fixed points in data

For far too long now, whenever someone shares my “graphics matter” series of posts, someone pipes up with a response that can be summarized as:

“We don’t know how many firearms there are in America, so we cannot draw any correlation or causation conclusions between firearms and the people they kill.”

It is time I address this notion.

The first phrase of the sentence is actually correct.  Not only are firearms a durable good – meaning that firearms produced before the Revolutionary War could still be used today so long as they were properly maintained – but national registration of non-NFA-regulated firearms is outlawed by the Firearm Owners Protection Act.

As well it should be – the government simply has no business knowing what I own.

“But that means the second phrase of the sentence has to be correct, right?”

Well, no.

The entire point of the “graphics matter” series is to examine the correlation of the number of firearms in America with the number of firearm-related fatalities or crimes in America, as well as the per-population rate of the same.  The fun thing about correlating two data sets is that you do not need to know their starting points.

“Wait, what?”

It is one of the fundamental aspects of correlation, really. “Positive correlation” means that “as data set A increases, data set B also increases”. “Negative correlation” means that “as data set A increases, data set B also decreases”.

(An important distinction I want to make before moving on is that this does not mean A’s increase causes B’s increase, or vice versa, or anything of the sort.  The world is full of correlations that have no causal relationship with one another.)

The reason the definitions are significant is this – you are looking at the rate of change. The “slope”, for those of you who remember… what was that, high school algebra?

But rate of change – slope – is determined between two points, and is completely independent of Y-intercept, or any starting point. As long as point 1 is separate from point 2 by the expected difference, it doesn’t actually matter what the individual values are.

In other words, the slope between the X/Y data points of 1/100 and 2/200, and the slope between the X/Y data points of 1/0 and 2/100 are exactly the same, despite the values being different.

It is kind of whacky to think about, but in most-basic terms, 2x+10 has the same slope as 2x+100, but entirely different values, and both correlate against 4x in exactly the same way (they both have a correlation value of 1 with respect to 4x).

In fact, since this is a graphically-related site, let us look at an example.

Here we have a plot of 2X + 10, 2X + 100, 4X, and X raised to the power of 1.5 over time.

As I mentioned above, both 2X + 10 and 2X + 100 correlate to 4X with a coefficient of 1, meaning that as the first two equations increase, the third equation also increases, and the ratio of the increases is always the same.  This makes sense – all three are straight lines, meaning their slope is constant along their lengths, so comparisons between those slopes will always be equal.

However, both of the first two equations correlate with X^1.5 with a coefficient of 0.99052.  Why?  Well, the slope of the fourth equation changes over time, since it involves a power.  The first two equations do not have the pronounced curve of the fourth, so their growth does not mirror the fourth’s growth, no matter how different that growth might be (as when comparing the first two equations with the third).  However, all three equations are increasing over time, hence their very strong correlation (coefficients can range from 1 to -1).

But the point – that I am perhaps belaboring – is that the first two equations have the exact same correlation with any other equation or line you care to throw on the chart with them.

Why does this matter?

We really do not have any idea how many firearms are in America.  We never will.  I use the 2003 Small Arms Survey as the basis for my “graphics matter” series because it was the most-current when I started the post series, and changing reference points midway through is generally bad.

But I literally could have started in 1981 with the (atrociously flawed) assumption that there were no firearms in America, and the math would still work out exactly the same.

“Uh… why?”

We will never know how many firearms there are in America at any given time, but we do have a very accurate accounting of how many firearms are produced and imported into the country every year.  The BATFE’s Firearms Commerce in the United States Annual Statistical Update provides us that data back to 1986, and then the Shooting Industry News covers the remainder.  How can this be so accurate?  National registries may be outlawed, but all new firearms commercially produced must be uniquely serialized, and must be declared to the BATFE at the end of the year.  The penalties for “fudging” numbers are… severe.

We have the yearly production data.  Which means we have the rate of change – the slope.

Likewise, we have a… noticeably less-accurate, but still-considered-reliable accounting of the American population and the number of Americans who were killed by other people using firearms at the CDC WISQARS Fatal Injury Report.  I refer to this as “less-accurate”, because I have personally witnessed the CDC correcting data five years past; while I would prefer accurate data over leaving the inaccurate data, it annoys me that, for example, they got the American population wrong by 300,000 residents in one year.

Having to go back and update my data aside, we have the yearly numbers of firearm-related fatalities, which means we can calculate the rate of change.

In other words, I – or you – can compare the two-year-paired slopes for each of those data sets, or the average slope as a whole, or any other combination, and it simply does not matter where the firearms data started.  Only the differences between each year’s data matters, and we have those differences tallied by “authoritative” sources.

