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firearms policy

The Theoretical Lethality Index is useful for military history but not for gun control policy

Professors Miller and Tucker miss the mark, while Saul Cornell disdains accuracy


An article by Duke law professor Darrell A.H. Miller and Wesleyan history professor Jennifer Tucker argues that gun control laws should vary based on the dangerousness of the firearm. They claim that danger is easy to assess by using the Theoretical Lethality Index (TLI), a metric developed in the early 1960s by military history analyst Trevor Dupuy. In this post, I explain why the TLI is useless as a guideline for the risks posed by different types of firearms in a nonmilitary context.

On the other hand, if TLI is valid in the civilian context, then the TLIs of modern firearms are not much different from those of a good rifle from the early 20th century. Thus, the level of gun control necessary from modern arms would not appear to be greater than the level of gun control in the early 20th century.

This post proceeds as follows:

  • Part I of the post briefly summarizes the Miller and Tucker article for the U.C. Davis Law Review.
  • Part II describes how gun control enthusiast Saul Cornell misused a blog post by Miller to fabricate preposterous claims about the lethality of AR rifles.
  • Part III examines the Theoretical Lethality Index in depth and explains why its military-oriented metrics do not provide useful information in a nonmilitary context about the relative dangerousness of different types of firearms.
  • Part IV calculates TLIs for the common modern firearms mentioned by Miller and Tucker: the 9mm handgun, and the semiautomatic AR rifle. ("AR" means "ArmaLite Rifle." The rifle was invented by ArmaLite in the 1950s.)
  • Part V addresses Miller and Tucker's claim that the American Founders were unfamiliar with dramatic technological changes in firearms — a claim that is refuted by Dupuy's data.

I. The Miller and Tucker article

Last Spring, the Giffords Law Center (a legal organization dedicated to gun control) and the U.C. Davis Law School held a symposium for gun control advocates. Among the articles published was one by Miller and Tucker. Common Use, Lineage, and Lethality, 55 U.C. Davis L. Rev. 2495 (2022). They argued that more lethal guns should be regulated more strictly than relatively less lethal guns. This post does not criticize or endorse that argument. According to Miller and Tucker, the relative dangers of different firearms are easy to quantify by using the Theoretical Lethality Index created by Trevor Dupuy. The Miller and Tucker article included a copy of a TLI table from one of Dupuy's books. Below is the same table, from the 1980 edition of Dupuy's book The Evolution of Weapons and Warfare. (My page cites, below, are to the Da Capo Press reprint of the 1984 edition.)

Dupuy created the TLI "as part of a study for the US Army: Historical Trends Related to Weapons Lethality (McLean, VA: 1966)." Trevor N. Dupuy, Understanding War: History and Theory of Combat 289 (1987). Although Dupuy is deceased, his website contains a bibliography of his prolific writing. According to the website, that "study, performed for the US Army, analyzes the relationship between weapons and military doctrine from the 4th Century BC to the end of the Korean War. The study focuses on revolutionary advances in the lethality of weapons and the impact of this increased lethality on battle losses and battle outcome. The process of introduction and assimilation of these new weapons is described." The Historical Trends report was revised and improved into Dupuy's 1980 book The Evolution of Weapons and Warfare.

The TLI number for "18th century flintlock" (the most common firearm type when the Second Amendment was ratified in 1791) is 43. The TLI for the standard American service rifle in the early 20th century, the 1903 bolt action Springfield rifle, is 495. Thus, the TLI of the standard American service firearm as of 1910 was about 11 times greater than the TLI of a standard service firearm in 1791.

These figures are relatively small compared to the massive lethality of a World War I machine gun (e.g., the Maxim gun), with a TLI of 3,463. All the more so for a World War II machine gun (e.g., the .50 caliber M2), with a TLI of 4,973. The TLI of a WWII machine gun is 115 times that of a flintlock. The TLI of a WWI machine gun is 80 times that of a flintlock.

Miller and Tucker did not attempt to calculate the TLI of any modern firearms. In a footnote, they wrote, "Situating the modern AR-15 (a successor to the German StG 44, the first 'assault rifle,' that was used in World War 2) anywhere near the Maxim machine gun makes it exponentially more lethal than the flintlock musket of the Founder's era."

This is true. The exponent to get from 43 to 3,463 is about 2.1651. Prudently, Miller and Tucker did not claim that an AR-15 actually should be "situated" near a WWI machine gun. Nor did Miller and Tucker make any other claim about the TLI of an AR semiautomatic or of any arm not listed in the TLI table above.

As will be detailed in Part IV, to the limited extent that TLI can be estimated for arms that Dupuy did not study, the TLI of an AR semiautomatic rifle is not even close to a Maxim gun. Instead, AR is a not very far above that of the 1903 Springfield rifle.

