[UPDATE] We had several readers recommend games they have used or would be suitable for simulating Multi-Domain Battle and Operations (MDB/MDO) concepts. These include several classic campaign-level board wargames:

Chris Lawrence recently looked at C-WAM and found that it uses a lot of traditional board wargaming elements, including methodologies for determining combat results, casualties, and breakpoints that have been found unable to replicate real-world outcomes (aka “The Base of Sand” problem).

What other wargames, models, and simulations are there being used out there? Are there any commercial wargames incorporating MDB/MDO elements into their gameplay? What methodologies are being used to portray MDB/MDO effects?

There are three versions of force ratio versus casualty exchange ratio rules, such as the three-to-one rule (3-to-1 rule), as it applies to casualties. The earliest version of the rule as it relates to casualties that we have been able to ﬁnd comes from the 1958 version of the U.S. Army Maneuver Control manual, which states: “When opposing forces are in contact, casualties are assessed in inverse ratio to combat power. For friendly forces advancing with a combat power superiority of 5 to 1, losses to friendly forces will be about 1/5 of those suffered by the opposing force.”[1]

The RAND version of the rule (1992) states that: “the famous ‘3:1 rule ’, according to which the attacker and defender suffer equal fractional loss rates at a 3:1 force ratio the battle is in mixed terrain and the defender enjoys ‘prepared ’defenses…” [2]

Finally, there is a version of the rule that dates from the 1967 Maneuver Control manual that only applies to armor that shows:

As the RAND construct also applies to equipment losses, then this formulation is directly comparable to the RAND construct.

Therefore, we have three basic versions of the 3-to-1 rule as it applies to casualties and/or equipment losses. First, there is a rule that states that there is an even fractional loss ratio at 3-to-1 (the RAND version), Second, there is a rule that states that at 3-to-1, the attacker will suffer one-third the losses of the defender. And third, there is a rule that states that at 3-to-1, the attacker and defender will suffer the same losses as the defender. Furthermore, these examples are highly contradictory, with either the attacker suffering three times the losses of the defender, the attacker suffering the same losses as the defender, or the attacker suffering 1/3 the losses of the defender.

Therefore, what we will examine here is the relationship between force ratios and exchange ratios. In this case, we will ﬁrst look at The Dupuy Institute’s Battles Database (BaDB), which covers 243 battles from 1600 to 1900. We will chart on the y-axis the force ratio as measured by a count of the number of people on each side of the forces deployed for battle. The force ratio is the number of attackers divided by the number of defenders. On the x-axis is the exchange ratio, which is a measured by a count of the number of people on each side who were killed, wounded, missing or captured during that battle. It does not include disease and non-battle injuries. Again, it is calculated by dividing the total attacker casualties by the total defender casualties. The results are provided below:

As can be seen, there are a few extreme outliers among these 243 data points. The most extreme, the Battle of Tippennuir (l Sep 1644), in which an English Royalist force under Montrose routed an attack by Scottish Covenanter militia, causing about 3,000 casualties to the Scots in exchange for a single (allegedly self-inﬂicted) casualty to the Royalists, was removed from the chart. This 3,000-to-1 loss ratio was deemed too great an outlier to be of value in the analysis.

As it is, the vast majority of cases are clumped down into the corner of the graph with only a few scattered data points outside of that clumping. If one did try to establish some form of curvilinear relationship, one would end up drawing a hyperbola. It is worthwhile to look inside that clump of data to see what it shows. Therefore, we will look at the graph truncated so as to show only force ratios at or below 20-to-1 and exchange rations at or below 20-to-1.

Again, the data remains clustered in one corner with the outlying data points again pointing to a hyperbola as the only real ﬁtting curvilinear relationship. Let’s look at little deeper into the data by truncating the data on 6-to-1 for both force ratios and exchange ratios. As can be seen, if the RAND version of the 3-to-1 rule is correct, then the data should show at 3-to-1 force ratio a 3-to-1 casualty exchange ratio. There is only one data point that comes close to this out of the 243 points we examined.

