Why 300, exactly?
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    Why 300, exactly?

    We all know the conventional wisdom. Buy a new semiauto (yeah yeah, hush you wheelgun types), and you shouldn't carry it until you've gotten through 300 trouble-free rounds. I've been wondering for a while, why 300? Is there a big difference between shooting 200 proof rounds, or 250, or 300, or 350?

    I did some thinking and some actual studying. I also ran it past this guy I know who has a Ph.D. in statistics, uses it every working day of his life, and has still forgotten more about statistics than I'd be able to retain with a solid year of study. He had some quibbles with my analysis, but if I followed his comments correctly, none of his comments would change my results by more than 1%. As in, if my method estimated 98.3% confidence, his methods might put the value at 99.3% or 97.3%. So for the purposes of real world decision making, my results below are very usable.

    So here's my reasoning. When you aim, press, bang with the sights on something very dangerous, one of two things happens. Either the gun goes bang and another round slides happily home to enable you to do it all over again, or something goes wrong; failure to extract, failure to eject, failure to feed, small bat perches on the feed lips at just the wrong moment, you know. But basically, either you are happy with the outcome or you aren't. That sounds like a binomial distribution; one or 'tother outcomes.

    To truly make a binomial distribution analysis valid, four criteria need to be met.

    • Fixed number of trials. Sure. It ain't 300.6ish.
    • There are only two outcomes. Okay, as handgunners we can quibble about this (you fix a FTExtract very differently than a failure to feed), but to a statistician, those all equate to "no go boom next time." So that really boils down to two outcomes.
    • Probability of each outcome remains constant from trial to trial. If your recoil spring is only good for 400 rounds, then your situation wouldn't meet this criterion. But for modern handguns in good repair, I'd say our question meets this criterion.
    • Each trial is independent. This is one that's the least of a slam dunk. We've all heard about (or seen) pistols that wouldn't feed reliably if loaded to full capacity, or always lock open on the next to last round. If you spent enough on ammunition (and it might be enough that you'd have to budget for recoil springs too), you might be able to measure the probability of the first round being successful through n + c (where c is the full capacity of the pistol). You might be able to come up with a measurably different probability for the first and last round, who knows? But I think for the real world, where there are so many other variables, the trials (each pull of the trigger is a trial) are independent enough for binomial calculations to be useful. It would be even more valid for revolvers, if you ignore things like bullets backing out of their cases under recoil.


    So, to calculate probabilities using the binomial distribution, we need to come up with a value for the probability referred to in the third criterion. If you complete 300 rounds with no problems, you have 100% probability of success so far. But that's not useful, because you also have 100% probability after completing 25 flawless rounds. So how do we get a probability out of 25 problem-free rounds and 300 problem-free rounds? Well, let's be conservative about this. To put it another way, let's make a worst case assumption. For these purposes, the conservative/worst case assumption is that wherever you stop, the next round would have failed. So for 25 rounds, the proven probability you've achieved is 25/26, which is .961358, or 96.1358%. For 300 rounds, you've obtained experimental evidence that the probability that a single attempt to fire would be successful is 300/301 = 99.6678%.

    Does that answer the question of "why 300 rounds exactly?" I don't think so. Few of us are willing to assume that we'll only need the first round in the weapon. If that were true, why does the PT92 hold 18 rounds? The real question is, if you need to use your 300-round-proven pistol to defend yourself, will it fire two rounds successfully? Three? Four? That's where the question (or more precisely, calculating answers to the question) becomes more complicated.

    What we really want to know is, given N proof rounds, what is the proven probability that you'll be able to successfully fire multiple shots from the pistol. That, to me, is the question.

    The math behind the answer is complicated. You can look it up if you like; I won't burden whoever has stuck with me thus far with the equations. They are easy to find on the net. And so is a calculator that will spit out the probabilities for you. Here's the one I used. Binomial Calculator In this one, you put the 300/301 probability value in the top line. The number of trials is the number of shots you expect to need to use to stop an attack. For our purposes, the number of successes is the same as the number of trials, because we want 100% reliability. The last line is the probability that all your defensive shots work flawlessly; the ultimate answer.

    So, I calculated probabilities for 25 proof rounds, 50 proof rounds, and on up from there to 500, in 50 round increments. The results were calculated for a number of defensive rounds from 1 to 10, and also for 18 rounds because the PT92 holds 17+1. So each row is a certain number of proof rounds, and each column is a certain number of defensive shots. Naturally, seeing a particular number in the table (i.e., 200 proof rounds, 3 defensive shots, 98.5% probability) doesn't mean that's the exact probability. It should really be read as the minimum proven reliability; the lowest reliability your experiment to date has firmly demonstrated. A gun you've fired 200 times may well go on to fire 1000 shots without a problem. But it should't do worse than the 98.5% shown in the table.