Miller wrote a blog post for the Duke Center for Firearms Law summarizing his article for the Giffords symposium, and other articles in the symposium. The post included a copy of the TLI table above.

II. Saul Cornell makes it up

Fordham history professor Saul Cornell writes for Slate magazine. On May 19, 2022, Cornell penned an article castigating in advance the Supreme Court for being likely to uphold the right to bear arms in the case New York State Rifle & Pistol Association v. Bruen. (As the Court in fact did, when the Bruen opinion was announced in late June.) The Horror in New York State Shows the Madness of the Supreme Court's Looming Gun Decision, Slate, May 19, 2022.

On May 14, a criminal with an AR rifle had murdered 10 people at a supermarket in Buffalo. A month before, a criminal with a Glock 9mm handgun had injured 23 people on a New York City subway. Cornell's opening paragraph called both guns "firearms whose lethality would have been unimaginable to the authors of the Second Amendment."

Cornell's second paragraph stated that "research from U.C. Davis" showed that the Buffalo criminal's rifle was "200 times" deadlier than an old-fashioned flintlock. For support, Cornell linked to Miller's blog post.

Several days later, National Review writer Kevin Williamson criticized Cornell's "200 times" claim. Saul Cornell's Preposterous Rifle Claims, National Review Online, May 24, 2022. Williamson did not make any arguments about gun control policy. He simply detailed the absurdity of Cornell's assertion that an AR semiautomatic is about twice as lethal as a World War II machine gun. For example, the AR has a much shorter range, fires far more slowly, and use a much smaller bullet than an M2 machine gun.

The next morning, May 25, Williamson wrote a follow-up article. A Little More Saul Cornell, National Review Online, May 25, 2022, 9:53 AM:

Saul Cornell, who is a professor of history when he is not writing for Slate, is engaged in intellectual dishonesty. He claims, as I note below, that a 1964 study of firearms lethality says something that it does not say (and, indeed, that it could not say, given its date of publication) in the course of trying to make modern sporting rifles sound scary for cheap propaganda purposes. Saul Cornell knows that this is false, and I know that he knows this is false, because I have told him, and he has acknowledged the fact in emails to me.

But the claim remains unretracted. Retracting the claim would mean admitting that the source he cites not only does not say what he says it says about AR-style rifles, but that it in fact does not say anything about those rifles at all.

Honest mistakes happen all the time in journalism. This is not one of those. This is a fabrication.

Williamson wrote another article on the afternoon of May 25. A Gun-Control Advocate and His Fabricated 'Facts', National Review Online, May 25, 2022. 3:02 PM:

When I asked Professor Cornell about this, he responded that he had used World War II–era machine guns as a stand-in for modern AR-style rifles. Which is to say, Professor Cornell's own explanation of this discrepancy is that he was willfully misrepresenting the data in the Dupuy study. World War II–era machine guns came in many different varieties, but all of them were, by definition, fully automatic weapons, and practically all of them fired cartridges that were far more powerful than the 5.56mm NATO round used in most AR-style rifles. For perspective, these weapons were used against light-armored vehicles and aircraft as well as against infantrymen — they were vastly more powerful than a modern sporting rifle.

When I called attention to this, Professor Cornell conceded that it had been a mistake to use World War II–era machine guns as a stand-in for AR-style rifles, and added that he should have instead used the 1903 Springfield rifle, which, by his estimate, would produce the much lower figure of 10x lethality for the AR-style rifle rather than 200x … I will happily provide the entire email conversation to the editors of Slate or to Fordham if either institution should ever stir itself to take an interest in this intellectual dishonesty.

But Professor Cornell's explanation, self-indicting though it is, still doesn't make sense: Substituting the World War II–era machine guns for the AR-style rifle, as he says he did, still would not produce that figure of 200x lethality. When I asked him about this, he replied that "this was all done quickly and I can't reconstruct the process I used to come up with the figure based on my computer drafts."

In response to my criticism, Slate has appended a correction to the article, which now says that the problem was an "extrapolation" error and that the real number is something like 50x. How that figure was arrived at is anybody's guess, given that Professor Cornell doesn't know how he arrived at the earlier one, but the most relevant point is that this explanation is a lie.

There was no extrapolation error, because there was no extrapolation, because there was nothing from which to extrapolate. The matter of AR-style rifles simply is not considered in the study, and there isn't anything comparable from which to extrapolate. This is just Professor Cornell assigning an arbitrary number to his subjective assessment — the subjective assessment of a not especially well-informed academic who as of Wednesday morning did not, by his own account, appreciate the difference between firearms that are used to shoot squirrels in 2022 and those that were used to shoot down airplanes in World War II.

Like any other working journalist, I have made arithmetic errors and misunderstood statistics. What should be emphasized here is not that Professor Cornell produced the wrong number but that he simply made up a number and then attributed it to a study that says nothing at all about the thing he claims it characterizes. The number could have been 10x, 10,000x, or pi times the radius squared — any figure would have been equally fictitious.

