# ‘One In A Billion’ Shot? More Like One In A Quarter Million

An extraordinary shot by a Colorado deputy during a gunfight is being described as a “one in a billion” shot. The shot is extraordinary, but the odds are much better than that.

It’s fairly common in a gunfight to get hit in the gun arm or gun hand. Or for their firearm to be hit. The gun is usually out front facing the person firing back. People tend to equate the gun with the threat, so they tend to focus on the gun. Where the eyes look, the bullets tend to go.

Deputy Jose Ramon Marquez told investigators about a Jan. 26 shooting in which two masked men attacked him. … In an exchange of gunfire that left him seriously wounded, Marquez hit one suspect in the leg, and another of his .45-caliber bullets made a “one in a billion” shot, according to a letter (deputy district attorney Rich) Orman wrote to Jefferson County Sheriff Jeff Shrader and Aurora Police Chief Nick Metz.

That round traveled up the barrel of the attacker’s gun, colliding with a cartridge in the chamber and rendering the .40-caliber pistol inoperable, the letter said.

Let’s do some math and calculate the odds. If the barrel is facing the threat, the bullet has to hit the barrel fairly close to its center axis for it or a significant fragment to travel down the bore. A reasonable assumption would be that the center of the bullet would have to hit within .1 inches of the bore axis.

It’s reasonable to believe that an average person would be able to keep his shots within a four foot square at pistol fighting distances. An expert should do much better. If you’re in the top 1%, I’d expect you to keep them with in one foot square, even during the stress of a gunfight. But everyone can’t be in that top 1%.  A 48″x48″ target area gives us a bit less than a quarter million .1 x .1 inch square impact areas.

That makes the odds of the shot Deputy Marquez pulled off about a quarter million to one. If you’re one of those top 1% shooters, those odds drop to about 15,000 to one. But that would presume that you’d be aiming for the gun. An expert usually aims for the heart or the spine.  Those targets are much more likely to stop an assailant with a gun from pulling the trigger.

In any case, nice shootin’, Deputy Marquez.

©2016 by Dean Weingarten: Permission to share is granted when this notice and link are included.

Gun Watch

1. Bob says:

So…proof 45 beats 40?

1. Oxygenthief says:

Haha! Epic flamebait is epic.

2. Chadwick P. says:

Rock, paper… 45acp!

3. Frank in VA says:

I feel like this is meme material. Along the lines of the classic “…but a .45 will kill their soul”.

I’m just not feeling creative enough to write the copy for it. Maybe after some bourbon…

4. Tom in Oregon says:

Nice!

1. James in AZ says:

Nice truck attack!

That was my WTF moment pulling up the news

2. Vanbulance says:

Also a moving target, which changes the probability just a smidge. I wouldn’t personally argue with the DA this time, ha!

3. Erik says:

I high the high estimates make more sense. The bullet would need to enter the barrel essentially straight on, I don’t think the countless possible different angles of grip and aim point are in the above calculations. Definitely time to play the lottery for that deputy!

1. 16V says:

I don’t know about “exaclty” straight-on. Once it’s in, and until it’s forward energy is shed through friction, it’s guided by the barrel.

But yeah, it’s gotta be pretty close. I’ve heard many of these stories from disparate (and generally) trustworthy sources. Saw the remnants once, though in that case the bullet made it halfway down the barrel. The few fractions of a second after the next trigger depression were very, umm, interesting.

2. Jeremy in AL says:

It’s just like busting womprats with my T-16 back home.

1. peirsonb says:

Yeah, but they’re not much bigger than 3 meters.

1. J says:

Pfff…virgins.

2. Owen says:

Thanks! That was a good laugh you guys!

3. BLAMMO says:

Why do people always say that AFTER someone has had an amazing stroke of luck?

It’s too late. You used it all up.

4. Shire-man says:

I wonder what the best method for clearing that malfunction is.
Drop the gun and draw another?

1. John says:

The drop the gun part of that sequence already had some ballistic assistance. It wasn’t the only projectile incoming on that position either. I think by the time the perp realized he had a malf, he had other, more pressing, concerns. Like how to keep his blood on the inside.

Good shooting.

2. Geoff PR says:

“Drop the gun and draw another?”

Yeah, a “Noo-Yawk” reload sounds appropriate…

5. TTACer says:

My uncle hit a robber’s gun, probably with both eyes closed.

6. Crowbar says:

You have to admit that no matter how it happened (luck, skill, full moon, or Ted Nugent was guiding the bullet while Astral projecting) it is pretty impressive.

7. Tom in Georgia says:

I can concede it being theoretically possible if Marquez’s weapon was 9mm or smaller, and the perpetrator’s weapon was a .45ACP or thereabouts, but the article states that Marquez, not the other guy, was shooting a .45. Which then brings me up to the first thing I thought about. How can a bullet travel up against the friction of another barrel without benefit of propellant, when many such bullets have been known to fail to exit at all when loaded with just a primer or even a partial load of propellant?

But hey, truth is all too often stranger than fiction so what do I know, right?

Tom

1. pwrserge says:

Fragmentation, the entire bullet doesn’t go up the barrel, pieces of it do.