If the FM 105-5 version of the rule as it applies to armor is correct, then the data should show that at 3-to-1 force ratio there is a 1-to-1 casualty exchange ratio, at a 4-to-1 force ratio a 1-to-2 casualty exchange ratio, and at a 5-to-1 force ratio a 1-to-3 casualty exchange ratio. Of course, there is no armor in these pre-WW I engagements, but again no such exchange pattern does appear.

If the 1958 version of the FM 105-5 rule as it applies to casualties is correct, then the data should show that at a 3-to-1 force ratio there is 0.33-to-1 casualty exchange ratio, at a 4-to-1 force ratio a .25-to-1 casualty exchange ratio, and at a 5-to-1 force ratio a 0.20-to-5 casualty exchange ratio. As can be seen, there is not much indication of this pattern, or for that matter any of the three patterns.

Still, such a construct may not be relevant to data before 1900. For example, Lanchester claimed in 1914 in Chapter V, “The Principal of Concentration,” of his book Aircraft in Warfare, that there is greater advantage to be gained in modern warfare from concentration of ﬁre.[3] Therefore, we will tap our more modern Division-Level Engagement Database (DLEDB) of 675 engagements, of which 628 have force ratios and exchange ratios calculated for them. These 628 cases are then placed on a scattergram to see if we can detect any similar patterns.

Even though this data covers from 1904 to 1991, with the vast majority of the data coming from engagements after 1940, one again sees the same pattern as with the data from 1600-1900. If there is a curvilinear relationship, it is again a hyperbola. As before, it is useful to look into the mass of data clustered into the corner by truncating the force and exchange ratios at 20-to-1. This produces the following:

Again, one sees the data clustered in the corner, with any curvilinear relationship again being a hyperbola. A look at the data further truncated to a 10-to-1 force or exchange ratio does not yield anything more revealing.

And, if this data is truncated to show only 5-to-1 force ratio and exchange ratios, one again sees:

Again, this data appears to be mostly just noise, with no clear patterns here that support any of the three constructs. In the case of the RAND version of the 3-to-1 rule, there is again only one data point (out of 628) that is anywhere close to the crossover point (even fractional exchange rate) that RAND postulates. In fact, it almost looks like the data conspires to make sure it leaves a noticeable “hole” at that point. The other postulated versions of the 3-to-1 rules are also given no support in these charts.

While we can attempt to torture the data to ﬁnd a better ﬁt, or can try to argue that the patterns are obscured by various factors that have not been considered, we do not believe that such a clear pattern and relationship exists. More advanced mathematical methods may show such a pattern, but to date such attempts have not ferreted out these alleged patterns. For example, we refer the reader to Janice Fain’s article on Lanchester equations, The Dupuy Institute’s Capture Rate Study, Phase I & II, or any number of other studies that have looked at Lanchester.[4]

The fundamental problem is that there does not appear to be a direct cause and effect between force ratios and exchange ratios. It appears to be an indirect relationship in the sense that force ratios are one of several independent variables that determine the outcome of an engagement, and the nature of that outcome helps determines the casualties. As such, there is a more complex set of interrelationships that have not yet been fully explored in any study that we know of, although it is brieﬂy addressed in our Capture Rate Study, Phase I & II.

[3] F. W. Lanchester, Aircraft in Warfare: The Dawn of the Fourth Arm (Lanchester Press Incorporated, Sunnyvale, Calif., 1995), 46-60. One notes that Lanchester provided no data to support these claims, but relied upon an intellectual argument based upon a gross misunderstanding of ancient warfare.

“If we maintain our faith in God, love of freedom, and superior global airpower, the future [of the US] looks good.” — U.S. Air Force General Curtis E. LeMay (Commander, U.S. Strategic Command, 1948-1957)

Curtis LeMay was involved in the formation of RAND Corporation after World War II. RAND created several models to measure the dynamics of the US-China military balance over time. Since 1996, this has been computed for two scenarios, differing by range from mainland China: one over Taiwan and the other over the Spratly Islands. The results of the model results for selected years can be seen in the graphic below.

