Gun ownership risk factors – A mathematical model

Gun ownership risk factors – A mathematical model

Goal:  To understand which risks associated with owning a gun are significant versus insignificant.  This is written for first-time gun owners, families with young children, or those considering buying their first gun.  Methods included using Probabilistic risk assessment and event trees.

To read the event tree, you start on the left assuming that you own a gun.  The factors analyzed include the chance of an accident, the chance of you being the victim of a violent crime, a factor measuring the percent chance that you have the gun accessible to you during the violent crime (do you conceal carry 24/7 or do you just keep it at home in a bedroom where it isn’t accessible to you for most of the day), and the contingent chance of being injured/killed during a violent crime (given if you have access to your defensive firearm or not).  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 (discussed later) and a range of values for each factor were tested in the model for sensitivity.  Putting it all together then, as an example, the probability of surviving a year of gun ownership without being victim of a violent crime is given as:

P(Safe due to no accident)*P(Survive due to not being the victim of a violent crime)

Testing different ranges of values for factors in the model 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.


Gun ownership does not significantly contribute to an increased risk of injury or death, for adults.

· To be conservative (mathematically, not politically), we combine the 430 unintentional firearm deaths per year with the 23,941 suicides by firearm annually to get a probability of accidental death of 0.01%.

· It is difficult to the estimate the rate of violent crime since it can be underreported.  Annual rates in the literature vary from 0.37% using emergency room visits for assault as a metric to 2.3% using violent crime rates in Justice statistics.  To be conservative, we used the largest value and multiplied it by 3, to account for underreporting, with a resulting probability of encountering a violent crime of 6.9% annually.

· Estimating how likely it is for an individual to have access to a defensive gun, at the moment of encountering a violent crime, is based on a few factors.  First, approximately 44% of US households own a firearm and 7.3% of US adults have concealed carry permits. Violent crimes can occur in the home (where the largest percentage of guns would be located and where people spend a significant portion of their time) but also can occur out in the world (where most people are not carrying a defensive firearm).  So, for the purposes of this risk model, we used values for the gun utilization factor ranging from 10 to 40%.

· Finally, the rate of injury or death resulting from being the victim of a violent crime can be estimated between 0.3%to 4%.

The conclusion, that the probability of dying due to a firearm in a year is 0.3% in our model, roughly matches data from the CDC’s WISQARS Data Visualization tool with a value of 0.8%, for adults.

Now, let’s shift our focus onto the potential risk to children in a home where a gun in present.  This is an important question for first-time gun owners or current gun owners who are reconsidering their weapons as they have a child.  The following graphs are sourced from the CDC and provide insights on the risks of firearms, to children.

To understand the impact of firearms on children, we first subtract the firearms components from the number of suicides, homicides, and accidents in the 1 to 12 year old range.  We then take that value (247) and create a new bin for the sum of these named “all firearm-related deaths.”  When the data is viewed this way, all firearm-related deaths becomes the 6th leading cause of death at 4.6% and is perceptively higher than the equivalent adult risk (of 0.3% to 0.8%).

Key takeaways:

1. Owning a gun does increase the risk of injury or death to members of the household

2. The amount of increased risk for injury or death, for adults, is fairly small (approximately 0.5% per year)

3. Children have a 9 times higher relative-risk of injury or death (approximately 4.6% per year) as compared to adults

4. Preventing children from accessing firearms would eliminate a large portion of the risk of all firearm-related deaths (suicide, homicide, or accidents)

5. Parents and caregivers need to carefully consider - Is it safe to have a gun in my home with children?  How can I improve gun safety around toddlers? Etc.

6. The guidance here also applies to gun owners who do not have children in their household but may occasionally have visitors with kids