I have a good deal of experience in writing about bias in gun-policy journalism. But this is not bias — it is fabrication. Here we have a professor at a major university writing an article in a major media outlet on the subject of a very contentious public-policy matter, and the first claim of fact in the piece is simply made up in order to bolster a weak argument made by a writer who believed — with good reason, apparently — that he could count on the bias and laziness of his editors and the stupidity of his readers to permit the fabrication to go undetected and unchallenged. This is precisely the sort of thing that undermines confidence in our journalistic institutions and fuels conspiracy-theory nonsense. If our institutions do not have enough self-respect to stand up for their own values, then who is going to do it for them?

We need honest journalists and honest academics. The Paul and Diane Guenther Chair in American History at Fordham University is not one of them.

The Slate article was corrected as follows:

Correction, May 25, 2022: This article originally misstated that an AR-15 is 200 times more deadly than Revolutionary War–era rifles. Based on an extrapolation from a research study, the ratio is more like 50.

The correction included no explanation of how the "extrapolation" of "50" was created.

Recall that Williamson's criticisms of Cornell's fabrications had said nothing about gun control policy. Williamson had simply pointed out that Cornell was making up his figures of "200" or "50." Here is Cornell's response to Williamson. The Right Found a New Way to Not Talk About a School Shooting, Slate, May 25, 2022, 4:46 PM.

[G]un rights activists would rather point to distractions instead of dealing with the issue before us. Despite being handed one legal and political victory after another, they continue to vent outrage and venom, eschewing reasoned debate and carrying forward the grievance culture that animates so much right-wing thought in America. This is readily demonstrated by Kevin Williamson of National Review, responding to Tuesday's [Uvalde] massacre by writing a nearly 700-word article about a minor factual error I made in a recent article, which Slate has since corrected.

The mistake was in an extrapolation that I made from an academic study to determine how much more powerful modern weapons were than Revolutionary War–era muskets. The study I briefly referenced did not discuss the AR-15, so I hypothesized based on this research that these guns were 200 times more lethal than the muskets used in the founding era. It turns out that the number is more likely closer to 50 times as deadly.

Working out of the lethality index developed early in the Vietnam War era, a better comparison would have been to suggest that modern weapons are more like 20 to 50 times as deadly as what founding-era soldiers would use, rather than 200.

Williamson's myopic response highlights the moral bankruptcy of his distorted and supersized vision of the Second Amendment.

If you address the madness of gun violence in America, then you have to acknowledge the intellectual and moral shallowness of the gun rights position adopted by Williamson and others of his ilk.

I think Kevin Williamson has given us a brief tutorial about why gun rights culture, a radical but vocal fringe element of gun owners, has effectively poisoned the well of public discourse on this issue.

That Cornell lied repeatedly about the TLI does not necessarily mean that the TLI is invalid. So let us return to the work of professors who did not lie about the TLI, namely professors Miller and Tucker.

III. The uses and limits of the TLI

A. The TLI formula

According to Dupuy, theoretical lethality indices "provide a basis for (a) selecting significant weapons developments in history for special analysis, and (b) relating weapon lethality to tactical dispersion and mobility for analytical purposes." Dupuy, Evolution, at 340.

Another book by Dupuy, Understanding War, presents his Theoretical Lethality Index as one element in a much more complicated metric, the Quantitative Judgement Method (QJM). The QJM is used to predict which side will prevail in military combat. It accounts for elements such as surprise, dispersion, terrain, and so on. The methods of calculation are described in Dupuy's book Numbers, Predictions, and War: Using History to Evaluate Combat Factors and Predict the Outcome of Battles (1979). Miller and Tucker do not cite this book, nor do they describe the TLI formula.

For hand-carried weapons such as spears, bows, or firearms, there are six factors in a TLI calculation. The TLIs for some other weapons, such as tanks, include factors in addition to the basic six. The total number of elements in calculating QJM (who will win a battle) is 73. The QJM factors include various aspects of terrain, fortification, surprise, soldier quality, and so on. Id. at 33.

Here are the data that Dupuy used to calculate TLIs, in Figure 2-3, pages 26-27, of his Numbers book:

The basic Theoretical Lethality Index is created by multiplying the following:

RF = Rate of Fire. This is not the theoretical rate of fire, but rather how many times a weapon can realistically be fired in an hour of combat.

R = Reliability. This accounts for the possibility that a weapon might malfunction. A perfect score is 1.0. In Dupuy's Figure 2-3 from Numbers, the reliability of a sword is 1.0. That is, you can assume that a sword is never going to malfunction. (Swords do break, but all of Dupuy's calculations are broad generalities.) Some other reliability figures are: English long bow .95; 17th century musket .55; 18th century flintlock .65; Springfield model 1903 rifle .95.

