be estimated using police data with hit rates of 30%to 50%.  Another way to capture accuracy under stress is visualizing the total encounter using the “Rule of three:” three seconds to fire three rounds from three yards distance.

Notice that weapon misfires, assuming a combination of a maintained handgun and military-grade ammunition, does not significantly contribute to either scenario.  There are many options, however, for self-defense-quality ammo that has a better performance rate and can further lower the chance of a misfire.

It is important to note that the presence of a defensive weapon is inherently escalating.  This is obviously true if you are open carrying where the aggressor is not intimidated because they are concealed carrying.  The more subtle point here is that even a defensive concealed carry weapon can escalate violence and the CCW holder has a responsibility to practice de-escalation.  For example, you may be concerned about losing consciousness or control of your concealed pistol in a grappling or fist fight. This may cause either you, due to the attacker, to move to deadly force where you may find yourself in a gray-zone with your local prosecutor for shooting an unarmed man.

Key takeaways:

1. If you chose to conceal carry a weapon, you have a responsibility to control yourself and the situations you bring that weapon into.

2. Training on the quick and accurate drawing and firing of your weapon, at close range, is the most effective effort one can make to improve your chances of surviving a defensive gunfight.