William M. Briggs

Statistician to the Stars!

Page 149 of 604

Probability And Shot Groupings

That’s some mighty fine shootin’, son.

Reader Paul Mullen writes:

I was reading the WikiPedia page on “accurizing” firearms, and came across a claim I find suspicious:

Statistical likelihood says the fewer shots that are fired, the smaller the dispersion will be. 3 or 5-shot groups are acceptable for zeroing the sights and rough accuracy estimates, but most shooters consider 10-shot groups to be the minimum for accuracy comparisons.

The cited authority:

For standardization, it is best to fire five-shot groups with the same aiming point. It is a statistical fact that group size will increase with the number of shots fired.

If I’ve learned anything from reading wmbriggs.com (and I do try), it is that probability distributions quantify our uncertainty about a future event, rather than describing how things would look if we could observe an infinite number of those events. In other words, we expect there’s a better chance that the next shot will be close to the last, rather than far (relatively speaking). But there’s still a chance that the second shot fired could be an outlier, while the 48 shots after it could all land on the same hole. Is there any reason to believe that the more shots we fire, the better idea we’ll have of the “true” group size?

First, I think we can all agree that accurizing is one of the worst gerunds since concretizing: it should be shot and put out of its misery.

Second, group size. As defined by Sniper Country: “It is the maximum distance between the centres of the two farthest shots in a group. The easiest way to do this is to measure from the outside edge of one bullet hole to the inside edge of the farthest one away.”

The claim “It is a statistical fact that group size will increase with the number of shots fired” is true. Fire one shot. What’s the group size? Zero inches. Fire a second shot. Unless you Robin Hood it (and there is a chance this happens) the group size for both shots will be larger than the group size for just one shot. The more shots you fire the greater the chance the rounds wander from their appointed path, and thus the larger the group size.

Probability does, as you say, quantify our uncertainty about future (or really any) events, even in cases where we have less than infinite information—which we never do. And experience does show that successive shots will be closer to one another than shots taken at widely different times.

It’s your last question that is of most interest: “Is there any reason to believe that the more shots we fire, the better idea we’ll have of the ‘true’ group size?” There is no such thing as true group size, but the more shots fired under a set of conditions the better we can characterize our uncertainty in what the group size will be.

There are sets of conditions; premises, if you like (to fit in with our usual language) which describe the “state of firing”. These includes physical conditions like (of course) weapon type, ammunition, position, distance to target, even the weather. But it also includes many intangibles such as your mood, blood alcohol content, health, and your interest in hitting the target, which might include noting whether the target is firing back at you, and so on.

Take a set of conditions and a number of rounds fired and marry that to some historical performance measurements and we could in theory calculate the probability (maybe only crudely) that the group size will equal some specific number, or that it will be between two given numbers. The number of rounds fired is crucial, because as we’ve already seen, the more shots the larger the group size usually.

This is different than actually measuring group size under a set of pre-specified physical conditions, as in competitions. There, the average of some number groups is taken, say 10 rounds of 5 shots, maybe varying the physical conditions slightly between rounds. The smallest average wins. Whatever your average is can be used as information to calculate the chance of future group sizes measurements.

Here’s some fun homework. The media, God bless them, often make much of the number of shots fired by policemen when they’re trying to take down a bad guy. Suppose the physical conditions include a bad guy firing back at the policeman. Further suppose that we know for a fact that each round the policeman fires has a 0.3 chance of hitting its target and incapacitating the bad guy. How many shots does the policeman have to fire so that there is at least a 99% chance of bringing down his target? The answer will surprise you and (probably not) delight your media friends.

Hint: if he fires only once, he has a 30% chance of bringing down his target. He does not have a 60% chance if he fires twice.

The Apes Do It So It’s Fine For Us Fallacy

I'm doing five to ten for apeslaughter.

I’m doing five to ten for apeslaughter.

Been awhile since we’ve done one of these. Time to restore the series. Once I overcome my innate laziness (a terrible sin) I’ll group them together and put them on the Classic Posts page (which is in a sorry state).

People are happy to discover any argument which supports a position they favor. So pleased are they to find any corroboration (however weak) that the argument is embraced even if it is fallacious. This series (Genetic, Hypocrisy) examines fallacies beloved by today’s dominant culture.