Rn = Range. This is calculated as follows. Assume that a weapon's effective range is 90% of its theoretical maximum range. (Unless there are other specific data on effective range.) Divide the effective range, in meters, by 1,000. Take the square root. Add 1. This is the Range Effect factor. So, per the Figure 2-3, Range Effects are as follows: Sword, range 1 meter, range effect = 1.03. English longbow, range 200 meters, range effect = 1.45. 17th century musket, range 150 meters, range effect = 1.39. 18th century flintlock, range 200 meters, range effect = 1.45. Mid-19th century rifle with conoidal bullets (that is, bullet that are not spheres, but instead have a cone-like shape), range 2,000 meters, range factor = 2.41. Springfield model 1903 bolt action rifle, range 2,000 meters, range factor = 2.41.

A = Accuracy. A subjective assessment. A 1.0 would be perfect. Dupuy gave the sword and the English longbow a .95. The 17th century musket was .55, and the 18th century flintlock was .65. An early 19th century rifle was .9, and the Springfield 1903 rifle was .95.

C = Number of targets per strike. For any firearm, sword, bow, etc., this is 1. Artillery weapons, such as cannons or howitzers, have a higher number.

RE = Relative effectiveness. Weapons vary in the probability that a hit will take the target out of the fight. With 1.0 being perfect, Dupuy assigned RE values as: sword .4; longbow .5, 17th century musket .6; 18th century flintlock .7; early 19th century rifle .8. From the early 19th century onward, no firearm has a relative effectiveness greater than .8.

Dupuy's Theoretical Lethality Index "compares the relative lethality of weapons against a theoretical target array of unarmored soldiers, standing on an infinite plane surface, each occupying one square meter of space." Dupuy, Understanding War, at 83. In other words, per the TLI table above, a soldier with a 17th century matchlock could theoretically kill 19 enemy soldiers per hour, whereas a soldier with an 18th century flintlock could kill 43.

In the Quantitative Judgement Method, the next step in the analysis is to adjust the TLI for factors affecting the other side, starting with dispersion. For example, because of area effects of artillery in the past two centuries, modern soldiers are much more dispersed than previously. They don't typically stand one meter apart, as they did in the olden days.

Dupuy's calculations and analysis provide a fascinating view of warfare from ancient times through the majority of the twentieth century. Because Dupuy focused on the most important changes in weaponry, he did not provide calculated figures on all sorts of arms. The firearms in the TLI table begin with the Spanish matchlock arquebus (a huge handgun) in the sixteenth century. The seventh firearm listed is the 1903 bolt action, magazine-fed Springfield rifle. After that, Dupuy considers only two other firearms worthy of TLI calculation: the machine guns of the First and Second World Wars.

From the arquebus to the Springfield 1903, Dupuy calculated a TLI for seven firearms that were very common infantry firearms. As for the common infantry firearms thereafter, Dupuy did not bother to calculate a TLI. Instead, his only calculated TLIs for post-1903 firearms were for WWI Maxim machine gun and their WWII successors. These guns were not the typical arms carried by a standard soldier.

While common infantry arms improved over the course of the 20th century, Dupuy apparently believed that the progress since 1903 did not make a big difference in the broad historical perspective.

Given that post-1903 improvements in non-machine gun firearms were not worthy of notice, figuring out a TLI for modern firearms is not simple. Miller and Tucker write:

Military experts must extrapolate from Dupuy's methods to say what the theoretical lethality index of a modern 9mm pistol would be, for example. Non-experts, or those without access to the proprietary methods of the Dupuy Institute, can only provide  estimates about where modern technology fit (a modern AR-15 is almost certainly more lethal than an eighteenth century musket and less lethal than a World War II medium tank, for instance). (p.2513).

Following Miller and Tucker's suggestion to extrapolate TLIs for 21st century arms involves a lot of guesswork. Some of the items in the TLI table are composites, such as "World War II machine gun" or "Eighteenth century flintlock." There were a tremendous variety of both.

Only two items on the table resemble modern firearms in common use. The "Late Nineteenth Century Breech-Loading Rifle" is exemplified by standard U.S. Army single-shot firearms such as the Springfield 1880. This is a starting point for extrapolating TLIs for other single-shot guns.

Also in Dupuy's TLI table is the Springfield 1903 bolt action magazine-fed rifle. Therefore, the Springfield 1903 is the only base for extrapolating TLIs of modern repeating firearms;  the vast majority of modern firearms are repeaters.

In Part IV, I will follow the Miller and Tucker suggestion, and attempt to extrapolate from the 1903 Springfield to calculate a TLI for the AR semiautomatic rifle and for a 9mm handgun. To the very limited extent that extrapolation is valid, the results contradict the Miller and Tucker theory that the firearms of 2022 are tremendously more lethal than the firearms of the turn of the previous century.

