Calculating stopping percentage with multiple shots...

This is a discussion on Calculating stopping percentage with multiple shots... within the Defensive Ammunition & Ballistics forums, part of the Defensive Carry Discussions category; I thought some would find this interesting, albiet possibly moot... In many previous discussions regarding One Stop Shots, aside from the debate of the relevance ...

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Thread: Calculating stopping percentage with multiple shots...

  1. #1
    Member Array krept's Avatar
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    Calculating stopping percentage with multiple shots...

    I thought some would find this interesting, albiet possibly moot...

    In many previous discussions regarding One Stop Shots, aside from the debate of the relevance of the data, I found that many people were openly wondering about the effectiveness of multiple shots. This especially came into play during discussions of FMJ or ball ammunition.

    The logic frequently went as such: if my 230gr .45ACP bullet has a 60% chance to get an OSS, then if I hit them twice according to the parameters (COM, etc) then I would have a 120% chance of stopping them... 60%+60% = 120%. Well, not quite :)

    The following equasion is one that you would use:

    1 - (1-X)^n (the "^" is meant to be superscript, i.e. to the "Nth power")

    X = the percent chance that the action occurs with one attempt (i.e. 50% = .5)

    n = the number of attempts.

    ---

    Therefore, with the aforementioned 60% OSS combined with two shots, we would have 1-(1-.6)^2 or .84... or an 84% chance to get a stop with 2 COM shots of ball. Again, IF the shots are placed according to the study AND if 60% is the correct OSS value (I think it was higher).

    Nonetheless, some food for thought.

    Cheers

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  3. #2
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    Thats just shows the need for a 3 shot shoot

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    I'm afraid there are so many variables in a shooting that percentages and statistics don't really mean much.

    It seems that all bullets work and all bullets fail. When they work and fail seems to be very, very difficult to analyze because of the great number of variables and relatively small numbers of similar cases.

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    Interesting to try and quantify this Erik but indeed - the number of variables we really need to include or introduce make it very hard to see a useful and reliable result.

    The only possibly reliable parameter is the one - ''shoot until the threat ceases''
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    Member Array amlevin's Avatar
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    Unfortunately I don't really understand the concept of a "One Shot Stopping Percentage". It depends so much on where the round hits that it would seem almost impossible to do much more than keep a large database of shootings, calibers, and "stops" that won't really have any bearing on the next shooting incident.

    A shot from a .22LR between one's "headlights" will have more effect than a .45acp that hits one in the "love handles" or other mostly fat tissue part of the body. Since there aren't many that carry .22LR chambered weapons the round is under-represented in the "database". The problem with statistics is that the sampling is usually skewed in favor of popular rounds.

    I don't advocate using .22 or .25acp rather than larger calibers, I merely use them to illustrate the absurdity of trying to calculate the so called One Shot Stopping "Index". Doesn't it really boil down to shot placement?
    ""If I shoot all the ammo I am carrying, I either won't need more or, more won't help me.""

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    Member Array chiefs-special-guy's Avatar
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    Krept-
    that seems to assume independent trials, which is an heroic assumption if you are getting shot. Think of it as the probability you are stopped with one shot given n one shot stop attempts...
    God Bless
    Six for sure...Uh, I mean Five. Five for sure..

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    Distinguished Member Array RSSZ's Avatar
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    krept, read your post several times and just hafta say that I don't understand it at all. I'm not saying that it is flawed. Hell,I don't understand it enough to debate it.

    FMJ.... I don't understand why some people will use them for CC. Now I don't claim to be an authority on the matter but I feel that everyone knows the difference between penetration and expansion. If you want a bullet to penetrate you don't want it to expand.(African big game solids,and/or hard cast)If you want a bullet to expand you design the nose with something that starts the expansion process very early in the penetration process.(a ball,polycarbonate tip,HP,wax.etc.)Something that will push the nose open and start the mushroom process.

    Now I also understand that all else being equal, two bullets that don't exit the target,one HP and the other FMJ,dump the same ammount of energy. Its just spread over more distance and over a longer period of time.

    If a person is using such a low powered weapon(for CC) that they feel that they need a FMJ just to get the proper penetration,then I feel that they need to step up a caliber or two.

    Hittin 'em more than once......If the ballistics table sez that one shot with caliber X,using bullet X,traveling at Xfps,produces X ammount of terminal energy,then I can't understand why the figures can't simply be doubled. This,provideing the BG isn't shot thru the same hole. And even if he is,if the bullet dosen't exit.