Caution: because an argument for a conclusion has been shown fallacious, this does not prove that all arguments for that conclusion are fallacious, merely that the argument in question should be abandoned. But also keep in mind that if the fallacious argument was all the conclusion had going for it, yet you still hold that it is true, your sole justification is your desire, a dangerous situation.

An argument for legalizing prostitution:

Whether it is legal or not, there is seemingly no place in the world where it doesn’t exist. Indeed, it’s even been found to exist among primates who have been taught how to use money. Given all of this, one wonders what the value in trying to ban the practice actually is.

This is easily seen to be fallacious in a parallel argument.

It is the case that chimpanzees and apes, which is to say primates, like men, from time to time kill fellow conspecifics, usually while in sour moods or in disputes over money or other resources. The practice has long been observed and in many places; indeed, there is seemingly no place in the world where these animals (chimps, apes, men) are found where these killings do not exist. Given all of this, one wonders what the value in trying to ban the practice actually is.

Arguments pointing to the behavior of non-human animals are often used to justify human actions. Sexual promiscuity is the most common: for example, the (so we are told) ever-randy bonobo has had much drool—sorry, ink—spilt recommending its amorous activities for the masses. From which we learn there are many lonely academics.

From the Friends of the Bonobo society here is an example of the Apes-Do-It fallacy. The argument is only implicit here, but to give them a pass on that account would be like forgiving a television comedian his political asininities as long as he ducks behind his status. “I’m only a comedian!” Besides, there are plenty of places where arguments similar to this are explicit.

But when you get to know bonobos, you’ll see they couldn’t be more different. Like humans, chimpanzees have war. The males are in charge, and they can occasionally be very violent. Sometimes they even kill each other.

Bonobos do not kill each other. The females are in charge of the group and they seem to keep everyone’s temper under control with sexual activity. It doesn’t matter how old you are, or if you’re male or female — if you’re a bonobo, sex plays a big part in living together peacefully.

The text acknowledges that humans and chimps are a murderous bunch, a well known truth. But the implicit argument that if female humans were “in charge” as female bonobos (seemingly) are, then human males, sated with sex doled out at regular intervals would cease knocking each other on the head is clearly silly.

Would there be a government bureaucracy devoted to this new welfare? The authors have also forgotten sexual dimorphism (perhaps female humans are meeker because their mates are so much larger and stronger?), procreation (who takes care of the inevitable issue promiscuity brings?), and—the worst sin—the Andrea “All Sex Is Rape” Dworkins of the world (who can imagine a feminist supporting this program?).

Strangely, we rarely hear calls to emulate dung beetles or blow files.

Reddit Bans Dissent

Reddit banishes another anti-revolutionary

Reddit banishes another anti-revolutionary

I tried posting a thing or two at Reddit a while back (by invitation), but one of my i’s wasn’t dotted, or a t wasn’t crossed, and the ankle biters who make up the bulk of its moderators and who act like over-zealous college freshman who just memorized Robert’s Rules of Order made the experience so unpleasant that I never went back.

Plus, too many folks who haunt that site, basking in the anonymity, engage in things like this: “‘I fought back with awesome’: Woman who lives with painful skin condition shames the bullies of Reddit who thought her picture was a laughing matter.”

I am therefore not in the least surprised that the Dear Leaders on the science forum on that site has banned dissent from the party line that global warming is going to strike—soon, soon—and destroy us all. Reddit is now no different from many major newspapers, television outlets, learned societies, and peer-reviewed journals.

It will be interesting to see if Reddit “cleanses” past posts of skeptical comments in the same way various Peoples regimes erase enemies from photographs.

Anyway, all these organizations (in their forums and house organs) have decided that the science is settled, and, that being the case, there is nothing more to say. A valid argument if the premise is true and the science really is settled, which they all believe. Strangely, though, given there is nothing more to say they still manage to keep on saying things and at ever-increasing rates.

What do they talk about? Us. Mostly, they talk about us.

They gather for the sole purpose of shaking their heads at each other in bewildered amazement that people like us could imagine that the science isn’t settled. “All the people who agree with our view that the science is settled,” they say to themselves, “say that the science is settled. Therefore the science is settled. The deniers who deny what we believe most faithfully must therefore be insane, wicked, evil, and whoppingly ignorant. We are the opposite.”

They also thus talk about themselves and how wonderful their selves are.