2. kenneth says:

Dispite the claim of hitting the round in the chamber, i doubt that the oversized bullet would travel that far. Just the smashing oif the bullet into the slide will destroy the front of the barrel and slide, thus rendering the firearm inoperable. There is no need for it to continue all the way down the barrel. Always take everything anyone says with a grain of salt, because most people haven’t the slightest idea what they are talking about, nop matter how many times thety are called ‘expert’
250,000 to a billion is off by 4000 times. That alone should illustrate that whoever wrote that is completely innumerate(mathmatically illiterate), like most.
The Paulos book is a good treatise on the subject:
https://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its-Consequences/dp/0809058405

8. Bob316 says:

I shoot about a thousand rounds a week. I could probably put a 9MM down the barrel of a pistol mounted in a vise 9 feet down range. If I carefully aimed my shot, concentrated on breath and trigger control…probably. Using defensive accuracy, while stressed, while relying solely on gross motor skills, while having a moving target, and while trying to vie for cover…not a chance in hell unless God granted me a miracle. 🙂

9. DavidinNC says:

Thanks, Debbie Downer.

10. jwm says:

Always carry a spare gun. 1 is none.

1. Bob316 says:

Unless you are a bad guy, then I would recommend one gun, perhaps something built by Hasbro that uses foam tipped projectiles.

11. Ian in Transit says:

Keeping in mind that paintball is a sport and gunfights are not, the similarities lend themselves very well to the math comparison. In the sport of paintball for two competitors exchanging fire while ducking in and out of cover it is very common for the paintballs themselves to strike one another in mid flight. Being hit into the end of your barrel is rare enough to still make you shrug in amazement when it happens but it is not uncommon.

Depending on the skill of the participants I tend to think the 15,000-250,000 to 1 numbers are fairly accurate. One billion to one is just padding the numbers for awe factor.

12. DMD says:

Check out the incredible (un)lucky .25 caliber block-long head shot killing Miami Beach narco detective Scott Rakow some 30 years ago for a similar shot !!! DMD

13. Well you spray andd pray enough your going to get a lucky shot. Pure luck here.

14. Priest of the center mass says:

.45 s are made from God particles.
They’ll take your soul.

15. Paul Hurst says:

Odds should be calculated empirically.

16. formerwaterwalker says:

Didn’t Mythbusters do this particular shot? Yeah it can see “difficult”-but not impossible…

17. JasonM says:

Mythbusters tested a similar story a few years ago. I believe in their story, the cop hit a revolver cylinder in one of the chambers, which prevented it from revolving. They researched it and found backing documentation that it had happened.

18. anonymoose says:

The odds of making that shot in the middle of a gunfight are about as high as shooting someone through their scope. That’s no 22Plinkster trick shot.

19. McCann says:

This is the most baseless “calculation” published to date. You can’t just make assumptions, assign them numeric values, and claim to be determining the odds of a given occurrence. Well, you can, but you’re writing nonsense when you do.

20. James69 says:

And a hearty Hi Ho Silver away!

21. Some Bloke says:

Your math is wildly incorrect and it’s a shame because you had a chance to be right and show some dramatically more interesting facts. Instead you were snarky and totally wrong in a way that smacks of trifling polemics.

While a 48×48 may have a quarter million distinct spots on it that measure .1x.1 (actually a hair over 230K) that has little to do with the probability of hitting inside the area subtended by the bore of a moving pistol. Within that 48×48 space there is not an even probability of distribution. Dude isn’t going to land 1 round precisely on each of those points given 230K shots at the target in general. The target in this case is also moving and the source of the magic bullet is moving too.

Any shooter will have a cone of distribution of shots which is composed of angular distances in 2 axes which are perpendicular to each other and where both of those axes are perpendicular to the direction of travel of the magic bullet. Just like with any distribution the shooter will have a much higher probability of hitting within the 2 central standard deviations on the distribution than any further block and the likelihood of hitting extremely far from the center is wildly lower than hitting nearer the center. If you figure a shooter’s actual average group size and departure from intended POI then calculate an additional imprecision coefficient based on shooter stress level then determine the rates of relative motion and distance of each gun from the other and count the total number of shots fired then you’d get a much more startling number that will be quite a lot lower.

Journalists that don’t know math shouldn’t write articles using it to make a point. Those of us that do know some see how little you know and it burns your credibility. Besides, that’s just the sort of BS tactic the left uses. Lies, damned lies and statistics.

1. Some Bloke says:

By my math I have a one in 100 shot if the target is at 7 meters distance.

2. The data that you so blythly require in your calculation is unknown and would require a research project costing tens of thousands of dollars and the voluntary cooperation of the Deputy to obtain a rough approximation. If the bores are roughly pointed at each other (a pretty good assumption in a gunfight) then it does not matter if they are moving laterally. That movement is insignificant compared to the speed of a bullet.

As a practical matter of calculating odds, simplifying assumptions have to be made because statistical distributions are unknown and/or unknowable. Assuming that the shot falls inside a four foot square is one such assumption.

Engineers at places like NASA make these sort of assumptions all the time. Data is unknown; an analysis is conducted to get a feel for the odds. In this case, real world experience, as mentioned in the discussion, supports the conclusion that the odds are much better than a billion to one.

1. McCann says:

“Engineers at places like NASA make these sort of assumptions all the time.”

NASA engineers know what the hell they’re doing. You don’t.