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    Now, have we answered the 300 question? I'm still not sure. If you assume a double tap is needed, you've proven 99% confidence in that being successful after 200 proof rounds. If you assume you need three shots, then you need 300 proof rounds to hit 99%. Bad news for you high-cap folks; if you assume you need 10 defensive rounds, not even 500 proof rounds gets you to 99% confidence. The seven-shot pistol crowd (TCP, 740) have proven an almost 99% confidence of being able to empty the gun when they've get to 500 proof rounds.

    Now, I've often been assuming (in this discussion) that 99% is the desired confidence that you can fire the specified number of rounds without a failure. Personally, I can certainly live with assuming that 3 shots being needed, and I can also live with anything above 95% confidence. If I were in gunfights twice a week, 95% might not be enough. I'd have trouble 5 times a year. But for most of us, gunfights are a none in a lifetime event. I'm on good footing at 100 proof rounds. Heck, that covers me (gets me above 95%) even if I decide I need 4 or 5 rounds to defend myself.

    So far, I've fired a little over 200 rounds through my 740. If I need to double-tap two attackers, I've got data to support 98% confidence that I can fire four times with perfect (four out of four successful shots) results.

    I hope someone else finds this informative/useful/a cure for insomnia. But that's what wondering about the 300 rounds figure got me.
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    "It is wonderful, in the event of a street fight, how few bullets seem to hit the men they are aimed at." Ranch Life and the Hunting Trail, Theodore Roosevelt, 1888

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    I hate to over simplify things after all the effort you put into this. Not everyone is a gun person. 300 rounds equals 6 boxes of 50 rounds. There were some that said 500 rounds or 10 boxes of ammo. The amount of range time to fire that much ammo gave the gun owner enough time to become familiar with the gun. The operation and take down, cleaning etc. Usually it takes several trips for the average shooter to burn that much ammo. Hopefully they learn to hit with it. The action should smooth out some and any problems be resolved. It wasn't a magic number just to prove the gun works. It is a combination of break in time for both gun and shooter. I like to run 100 rounds through a new gun more to learn the gun and how it shoots than reliability. You can have two of the same model and caliber and the poa/poi be different. Shooting helps with any gun. For a couple years almost everyday I fired at least one shot at a steel target with my carry gun. When I stopped I had hit every day for almost a year. Target was full man at 100 plus yards. It is not a magic number, it is shooting enough to build confidence.

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    Fail mechanism changes.

    Look up "bathtub curve" for failures of an item out of a population of "identical" items. initially infant mortality failure rate is high, but drops quickly. Items that survive this initial period then have very low failure rate until wear out failures occur. 100, 200, 300, 500 are all common numbers of uses to see if the item is in the infant mortality population or the high reliability population. The greater the number of successful uses, the higher the confidence you are in the good population.




    Generic curve
    Last edited by john_bud; 04-01-2015 at 11:00 PM.
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    What, me, overthink it?
    "It is wonderful, in the event of a street fight, how few bullets seem to hit the men they are aimed at." Ranch Life and the Hunting Trail, Theodore Roosevelt, 1888

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    My head hurts

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    Wow. I know I am opening a can of worms, but it seams to me that you just made a good math case for a .45 (fewer rounds needed, higher %) I am not even a .45 guy.
    1. Muzzle Controll: Always point in a safe direction
    2. Keep your finger off the trigger until your sights are on the target.
    3. Keep it unloaded until ready to use.
    4. Know your target and what is beyond.


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    You also need to take custom type guns into thought. Years back a gunsmith friend built custom 1911 target/hardball guns. He tightened the slides and actions. He polished everything and would tell you to run a few hundred rounds through the gun. That would loosen the gun up a little and give you enough trigger time to see if you wanted to change anything. I miss the guy, he got me started building Contender barrels and doing other things. He was also one of the best on revolvers. He preached that there was no substitute for burning powder in handguns. It shows up flaws in guns and shooters.
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    I think I need a drink.
    Definition of clip

    1: any of various devices that grip, clasp, or hook
    2: a device to hold cartridges for charging the magazines of some rifles; also : a magazine from which ammunition is fed into the chamber of a firearm.

    http://www.merriam-webster.com/dictionary/clip

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    Wow!!! Too much information this early in the morning.
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    This is why I am a electronics engineer, stats bore the crap out of me.
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    “When governments fear the people, there is liberty. When the people fear the government, there is tyranny. The strongest reason for the people to retain the right to keep and bear arms is, as a last resort, to protect themselves against tyranny in government.”

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