Quantifying Lethality on the Back of a Napkin

July 09, 2019
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Lethality is one of the latest buzzwords to gain traction in the Department of Defense. It was quietly inserted into the department’s 2018 mission statement, and former Secretary of Defense James Mattis touted lethality as his number one line of effort while launching a Task Force focused on increasing it. But exactly what is lethality?

The textbook definition, according to the Oxford Dictionary, is:

Lethality, noun. The capacity to cause death or serious harm or damage. Example, 'the increasing lethality of modern weapons.'

Lethality is a subject of interest in various fields. Medical researchers, for example, use the term when evaluating how well an antiviral reduces the lethality of an infection, or when evaluating the outcomes of various suicide attempts; law enforcement personnel use it to express the deadliness of different types of criminal assaults. The common thread in all these definitions is, of course, the death of a person.

That said, there is little literature assessing what lethality means in a military context. As Mackenzie Eaglen of the American Enterprise Institute notes, "While lethality is intended as a driver for many decisions the force will undertake over the course of implementation, it is never explicitly defined." The Defense Department’s 2018 mission statement has disappeared completely from its website. What you will find is a trove of articles, 46 at last count, listed under the heading of “lethality.” And while some of these articles address serious issues related to lethality of the force, this buzzword has become so ubiquitous that under this heading you will also find articles on such topics as roadkill dinners, benefits of tax law changes, and a quiz featuring Santa in a fighter jet.

In one of the only articles we could find that attempted to provide a military definition for this term, Marine officer Olivia Garard didn’t offer a final definition, and she stopped short of giving an answer about how one would measure lethality. She wrote in a follow-up correspondence, “I wouldn’t measure it quantitatively at all. I would measure it by the success of one’s strategy to achieve political ends.”

The authors disagree.[1] We argue lethality can, and should be, defined, so it can be methodically improved. As Peter Drucker, widely hailed as the father of modern management, observed, “If you can’t measure it, you can’t improve it.”

The idea of lethality, and the drive to increase it, is being used in strategic documents to drive policy on how the Department of Defense recruits, trains, equips, and fights. It is imperative the United States has an objective metric for lethality that can be applied to quantitatively assess and compare the results of ongoing efforts in modeling, simulation, training exercises, and wargames. This same metric could also be applied to quantify lethality after actual conflicts, allowing an objective assessment of current tactics, technology, and training, as well as a means for comparison modeled or simulated alternatives.

Many senior leaders have suggested that this thing or that thing such as spousal employment or women in combat will increase, or detract from, the lethality of America’s armed forces. Once an objective metric for lethality is developed, such statements can be proven or disproven using computer modeling and training exercises in which Red and Blue casualties are substituted into the equation, or by applying the metric to historic battles where one side did or did not possess the thing in question. Without a metric that we can use to examine the impact of weapons, training, or force diversity on the objective of lethality, statements claiming such impacts are merely conjecture.

The authors acknowledge that each engagement is unique and that no single metric could ever fully account for the complexities of war. However, in order to make informed decisions with the goal of improving the lethality of its force, the United States needs to at least attempt to develop a rudimentary lethality metric that could be applied to comparatively analyze the impact of policies, equipment, operations, tactics and training. 

Quantifying Lethality

How might lethality be measured quantitatively? First, focus on the fundamental definition: What percentage of the enemy force was destroyed? Where E is the total size of the enemy force and DE is the number of deaths, or fatal casualties suffered by the enemy, this measure, LE, is simply:

While this initial metric captures the enemy’s losses, it does not account for the loss of friendly forces. Suppose we are comparing the lethality of two special forces companies, both of whom have finished an engagement in which they completely wiped out the enemy. If we only use LE as the metric, then each would get a score of 100 percent. However, suppose one of the companies accomplished this mission with no loss of U.S. personnel, while the other suffered heavy casualties and lost half of its personnel. To account for this difference, we define a new piece of the metric that accounts for the survival of friendly forces, SF, where F is the total size of the friendly force, to include involved allies and partners, and DF is the number of fatal casualties suffered by friendly forces.
Using these two components, LE and SF, we propose the following metric for lethality of our forces in that engagement:

This simple metric gives us a lethality of 100 percent when a military force kills all of the enemy without any friendly loss, and a lethality of 0 percent when it suffers a complete loss of friendly forces without inflicting any fatalities to the enemy. Indeed, for any given engagement, the lethality scores of the friendly and enemy forces are complementary, meaning they total 100 percent; so, if our own forces are 90 percent lethal, we know that the enemy was only 10 percent lethal in that engagement.

In the case of unmanned weapons systems—including mines, improvised explosive devices, and drones—this metric is designed to include those involved in the mission as part of the force. By including these personnel who played a critical role in the mission, we accurately count them as at risk. For example, an improvised explosive device planter might be killed while carrying out their task, as might a drone pilot. 