The capabilities listed in the RAND study are interesting, notable in that the air superiority category, rough parity exists as of 2017. Also, the ability to attack air bases has given an advantage to the Chinese forces.

Investigating the methodology used does not yield any precise quantitative modeling examples, as would be expected in a rigorous academic effort, although there is some mention of statistics, simulation and historical examples.

The analysis presented here necessarily simplifies a great number of conflict characteristics. The emphasis throughout is on developing and assessing metrics in each area that provide a sense of the level of difficulty faced by each side in achieving its objectives. Apart from practical limitations, selectivity is driven largely by the desire to make the work transparent and replicable. Moreover, given the complexities and uncertainties in modern warfare, one could make the case that it is better to capture a handful of important dynamics than to present the illusion of comprehensiveness and precision. All that said, the analysis is grounded in recognized conclusions from a variety of historical sources on modern warfare, from the air war over Korea and Vietnam to the naval conflict in the Falklands and SAM hunting in Kosovo and Iraq. [Emphasis added].

We coded most of the scorecards (nine out of ten) using a five-color stoplight scheme to denote major or minor U.S. advantage, a competitive situation, or major or minor Chinese advantage. Advantage, in this case, means that one side is able to achieve its primary objectives in an operationally relevant time frame while the other side would have trouble in doing so. [Footnote] For example, even if the U.S. military could clear the skies of Chinese escort fighters with minimal friendly losses, the air superiority scorecard could be coded as “Chinese advantage” if the United States cannot prevail while the invasion hangs in the balance. If U.S. forces cannot move on to focus on destroying attacking strike and bomber aircraft, they cannot contribute to the larger mission of protecting Taiwan.

All of the dynamic modeling methodology (which involved a mix of statistical analysis, Monte Carlo simulation, and modified Lanchester equations) is publicly available and widely used by specialists at U.S. and foreign civilian and military universities.” [Emphasis added].

As TDI has contended before, the problem with using Lanchester’s equations is that, despite numerous efforts, no one has been able to demonstrate that they accurately represent real-world combat. So, even with statistics and simulation, how good are the results if they have relied on factors or force ratios with no relation to actual combat?

What about new capabilities?

As previously posted, the Kratos Mako Unmanned Combat Aerial Vehicle (UCAV), marketed as the “unmanned wingman,” has recently been cleared for export by the U.S. State Department. This vehicle is specifically oriented towards air-to-air combat, is stated to have unparalleled maneuverability, as it need not abide by limits imposed by human physiology. The Mako “offers fighter-like performance and is designed to function as a wingman to manned aircraft, as a force multiplier in contested airspace, or to be deployed independently or in groups of UASs. It is capable of carrying both weapons and sensor systems.” In addition, the Mako has the capability to be launched independently of a runway, as illustrated below. The price for these vehicles is three million each, dropping to two million each for an order of at least 100 units. Assuming a cost of $95 million for an F-35A, we can imagine a hypothetical combat scenario pitting two F-35As up against 100 of these Mako UCAVs in a drone swarm; a great example of the famous phrase, quantity has a quality all its own.

How to evaluate the effects of these possible UCAV drone swarms?

In building up towards the analysis of all of these capabilities in the full theater, campaign level conflict, some supplemental wargaming may be useful. One game that takes a good shot at modeling these dynamics is Asian Fleet. This is a part of the venerable Fleet Series, published by Victory Games, designed by Joseph Balkoski to model modern (that is Cold War) naval combat. This game system has been extended in recent years, originally by Command Magazine Japan, and then later by Technical Term Gaming Company.

The first was chosen to provide a historical context for the 3:1 rule of thumb. The second was chosen so as to examine how this rule applies to modern combat data.

We decided that this should be tested to the RAND version of the 3:1 rule as documented by RAND in 1992 and used in JICM [Joint Integrated Contingency Model] (with SFS [Situational Force Scoring]) and other models. This rule, as presented by RAND, states: “[T]he famous ‘3:1 rule,’ according to which the attacker and defender suffer equal fractional loss rates at a 3:1 force ratio if the battle is in mixed terrain and the defender enjoys ‘prepared’ defenses…”

Therefore, we selected out all those engagements from these two databases that ranged from force ratios of 2.5 to 1 to 3.5 to 1 (inclusive). It was then a simple matter to map those to a chart that looked at attackers losses compared to defender losses. In the case of the pre-1904 cases, even with a large database (243 cases), there were only 12 cases of combat in that range, hardly statistically significant. That was because most of the combat was at odds ratios in the range of .50-to-1 to 2.00-to-one.