    For me it's less penetration and I want energy dump over a shorter period of time with a larger wound channel(this,given we can't have the best of both worlds). The FBI(or other statistics guru's) say you gotta put it in 12". Take a 12" ruler to your buddy. Have him turn sideways and figure how far a 12" penetration will take the bullet. Now I understand the bullet might have to go thru a bicept before the chest and all the other bad places the you could hafta hit him. Still,to me a foot is extreme. I feel that COM, either front or back,8"would be plenty.(with massive and quick,wound channel)

    Again,I don't claim to be an expert on ballistics,terminal or otherwise. These are just my feelings on the much debated subject. -------

  9. #8
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    Quote Originally Posted by krept
    ...The logic frequently went as such: if my 230gr .45ACP bullet has a 60% chance to get an OSS, then if I hit them twice according to the parameters (COM, etc) then I would have a 120% chance of stopping them... 60%+60% = 120%. Well, not quite :)

    The following equasion is one that you would use:

    1 - (1-X)^n (the "^" is meant to be superscript, i.e. to the "Nth power")

    X = the percent chance that the action occurs with one attempt (i.e. 50% = .5)

    n = the number of attempts.

    ---

    Therefore, with the aforementioned 60% OSS combined with two shots, we would have 1-(1-.6)^2 or .84... or an 84% chance to get a stop with 2 COM shots of ball. Again, IF the shots are placed according to the study AND if 60% is the correct OSS value (I think it was higher).

    Nonetheless, some food for thought.

    Cheers
    krept,

    I think we, I know I, may have missed part of your point, which BTW was well made. That was the math of combined percentages assuming similar effectiveness of bullets. There is much misunderstanding about percentages, etc. and probably even moreso about the stopping effects of bullets.

    But, while the math is correct, it doesn't, and we can't, take into account mathematically, the way an animal or human is going to react to being shot.

  10. #9
    Member Array Lumberjack98's Avatar
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    Shoot to stop. Don't count your shots.

    Must be an engineer or math major type.
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  11. #10
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    Here is my formula for stopping.... Shoot till the target is no longer a threat. Handgun and even rifle rounds are not effective 1 shot stoppers unless CNS is hit. Rifle rounds may give you the luxury of waiting for 1 shot to take effect. (distance ,cover, ect)
    "In matters of style, swim with the current; in matters of principle, stand like a rock." Thomas Jefferson


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  12. #11
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    In all fairness guys, I don't think krept's intent was to establish stopping power based on mathematically manipulating one shot percentages. Nor does it appear to me that he was suggesting a way to deal with a threat. From the context of his post, he was simply pointing out a potential trap when considering percentages - the point being you can't just add the one shot stop percentages to get a total effect of multiple shots.

  13. #12
    Distinguished Member Array AutoFan's Avatar
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    Not to mention that multiple gunshot wounds cannot be considered equivalent events in the classical sense of statistics, since the initial conditions change after each shot (i.e. your target is already bleeding, lowering the starting blood volume, adrenaline is raising heart rate and blood pressure, your previous shot has already damaged some bodily structures, etc.), so the single shot numbers cannot be manipulated to generate valid multiple shot numbers. But I do understand krept's point about how you would manipulate them if it were valid.

  14. #13
    Member Array krept's Avatar
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    :) thanks for the great points to all of you. I am definitely in agreement.

    The original post was more to be taken into the context of exactly how Tangle so eloquently explained it above. Sometimes I get so caught up on adding caveats that they end up detracting from the focus (like the photo of a sign that says BEWARE THIS SIGN HAS SHARP EDGES!!! by the way, the bridge ahead is out).

    The main reason why I became interested in this was because when Marshall and Sanow data are usually discussed, the folks who stoke their carry weapons with FMJs usually take the leap that if the bullet has X% to stop, if you shoot twice hitting COM you get 2*X% to stop, frequently totalling over 100%.

    For the life of me, I had the hardest time trying to get a forumla to explain why it was not additive and someone helped me out with it.

    Just for the record, shoot till the threat is stopped is what I was taught. M&S, Fackler, etc. just provide a decent basis for discussion IMO.

    thanks again folks, this place is great.

  15. #14
    Distinguished Member Array randytulsa2's Avatar
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    Too many variables in any give situation to calculate with any real precision, and placement is by far the most important of those variables.

    But some calibers and loads are more effective than others. I don't know how to measure that effectiveness, nor can I prove the truth of the statement.

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    Post Chuck Taylor & His Old WAVY Formula

    Chuck Taylor's formula for the stopping power of a bullet.

    WAVY over 1000
    W=Bullet weight in grains
    A=Bullet cross section in square inches
    V=Bullet velocity in FPS
    Y=If V=1088FPS or more then bullet expands and 1.25 is the value. If bullet doesnt expand then 1.00 is the value.
    The product is divided by 1000

    Real Good Chuck. Not one of your shining moments.

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