Measuring Civilian Casualties

This simple metric only accounts for loss of combatant lives, but the last century saw a transition away from clearly defined battlefields, and militaries often find themselves operating in arenas that contain civilians.

We propose to capture this in the survival component of the metric, as ideally all friendly personnel and all civilians would stay alive during an engagement. We also propose giving equal weight to the life of one of our own and the life of a civilian. With these changes, our updated survival of friendly and civilian, SF + C, is given by:

In this case, C is the number of civilians who were at immediate risk during the engagement, and DC is the number of civilians who died as a result of the engagement. Notably, DC includes civilians inadvertently killed by friendly forces as well as enemy-inflicted deaths of civilians, because civilian deaths at the hands of enemy forces indicate, at best, a lack of control and the inability to provide security by the friendly force, and at worst, may cause additional fighters to take up arms against the friendly force, especially in an unconventional fight. Thus, the total survival figure roughly approximates to the percentage of our total force—soldiers and civilian—killed in the engagement. 

The resulting lethality of friendly forces would be given by:

In short, the objective metric for lethality developed here is simply the average of the destruction inflicted on the enemy force and the survival of the friendly force and any civilians in the engagement area.

Applying the Metric

As noted, we seek a metric that can be applied to the results of models, training exercises, wargames, and simulations to inform future decisions. But it is important to validate the proposed model by applying it to past engagements and seeing what lethality scores it would produce. First, we apply the metric to a pair of infantry battles 55 years apart and compare those results. Next, to illustrate that this formula can be applied to other types of combat, we look at an aerial encounter in the Pacific campaign of World War II.

We start with the Korean War—specifically, the first night of battle between a company of U.S. Marines in the defense and a battalion from the Chinese 59th Division who were attempting to seize the vital Toktong Pass to cut off the withdrawal of U.N. forces from the Chosin Reservoir. As described in The Last Stand of Fox Company, the U.S. commander had 250 marines at the start of the battle; the Chinese sent in approximately 850 infantry soldiers to clear the pass of the American defenders.

We choose to apply the lethality calculation to this first battle rather than the ensuing five days of heavy fighting, because it represents something close to a pure infantry fight, as neither side enjoyed artillery, air, or armor support. The battle was fought for approximately four hours and resulted in the deaths of 24 marines and an estimated 450 Chinese soldiers. At the end of the first night, the marines retained control of the pass, and the heavy casualties did not render them combat ineffective. Clearly, the marines won this phase of the battle, so if the metric works correctly, they should have a higher lethality score. When we apply the proposed metric, we find that by killing 450 of the 850 Chinese, the loss of the enemy is 52.9 percent, while the loss of 24 of the 250 marines results in a survival rate of 90.4 percent. Averaging these gives the marines a lethality score of 71.7 percent. Due to the design of the metric, rather than recalculating everything to determine the Chinese lethality, we know:

So, the Chinese infantry’s lethality score for this battle is 28.3%. The resulting disparity in lethality scores aligns with the outcome of the battle. Also, if our metric works as advertised, this calculation gives us a benchmark for a high level of infantry lethality during the Korean War period, and allows us to make some useful observations after applying the metric to another infantry battle by a much more modern force half a century later.

For an example of a more modern infantry fight, we can look at the actions of Raven Squad from the 617th Military Police Company of the Kentucky National Guard on March 22, 2005. On that day, Raven Squad repulsed an ambush by approximately 45 Iraqi insurgents on a convoy in the vicinity of Salman Pak. The American forces routed their opponents, killing 26; all 10 members of the squad survived, though three were injured, but three of the civilian convoy drivers were killed before the insurgents could be driven off. Running the numbers, the killing of 26 of the 45 insurgents gives a 57.8 percent loss of the enemy. While all of Raven Squad survived, they lost three civilian drivers, so their survival rate is 92.5 percent. Averaging the enemy losses with the friendly survival results in a lethality score of 75 percent for Raven Squad and 25 percent for the insurgents. Note that these results are very similar to the numbers from Fox Company 55 years before. This is also an interesting case because two of the 10 U.S. soldiers were female; their presence in the unit and their actions during the firefight do not appear to have in any way diminished the unit’s lethality when held in direct comparison to the Korean case. While far from conclusively demonstrating a broadly generalizable statement, the evidence here is when held in direct comparison to the Korean case. While far from conclusively demonstrating a broadly generalizable statement, the evidence here is contrary to the oft-trumpeted opinion that women reduce the lethality of units engaged in close combat and the squad remained combat-effective after this engagement.