B. The TLI has virtually no relation to a firearm's dangerousness in a civilian context.

Miller and Tucker write that "the TLI number is not influenced by a military or civilian context." (p. 2506). The statement is true in the sense that TLI formula can be applied to any given arm. However, in practice the TLI does not at all predict which firearms are the most dangerous in a civilian context.

Empirically, the most dangerous civilian arms are those that kill the most people. According to the FBI's Uniform Crime Reports for 2021, the types of weapons used in murders that year were:

  • Handguns 6,012.
  • Firearms, type not stated 4,740.
  • Other weapons or weapons not stated 1,059.
  • Knives or cutting instruments 1,035.
  • Personal weapons (hands/fists/feet) 461.
  • Rifles 447.
  • Other guns 277.
  • Blunt objects (clubs, hammers, etc.) 243.
  • Shotgun 152.
  • Narcotics 117.
  • Fire 73.
  • Asphyxiation 55.

Although all of the above arms have military applications today, Dupuy's analysis of modern combat pays virtually no attention to handguns or shotguns, which are short range arms that have little impact on most battles. Likewise, contact weapons, such as blades or clubs, were important in what Dupuy calls "The Age of Muscle," but comparatively insignificant in "The Age of Gunpowder" and then "The Age of Technological Change."

In a modern military context, rifles are much more lethal than knives or handguns. But in the civilian context — with danger measured by murders — rifles are much less dangerous than knives or handguns.

As Miller and Tucker point out, the TLI of rifles soared starting in the 1850s when spherical bullets were replaced with conoidal ones. According to Dupuy, the conoidal bullet changed warfare because of its vastly better greater range and accuracy. The conoidal shape greatly improves a bullet's aerodynamic stability, making the bullet relatively less susceptible to air friction and gravity. In the Civil War, the conoidal bullet meant that rifles had a range equal to the artillery of time. Which meant that riflemen could shoot at enemy artillery batteries, "with results severely damaging to the performance of artillery and the health of artillerymen." Dupuy, Understanding War, at 203. "No other technological change in weaponry, before or since, has had a comparable, directly discernable, immediate effect on the battlefield." Id. at 201. So during the Civil War, the relative effectiveness of artillery in combat was much reduced compared to earlier times. Subsequently, improvements in artillery allowed artillery to be deployed further back, out of range of enemy firearms, and artillery reclaimed its former importance. Dupuy, Evolution, at 170, 191, 292-93, 318.

With the conoidal bullet, we see how the TLI measures combat effects, not civilian self-defense or criminal gun misuse. A shot from a conoidal bullet of the 1860s was not substantially more likely to be incapacitating than a shot from a spherical bullet of half a century before. According to Dupuy, the "relative effectiveness" of all long gun bullets since the early 19th century has been a constant 0.8.

The conoidal bullet changed everything not because of its lethality, but because of its range. In the TLI, the 1850s rifle with a conoidal bullet has a range factor of 2.41, compared to the 1.74 of its predecessor half a century before with a spherical bullet. Dupuy, Numbers, at 26.

So range is hugely important in the TLI, as it is in military combat. Range also makes a big difference in hunting. But for civilian gun crime or defensive gun use, extra range is much less important. The overwhelming majority of such encounters take place at distances of 50 feet or less, most often under 10 feet.

The only formal data on the subject are the FBI's "Law Enforcement Officers Feloniously Killed." According to the 2019 data, of the 33 LEO homicides for which distance data are known, 31 were at distances under 50 feet. Of those 31, there were 23 at 10 feet or less. For homicides for which the type of gun was known, 34 were by handgun, 7 by rifle, and 1 by shotgun.

Again, the firearms that in practice are most dangerous in a civilian context (handguns) are very different from the firearms with the highest TLIs (rifles).

Miller and Tucker write:

[I]f one believes that right metric for self-defense weaponry is that kind of defensive armament most effective at countering a typical criminal threat, the TLI offers a number. How many people per hour is it necessary to kill in order to supply an adequate deterrent to common criminal perpetrators? (p. 2512).

The question demonstrates the absurdity of using TLI as a civilian defensive metric. While many military battles last an hour or more, typical civilian defensive shootings are over in a matter of seconds or minutes.

The relevant question for civilian self-defense is whether a firearm provides the ability to incapacitate every one of the criminals who is attacking the victim. The answer would take into account the fact that most defensive shots, whether by law enforcement officers or others, are misses, and that most hits do not instantly incapacitate.

IV. Extrapolating from the TLI

I agree with Kevin Williamson that extrapolations about 21st century firearms from the TLI table are dubious. With that caveat, as an intellectual exercise I will attempt to follow the Miller and Tucker suggestions to extrapolate TLI for a semiautomatic AR platform rifle and for a semiautomatic 9mm handgun.