The count of number of engagements by odds in the pre-1904 cases:

As the database is one of battles, then usually these are only joined at reasonably favorable odds, as shown by the fact that 88 percent of the battles occur between 0.40 and 2.50 to 1 odds. The twelve pre-1904 cases in the range of 2.50 to 3.50 are shown in Table 1.

If the RAND version of the 3:1 rule was valid, one would expect that the “Percent per Day Loss Ratio” (the last column) would hover around 1.00, as this is the ratio of attacker percent loss rate to the defender percent loss rate. As it is, 9 of the 12 data points are noticeably below 1 (below 0.40 or a 1 to 2.50 exchange rate). This leaves only three cases (25%) with an exchange rate that would support such a “rule.”

If we look at the simple ratio of actual losses (vice percent losses), then the numbers comes much closer to parity, but this is not the RAND interpretation of the 3:1 rule. Six of the twelve numbers “hover” around an even exchange ratio, with six other sets of data being widely off that central point. “Hover” for the rest of this discussion means that the exchange ratio ranges from 0.50-to-1 to 2.00-to 1.

Still, this is early modern linear combat, and is not always representative of modern war. Instead, we will examine 634 cases in the Division-level Database (which consists of 675 cases) where we have worked out the force ratios. While this database covers from 1904 to 1991, most of the cases are from WWII (1939- 1945). Just to compare:

As such, 87% of the cases are from WWII data and 10% of the cases are from post-WWII data. The engagements without force ratios are those that we are still working on as The Dupuy Institute is always expanding the DLEDB as a matter of routine. The specific cases, where the force ratios are between 2.50 and 3.50 to 1 (inclusive) are shown in Table 2:

This is a total of 98 engagements at force ratios of 2.50 to 3.50 to 1. It is 15 percent of the 634 engagements for which we had force ratios. With this fairly significant representation of the overall population, we are still getting no indication that the 3:1 rule, as RAND postulates it applies to casualties, does indeed fit the data at all. Of the 98 engagements, only 19 of them demonstrate a percent per day loss ratio (casualty exchange ratio) between 0.50-to-1 and 2-to-1. This is only 19 percent of the engagements at roughly 3:1 force ratio. There were 72 percent (71 cases) of those engagements at lower figures (below 0.50-to-1) and only 8 percent (cases) are at a higher exchange ratio. The data clearly was not clustered around the area from 0.50-to- 1 to 2-to-1 range, but was well to the left (lower) of it.

Looking just at straight exchange ratios, we do get a better fit, with 31 percent (30 cases) of the figure ranging between 0.50 to 1 and 2 to 1. Still, this figure exchange might not be the norm with 45 percent (44 cases) lower and 24 percent (24 cases) higher. By definition, this fit is 1/3rd the losses for the attacker as postulated in the RAND version of the 3:1 rule. This is effectively an order of magnitude difference, and it clearly does not represent the norm or the center case.

The percent per day loss exchange ratio ranges from 0.00 to 5.71. The data tends to be clustered at the lower values, so the high values are very much outliers. The highest percent exchange ratio is 5.71, the second highest is 4.41, the third highest is 2.92. At the other end of the spectrum, there are four cases where no losses were suffered by one side and seven where the exchange ratio was .01 or less. Ignoring the “N/A” (no losses suffered by one side) and the two high “outliers (5.71 and 4.41), leaves a range of values from 0.00 to 2.92 across 92 cases. With an even distribution across that range, one would expect that 51 percent of them would be in the range of 0.50-to-1 and 2.00-to-1. With only 19 percent of the cases being in that range, one is left to conclude that there is no clear correlation here. In fact, it clearly is the opposite effect, which is that there is a negative relationship. Not only is the RAND construct unsupported, it is clearly and soundly contradicted with this data. Furthermore, the RAND construct is theoretically a worse predictor of casualty rates than if one randomly selected a value for the percentile exchange rates between the range of 0 and 2.92. We do believe this data is appropriate and accurate for such a test.