Additionally, and perhaps even more importantly, it suggests that the small-unit lethality of U.S. Forces has not mathematically improved in over a half-century. This is likely due to the fact that while aircraft have gone from 1st Generation to 5th Generation, and armor has evolved has evolved to 3rd Generation, the U.S. infantry is still very much a 1st Generation force. For example, the .50 caliber machine guns mounted on Raven Company's Humvees were the exact same models found in Fox Company's defensive positions.

Finally, to demonstrate this formula can be applied beyond only infantry-level combat, let’s look at the first true carrier battle as described in The Coral Sea 1942. There, 127 Japanese carrier-borne aircraft faced off against the 128 aircraft of two U.S. Navy Task Forces under Admirals Fletcher and Fitch. While both sides suffered significant aircraft losses for reasons unrelated to air-power lethality––such as crashing during landing or being destroyed by fire from surface ships––for the purposes of calculating lethality of the aerial combatants we only consider those planes that were shot down by other aircraft. This results in a tally of 18 Japanese aircraft and 13 U.S. aircraft shot down in air-to-air combat.

Under overcast skies, an A6M Zero fighter leads the air group launch off the deck of Shōkaku the morning of 8 May. (Wikimedia)

As with the example of Fox Company, there were no civilian casualties, and substituting the relevant numbers into our equation, we see the lethality in air-to-air engagements was fairly even; 52 percent for the U.S. pilots, 48 percent for the Japanese. Tactically, the engagement was a draw while operationally and strategically, it was a victory for the U.S. forces, which had averted the planned Japanese attack on Port Moresby and set the stage for a favorable engagement at Midway. We see that our metric mirrors the qualitative assessment, with close lethality scores that slightly favor the U.S.

Having examined these cases, we see this formula not only accurately represents lethality, it also scales from the squad level to the operational level, is applicable across multiple domains, and drives us to reduce friendly and civilian losses to improve our lethality score. That said, the work presented here is only the beginning of a conversation, and much remains to be done, including running this model against more historical battles and skirmishes to evaluate its predictive potential and working to tie it in to the “virtual environments enhanced by augmented reality technologies” that the Close Combat Lethality Task Force is designing to train tomorrow’s close combat troops. It would also be worthwhile to examine factors on the modern battlefield that go into maximizing enemy casualties while minimizing friendly and civilian deaths, and to take on the more mathematically complex problem of accurately determining how lethality is assessed in a multi-domain battle, and how to use it to make procurement and operational decisions. For example, given a combined enemy force consisting of armor and infantry defending a city, what friendly force composition—artillery, armor, infantry, air, unmanned—will have the highest lethality vis-à-vis the enemy force, and how will that composition change if significant numbers of civilians are still trapped inside the city in question?


Given that lethality is the department’s top line of effort, a forward-looking approach would make it possible to assess the validity of claims about how various programs impact lethality. Moreover, decision-makers need a way to decide between allocating funds to technologies or training that improve survivability (or those that increase the ability to kill enemy soldiers). Furthermore, without a forcing function that drives the department to increase the survivability of civilian populations, the U.S. will likely continue to make the morally and strategically unsound choice to level civilian population centers in an attempt to minimize friendly casualties, as happened in the recent Battle of Hajin.

It is our hope that this article spurs a deeper and more nuanced discussion of this latest Beltway buzzword. Our concept is admittedly very much human-focused. What happens to the equation when some or all of one of the forces is unmanned? Should mission kills figure in to this equation?  Should the metric address the logistics capacity of a force (i.e., the case where one side kills the entirety of the opposing force, but expends all of its ammunition in doing so, leaving it completely vulnerable to a counterattack)? These and many other questions remain to be explored, and we hope to do so in concert with other deep thinkers in the field of military science.

The lethality metric is a useful contribution to analysis when looking at the historical mission of the Department of Defense. Given the U.S. and its peers are technologically capable of wiping out the entire human population with a set of nuclear attacks, perhaps the mission of the U.S. military is not to increase its efficacy at killing en masse, but instead to understand the best means of sharpening its lethal sword such that it can leverage its might to avoid lethal conflict, and, should a conflict become lethal, to engage in a way that minimizes loss of all life while securing the objective.

Edward H. Carpenter is an officer in the U.S. Marine Corps. Jessica M. Libertini, is an Associate Professor at Virginia Military Institute. The opinions expressed are those of the authors and do not reflect those of the U.S. Marine Corps, Virginia Military Institute, the Department of Defense, the U.S. Government, or the United Nations.

This article appeared originally at Strategy Bridge.


[1] Lt Col Edward Carpenter (USMC) and Dr. Jessica Libertini come to the topic of lethality from very different perspectives. She is an applied mathematician; he is a logistician. Both believe that key measures of military effectiveness, to include lethality, must be objectively measured if they are to be improved.

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