Feel free to play with the situation yourself; I have uploaded the spreadsheet for the above graphic, and you can fiddle with the numbers to see how things change.

We genuinely have no idea how many firearms there are in America, and that is fine.  We do know how many have been produced a year for the past ~35 years, and the only correlation between the change in firearms in America and the change in firearm-related fatalities is negative-to-non-existent, for both raw numbers and per-American rates.  Thus, “more guns = more deaths” cannot be true.

“just another law”?

Now that school shootings are back in the news again, “gun control” extremists are predictably clamoring for additional laws to be put into place to “prevent” things like this.  Frequently, they have no idea what laws are presently on the books – or even how many present laws we have – but are absolutely convinced that one more will do the trick.

Here is the thing, though.

In 1933, in this very country, a teenager with enough money could literally mail-order a fully-automatic Thompson submachine gun to their very door.  This is the very firearm that was used by United States troops during World War II, gangsters and police during the Prohibition, and, yes, average American citizens who wanted them.

Again, delivered to his door.

No paperwork.

No records (aside from whatever logs the retailer kept).

No background check.

No FFL.

No 4473.

Nothing more than two peaceful Americans engaging in mutually-beneficial commerce, and thereby exercising at least three basic rights – the right to self defense, the right to own property, and the right to enter into contractual agreements with others.

Why did I choose 1933 as a seemingly arbitrary date?

Well, in 1934, everything started to change.

First came the National Firearms Act.  Then came the Federal Firearms Act, the Gun Control Act of 1968, the Omnibus Crime Control and Safe Streets Act of 1968, the Hughes Amendment to the Firearm Owners Protection Act, the Undetectable Firearms Act, the Gun-Free School Zones Act of 1990, the Brady Handgun Violence Prevention Act, the Gun-Free Schools Act of 1994, various executive orders penned by President Clinton, the activation of the National Instant Criminal Background Check System, the agreement between Smith & Wesson and the Department of Housing and Urban Development, the Child Safety Lock Act, and the NICS Improvement Amendments Act.

That is quite the list, is it not?

Since 1934 with the NFA, those are all the major federal firearm regulations that were enacted (with the exclusion of the Assault Weapon Ban, which was not renewed and thus omitted), and specifically those intended to keep firearms out of schools.

Before we even talk about additional laws to prevent school shootings, we should at least examine how the previous ones are doing.

Unfortunately, thanks to “gun control” organizations repeatedly lying about school shootings, it is rather difficult to build a full picture.  No US law enforcement agency has a universal definition of what constitutes a “school shooting” or even a “mass shooting”, unlike “mass murder” which is defined by the FBI as “a number of murders (four or more) occurring during the same incident, with no distinctive time period between the murders”.

So, while I hate to do this, I am going to use Wikipedia as a primary source for the number of school shootings over history.  I have not yet dug through all of their references to cross-check every single shooting they note, but given that they are presently at 569 references and climbing, I may never.  As such, I make no claims as to the veracity or accuracy of the data, and I exclusively accept it for the purposes of debate.

Ok, so with all these laws in place – and with unlicensed individuals bringing loaded firearms to schools being doubly illegal by way of the GFSZA and GFSA – surely these laws have been decreasing the number of shootings, yes?

… Huh.

It almost seems like the number of laws and the school shootings directly correlate.  (Note, I am not claiming causality, in either direction – as always, correlation is not causation.)

In fact, it almost looks like those laws have accomplished… a lot of nothing.

Now, yes, there is absolutely the argument that “school shootings could be worse if we didn’t have those laws”, and it is a valid argument.  The trick is this: the only way to control for whatever impact those laws may be having is to repeal them and see what happens.  School shootings go up?  The argument could be made that the laws were doing something.  School shootings stay the same or drop?  Well… the laws were not helping, so why do we have them?

And that is part of the problem – “gun control” extremists never talk about repealing anything.  In fact, the current debate about affording teachers the choice to concealed-carry firearms – should they so desire – is immediately turned around by them and reframed as, “No one should be forced to carry a firearm!”  No pro-rights advocate is talking about forcing anyone to do anything; we are just asking that we stop forcing them to not carry.

The unfortunate reality is that when school boards are intentionally sweeping violent and dangerous students under the rug so as to improve the public perception of their district, “more laws” is a wholly inadequate response.  When the FBI was tipped off twice with regards to a school shooter and sat on the information, “more laws” will not matter.  When school shooters have documented histories of holding firearms to other people’s heads and no one does anything, “more laws” are strictly a “feel good” measure.

Absolutely no one wants to see children murdered.  We already have so many laws that do not appear to be accomplishing much of anything aside from unjustly limiting peaceful Americans’ rights; passing more knee-jerk laws born out of an emotional response is not the way to prevent those murders.