As Saul Cornell acknowledged to Kevin Williamson, the closest comparator to an AR from Dupuy's table is the 1903 Springfield bolt action magazine-fed rifle. The TLI for that rifle is 493, eleven times that of an 18th century flintlock.

Springfield bolt action rifles and their venerable .30-'06 cartridge are among the most common American civilian firearms, with countless variants from different manufacturers. Such guns are still very popular today. Old Uncle Fred's favorite deer rifle is reasonably likely to be a close relative of the Springfield 1903.

During World War II, the U.S. Army became the first army in the world to begin issuing semiautomatic rifles to ordinary infantry troops. The most precise data come from 1940 tests by the Marine Corps, pitting the 1903 bolt action Springfield against the semiautomatic M1 Garand, as well as semiautomatics made by Johnson and by Winchester. The latter two were judged by the Marines to be overall inferior to the Garand.

All the Marines in the test were trained and fit. Some were new soldiers who had qualified at the "sharpshooter" level. Others were experienced veterans and expert shots. All the data about the tests are in Julian S. Hatcher, The Book of the Garand: Development of Semiautomatic Rifles 142-53 (2012 reprint, 1st pub. 1948).

The table below presents the average number of "hits per minute" for tests at various ranges and targets. Hits per minute combines rate of fire and accuracy. Because the Garand, like all semiautomatic firearms, reduces felt recoil to the shooter, users of the Garand did not suffer notable fatigue during the five-minute course of fire, whereas users of the Springfield bolt action did. The hits per minute reflect the ergonomic superiority of the Garand.

Test Springfield 1903 hits per minute M1 hits per minute Hits per minute superiority of the Garand
Stationary targets, mean distance 325 yds. 3.85 4.23 10%
Moving targets, mean distance 300 yds. 10.20 12.85 26%
Same as above, but larger target, size of a combat vehicle 3.27 3.54 8%
Average Garand superiority 14.67%


As for reliability, under "Fair to Ideal Conditions," the tests showed that "all rifles performed with very few malfunctions." Hatcher at 349. Under tests for various adverse conditions, such as lengthy intermittent rain or heavy dust, the bolt action Springfield was much less likely to malfunction than the semiautomatics; of the semiautos, the Garand was the most resilient.

In the "Endurance and Fatigue" test, twelve thousand rounds were fired through rifles, with periodic cleaning and lubrication. Over the course of the 12,000 rounds, an average Springfield bolt action would have 53 malfunctions, whereas an M1 Garand would have 370. The average number of parts broken, replaced, or repaired per rifle was 3.00 for the Springfield, and 12.25 for the Garand. The figures were 2 to 3 times worse for the other semiautomatics.

Thus, the semiautomatic M1 Garand was superior in practical firepower to the Springfield 1903, albeit less reliable under bad conditions or very heavy use. At the first major U.S. offensive action in World War II, the invasion of the Japanese-held island of Guadalcanal, Marines far preferred the Garand to the Springfield. Hatcher at 141-42.

All semiautomatics have a generally similar rate of fire. As the Marine tests showed, accuracy is affected by ergonomics. I don't know of any tests that have compared semiautomatic AR rifles to either the Springfield bolt action or to the semiautomatic Garand. For sake of argument, assume at the AR semiauto doubles the Garand's superiority over the Springfield. That would mean the AR has a 29.34% higher hits per minute rate than the Springfield.

Recall that the TLI for the 1903 Springfield is 11.47 times that of the 18th century flintlock. Give a semiautomatic a 29.34% bonus for rate of fire; then the TLI difference grows to 14.15 times. Also for sake of argument, we will not give the AR any reduction for reliability compared to the 1903 Springfield or the Garand. So a modern AR semiauto rifle would have a Theoretical Lethality Index about 14 times greater than an 18th century flintlock.

Regarding Miller and Tucker's proposal to extrapolate a TLI for a modern 9mm semiautomatic pistol, proceed as follows: all semiautomatics fire at nearly the same rate, so we will give a 9mm pistol the same 29.34% bonus for rate of fire.

As for range, modern handguns are puny compared to rifles. An excellent handgun shooter can be accurate at 50 yards. A hit at 100 yards would be a very fine shot indeed. According to Dupuy, the effective range of a Springfield 1903 was 2,000 meters. (This implies excellent sniping skills, akin to the marksman who can hit 100-yard targets with a handgun.) For sake of argument, say that the maximum effective range of a 9mm pistol is 200 meters. Thus, the range factor in Dupuy's formula is: [square root of (200/1,000)] + 1 = 1.45. Compared to the range of the Springfield 1903, which is 2.41.

So, start with the 1903 Springfield's TLI of 495. Multiply by 1.2934 (hypothesized hit rate advantage of a modern semiautomatic). Then multiply by (1.45/2.41) (range factor). The result is a TLI of 385.