They talk about the many, many failed forecasts and say, “Those darn deniers don’t understand that these forecasts haven’t failed. They were off in observation, but they were right in spirit. And since they were right in spirit, the science is still settled and the end is still nigh.” Right in spirit means wrong in reality, yes, but the theory which defines the spirit is so achingly beautiful that it is truer than reality.

They talk about the motivations of skeptics. “They’re all in the pay of big oil! And those vile Koch brothers!” “I know just what you mean. I was so mad about it I almost couldn’t finish my grant application to study the effects of global warming on racism.”

They talk about what awards they should give each other. “Oh! How about calling the James Hansen Bravery…

Skip it. This kind of thing is now utterly routine. The party of tolerance and openness and diversity and honest debate doing what they do best.

The Endangered Species Act & Counterfactual Arguments

It can't be real. The Endangered Species Act outlaws them.

It can’t be real. The Endangered Species Act outlaws them.

Most species that have ever lived on this our glorious planet Earth have been put on permanent hiatus. And by “most” I mean something approaching, but obviously not yet reaching, every damn one of them.

Some 250 million years before mankind appeared nearly all life in the oceans and a goodly portion on land was rubbed out. And this before the invention of plastic. There were no journalists at the time, so the best candidate to blame for the Permian-Triassic extinction event remains unknown.

This wasn’t the only horror show. Two hundred million years (or so) before the PT party was the Ordovician-Silurian extinction event which, while in earnest, couldn’t match PT’s record and only massacred two thirds of all life. And there are many, many, really very many more of these (let us unemotionally call them) incidents. The last big one was 66 million years ago when Earth, not looking in her rear-view mirror, backed into an asteroid. These things happen.

What can we learn from this? That species come and species most certainly go—and sometimes they go in spectacular fashion. Incidentally, there was a theory bruited some 20 years ago which held mass extinctions were periodic with a “return period” of about 50 million years, which means we’re way past due. My opinion is that the periodicity is a statistical artifact, but I could be wrong. Plan accordingly.

But as you do so, rest assured your beneficent government has taken action! Forty years ago, almost to the date (28 December), Congress got off its collective keister and did what everybody constantly demands it do: they did something. This something was the Endangered Species Act which guaranteed by law and full faith of the United States of America that, henceforth, no species shall ever go extinct again!

For, as we all agree, no species should go extinct. Even though most have.

According the official press release from the US Fish and Wildlife Service which somehow found its way into my in-box, the Act is (self) “credited with saving hundreds of species from extinction”.

“I’m suspicious,” you might be thinking. “Give me an example.” Okay, mister, I’ll give you two: the orange foot pimpleback and the rough pigtoe. Before the government acted, there were fewer of these slimy beasties than the government thought tolerable. They say there are now, because of the Act, just the right number of them.

How many of each species should there be? What a strange question! Why should you worry about that? The government, using a formula so secret that no civilian has ever seen it, has calculated the ideal number of every species which roots, crawls, burrows, swims, floats, flies, or flowers.

“How could they know that?” you might ask. “It’s like the government saying they know the ideal global average temperature and world-wide pattern of climate and weather.”

You have a point, friend. But I for one am more trusting than you. Our government is manned by experts who, by virtue of their appointment, are virtuous and disinterested. If they say they know just how many of each species there should be and where the members of those species should live (and at what temperature), then I am prepared to believe them.

A complication: new species are being discovered at a constant clip. How is it that, as scientific as we are, an animal as large as the Tapirus kabomani (about the size of a golden retriever) had to wait until last week to be spotted?

I bet the government already knows the proper number of these tapirs.

Some bad news: if we haven’t discovered all species, it’s therefore likely we will discover some after it’s too late and they’re already extinct. Looks like we’re going to need some stronger laws to prevent these situations.

How many species need our welfare? I had a go at counting, but the government’s websites are strangely not so good. Near as I can tell, it’s somewhere north of 1,500 just in the USA, another 600+ in distant lands. Must take a lot of paperwork to track.

What’s this about counterfactual arguments? The government claims it “saved” “hundreds” of species from extinction, that if it did nothing, these species would have gone extinct. But how can the government know this? It couldn’t have run an experiment. It’s possible these species could have increased without intervention. Worse, other species could have gone extinct because of the government’s actions. Beyond the obvious positive effect of arresting nutballs who shoot bald eagles, there’s no way to prove how efficacious the Act was.

That’s the problem with counterfactual arguments. The side which wins them is usually that which yells the loudest.

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