Immumerancy on the Internet

In a blog post by Andrew Tuohy entitled Revolvers Are Not Perfect, Or, The Problem With Revolver Fanatics I learned that thinking the revolver is still a relevant fighting tool and in private sector self defense is sometimes superior to the autoloader makes me insane.

I would urge anyone who still believes, in the 21st century, that revolvers are superior to automatics as defensive or fighting handguns to strongly consider the facts about revolvers and the state of automatic pistols today. Also, you're insane.

That is a serious accusation. Insane people are generally considered not mentally fit to own much less carry a firearms. It is possible that the last sentence is just empty rhetoric by Mr Tuohy intended to drive traffic to his blog. On the other hand he may actually mean what he wrote. I'll leave it the reader to decide if was hyperbole or honesty.

Normally, I ignore jokers like that. IF Mr.Tuohy want to think I am insane well I am equally free to think him incredibly stupid and ignorant. However, just as a broken tooth draws the tongue, I found myself reading the damn comments. A few posters tried to defend the revolver's relevance but, face it, that is an exercise in futility. Someone who considers you insane has already created the perfect excuse to ignore any evidence you might present.

Nevertheless I continued to yield to my inner masochist and read on until I came across a comment that really is -- well -- the word "stupider" comes to mind. The part that really bothered me is this:

I tried to attach a bunch of statistics online (mostly are police related shootings), and you are correct in that most engagements are around 3 rounds. But also over 3/4 of those are against people that were not shooting. Once officers were on the 2-way range, and being shot at their hit percentage goes down to 13% (NY Times), basic math will tell you that statistically that is zero hits from a 5-6 shot revolver, let alone a killing shot

OK, people like to toss out statistics. Most people who use statistics to "prove" things usually just display their ignorance. This guy is using them so badly, however, he is flaunting it.

Perhaps I am insane but I also remember my sophomore statistics and the binominial distribution. It is not really hard to use and every spreadsheet for the past decade or so can do it for you so you don't even need to remember the formula. Perhaps since it was first described in the 17th Century it is also too old and outdated to be relevant in the modern world.

Anyways, for a constant hit probability of 13%, the odds of making least X hits in N shots can be calculated by a simple binomial distribution and the cumulative probability.

In percent:

	Minumum number of hits
Number of shots	1	2	3
1	13	0	0
2	24	2	0
3	34	5	0
4	43	8	1
5	50	13	2
6	57	18	3
7	62	23	5
8	67	28	7
9	71	33	10
10	75	38	13
11	78	43	16
12	81	47	20
13	84	52	23
14	86	56	27
15	88	60	31
16	89	63	35
17	91	67	38
18	92	70	42
19	93	73	46
20	94	75	49

So the real statistic for at least one hit is not zero percent as alleged but 50% for five shots and 57% for six.