Then adjust for relative effectiveness and accuracy. The Dupuy Numbers book does not provide calculated TLIs for modern firearms, but it does include some data for the intended benefit for wargame designers, namely some metrics for the Soviet firearms of the 1970s. In particular, the Makarov semiautomatic pistol and AK ("Avtomat Kalashnikov") rifles.

The figure below is from pages 226-27 of Dupuy's numbers book. He is calculating "Operational Lethality Index." This is a part of the Quantitative Judgement Method that follows calculations of a TLI. For our purposes, the figure is useful because Dupuy provides estimates on accuracy and relative incapacitating effect of handguns vs. rifles.

The caliber of a Makarov semiautomatic pistol, pervasive in the militaries of the Warsaw Pact, was 9 x 18mm, very close to the 9 x 19mm caliber typical in modern American semiautomatic handguns. The AK-47, and its variants such as the AKM, were automatic rifles. So their rate of fire was much higher than that of a semiautomatic. But for a more general rifle to handgun comparison, first consider accuracy: the handgun will have less because it has a shorter barrel. Second, consider relative effectiveness, i.e., stopping power. The handgun will have less because it has a shorter barrel, and therefore the bullet is propelled for less time by expanding gunpowder gas than is a rifle bullet. Thus the handgun bullet has lower velocity and less kinetic energy to transfer to the target.

According to Dupuy, the accuracy and the relative incapacitating effect of the semiautomatic Makarov pistol are .7 and .7. The same numbers for the AK rifle are .8 and .8. Hypothesizing that the accuracy and incapacitating effect of the AK rifle are generally similar to the 1903 Springfield, the final TLI for a 9mm semiautomatic pistol is: 385 x (.7/.8) x (.7/.8) = 295.

QED, the Theoretical Lethality Indices are as follows:

  • 18th century flintlock: 43.
  • 1903 Springfield bolt-action magazine-fed rifle: 495.
  • Modern AR semiautomatic rifle: 640.
  • Modern 9mm semiautomatic handgun: 295.

Bottom line: the TLI of a 9mm handgun is far below that of the 1903 Springfield, and the TLI of the AR rifle is not greatly above that of the Springfield.

This is consistent with Robert Held's 1957 thesis that "the age of firearms" came to an end in the late 19th century. The Age of Firearms (1957). Although manufacturing quality has always been improving, and small design refinements have been made, in the 20th century there were no major innovations in firearms. The firearm you own today is just an improved and more affordable version of types that your great-great grandparents could have bought in 1895. The only exception is for optics, thanks to lasers (now broadly affordable for most defenders) and computers (for long range hunting accuracy). The accuracy improvements of better optics would be barely noticeable on the grand scale of Dupuy's history of weapons.

V. The Founders were well aware of technological progress in firearms

Miller and Tucker write:

The Founders lived in a period when they could perhaps be forgiven for thinking that "a gun is a gun is a gun," because the basic flintlock hadn't really become significantly more lethal in the previous 150 or so years. If the Constitution had been written in the middle of the nineteenth century, instead of the 1780s, the Founders would have been much more aware of the pace of innovation. (p. 2511).

This is incorrect. The American colonists from Europe who arrived in the early 17th century came mainly with matchlocks. In a matchlock, pressing the trigger lowers a smoldering hemp cord to touch the gunpowder in the firing pan. Over the course of the century, Americans shifted to the more expensive flintlock. In a flintlock, pressing the trigger causes a sharpened flint (held in the gun's "jaws") to fall forward. The flint strikes a piece of metal, and the shower of sparks ignites the gunpowder in the firing pan.

Unlike matchlocks, flintlocks can be kept always-ready. There is no smoldering cord to give away the location of the user. Flintlocks are much more reliable than matchlocks, and all the more so in adverse weather. They are also simpler and faster to reload.

Americans made the shift from matchlocks to flintlocks sooner than did European armies or European civilians, because the flintlock was so vastly superior for use in the dense woods of the eastern seaboard, and for Indian fighting, which was very different from the rigidly organized, linear tactics of European warfare. For the same reasons, American Indians greatly preferred flintlocks to matchlocks. The TLI of a 17th century musket is 19 and the TLI of an 18th century flintlock is 43. So the transition of firearm type in the American colonies more than doubled the TLI. There is no reason to believe that the American Founders were ignorant of how much better their own firearms were compared to those of the early colonists.

The graph below from Dupuy's Numbers book shows changes in TLI over time. The scale is logarithmic. Examine the line for "Smoothbore Small Arms," in the lower right corner. A smoothbore is a gun whose interior, the bore, is smooth. Modern shotguns are smoothbores. Historically, the TLI for smoothbores starts off low, with the Spanish arquebus in the 1500s. By the early 1600s, when the American colonies were getting on their feet, the smoothbore's TLI is 19. Before the middle of the 1700s, the smoothbore TLI has risen to 100, and it plateaus thereafter.