As there are only 19 cases of 3:1 attacks falling in the even percentile exchange rate range, then we should probably look at these cases for a moment:

One will note, in these 19 cases, that the average attacker casualties are way out of line with the average for the entire data set (3.20 versus 1.39 or 3.20 versus 0.63 with pre-1943 and Soviet-doctrine attackers removed). The reverse is the case for the defenders (3.12 versus 6.08 or 3.12 versus 5.83 with pre-1943 and Soviet-doctrine attackers removed). Of course, of the 19 cases, 2 are pre-1943 cases and 7 are cases of Soviet-doctrine attackers (in fact, 8 of the 14 cases of the Soviet-doctrine attackers are in this selection of 19 cases). This leaves 10 other cases from the Mediterranean and ETO (Northwest Europe 1944). These are clearly the unusual cases, outliers, etc. While the RAND 3:1 rule may be applicable for the Soviet-doctrine offensives (as it applies to 8 of the 14 such cases we have), it does not appear to be applicable to anything else. By the same token, it also does not appear to apply to virtually any cases of post-WWII combat. This all strongly argues that not only is the RAND construct not proven, but it is indeed clearly not correct.

The fact that this construct also appears in Soviet literature, but nowhere else in US literature, indicates that this is indeed where the rule was drawn from. One must consider the original scenarios run for the RSAC [RAND Strategy Assessment Center] wargame were “Fulda Gap” and Korean War scenarios. As such, they were regularly conducting battles with Soviet attackers versus Allied defenders. It would appear that the 3:1 rule that they used more closely reflected the experiences of the Soviet attackers in WWII than anything else. Therefore, it may have been a fine representation for those scenarios as long as there was no US counterattacking or US offensives (and assuming that the Soviet Army of the 1980s performed at the same level as in did in the 1940s).

There was a clear relative performance difference between the Soviet Army and the German Army in World War II (see our Capture Rate Study Phase I & II and Measuring Human Factors in Combat for a detailed analysis of this).[1] It was roughly in the order of a 3-to-1-casualty exchange ratio. Therefore, it is not surprising that Soviet writers would create analytical tables based upon an equal percentage exchange of losses when attacking at 3:1. What is surprising, is that such a table would be used in the US to represent US forces now. This is clearly not a correct application.

Therefore, RAND’s SFS, as currently constructed, is calibrated to, and should only be used to represent, a Soviet-doctrine attack on first world forces where the Soviet-style attacker is clearly not properly trained and where the degree of performance difference is similar to that between the Germans and Soviets in 1942-44. It should not be used for US counterattacks, US attacks, or for any forces of roughly comparable ability (regardless of whether Soviet-style doctrine or not). Furthermore, it should not be used for US attacks against forces of inferior training, motivation and cohesiveness. If it is, then any such tables should be expected to produce incorrect results, with attacker losses being far too high relative to the defender. In effect, the tables unrealistically penalize the attacker.

As JICM with SFS is now being used for a wide variety of scenarios, then it should not be used at all until this fundamental error is corrected, even if that use is only for training. With combat tables keyed to a result that is clearly off by an order of magnitude, then the danger of negative training is high.

A friend tipped me off to RAND Corporation‘s “Events @ RAND” podcast series on iTunes, specifically a recent installment titled “The Serious Role of Gaming at RAND.” David Shlapak, senior international research analyst and co-director of the RAND Center for Gaming, gives an overview of RAND’s history and experiences using gaming and simulations for a variety of tasks, including analysis and policy-making.

Shlapak and Michael Johnson touched off a major debate last year after publishing an analysis of the military balance in the Baltic states, based on a series of analytical wargames. Shlapak’s discussion of the effort and the ensuing question and answer session are of interest to both those new to gaming and simulation, as well as wargaming old timers. Much recommended.