Now look at the line "Rifled Small Arms" in the lower right corner. In a rifle, grooves are cut into the bore. The grooves make the bullet spin on its axis; thus the bullet is more aerodynamically stable, and can shoot accurately at longer distance. All rifles (by definition) and almost all modern handguns are rifled. In the graph, the rifle comes on stage in the early 1600s, when Swiss and German gunsmiths invented Jaeger rifles. Many German-speaking Protestant gunsmiths emigrated to America starting in the early 1700s, especially to Pennsylvania, thanks to that colony's offer of religious freedom. The TLI for rifles increases sharply from the early 17th century to the late 18th (the time of the Second Amendment). An absence of continuing improvements in firearms would have been unexpected to the American Founding generation.

Miller and Tucker are incorrect that "the basic flintlock hadn't really become significantly more lethal in the previous 150 or so years." As lovingly detailed by Robert Held in The Age of Firearms, the flintlock was continuously improved. The general appearance of a flintlock did not change much, but the small parts and the inside of the barrel (the bore) did.

When the Pilgrims established the Plymouth Colony in 1620, their military leader, Captain Myles Standish, was perhaps the first flintlock owner in North America. By the late 18th century, flintlocks were vastly better. For example, thanks to English gunsmith Henry Nock's 1787 newly patented flintlock breech, "the gun shot so hard and so fast that the very possibility of such performance had hitherto not even been imaginable." Held at 137.

As for repeating firearms, they had been invented two centuries before the Second Amendment. American gunsmiths had been making them since at least the 1720s. In 1777, during the American Revolution, inventor Joseph Belton demonstrated for General Horatio Gates and scientist David Rittenhouse a rifle that could fire sixteen rounds without reloading. The Continental Congress wanted to order a hundred, but the deal fell through because Belton's price was too high. While repeating firearms were well-known, the labor cost of manufacture made them unaffordable to the average person. Repeating firearms have more small internal parts than do single shot guns, and those parts must fit more precisely. In an artisanal age, a repeater was a special gun for a rich man.

The problem of manufacturing cost was ultimately solved, and the American Industrial Revolution begun, thanks to a program initiated during the presidency of James Madison, author of the Second Amendment. Congress began appropriating large sums to the federal armories at Springfield, Massachusetts, and Harpers Ferry, Virginia. The appropriations made it possible for inventors at those armories to invent machine tools (tools to make other tools), which eventually made possible the mass production of firearms with interchangeable parts.

The federal armories insisted that all discoveries be shared with private manufacturers, such as those in the Connecticut River Valley. And the private companies in the Springfield network had to share their own innovations. Nicknamed "Gun Valley," the Connecticut Valley was the Silicon Valley of its era, with job-hopping entrepreneurs and machinists disseminating and advancing new techniques of manufacture.

Even before that, the Lewis and Clark Expedition dispatched by Thomas Jefferson had carried an American-made version of the Girandoni air rifle. Originally invented for Austrian army snipers, the Girandoni was ballistically equal to a powder gun. It could take an elk and could fire 22 shots as fast as the user could pull the trigger. Citations and details for the above are in "The Evolution of Firearms Technology from the Sixteenth Century to the Twenty-First Century," which is chapter 23 of Firearms Law and the Second Amendment: Regulation, Rights, and Policy (Aspen Pub., 3d ed 2021), by Nicholas J. Johnson, David B. Kopel, George A. Mocsary, E. Gregory Wallace, & Donald E. Kilmer.

In short, the idea of continuing major technological progress in guns was familiar to the Founding generation. The Madison administration's industrial policy, starting in 1815, was intended to and did in fact set the stage for many advances in subsequent decades. Although James Madison is today extolled by "small government" advocates, his administration's subsidies for firearms manufacture innovation provided the foundation for the United States to become a global manufacturing powerhouse in the nineteenth century.


The Theoretical Lethality Index functions as intended; it is a useful metric for examining major historic changes in military arms. Extrapolating from the historic arms that Dupuy studied to present-day arms is questionable.

In my view, professors Miller and Tucker are incorrect in theory, because the TLI has no utility in assessing the relative dangers of modern firearms in a nonmilitary context. On the other hand, if Miller and Tucker are theoretically correct that TLI extrapolation is a useful guide to the dangers of modern firearms, the TLIs for AR rifles or for 9mm handguns are similar to or less than the TLI of the classic American early 20th century rifle. Thus, there is no need for gun controls beyond those that existed around the turn of the twentieth century. As for Professor Cornell's assertions that AR semiautomatic rifles are "50 times" or "200 times" more lethal than flintlock rifles, there was never any basis in fact.