Measuring the Overall Contribution of Factors to Combat Effectiveness: A Novel Method Based on Two-Dimensional Frontline Advancement Acceleration

Introduction

Method

Case Analysis I&II: Ancient Wars

Case Analysis III&IV: Modern War

Case Analysis IV: The first stage of the Korean War (1950-1951)4

From June 25 to September 15, 1950 (from the start of the war to the Incheon Landing), the Democratic People's Republic of Korea (DPRK) exhibited superior combat effectiveness relative to the Republic of Korea (ROK). This resulted in North Korea occupying approximately 93,000 square kilometers of territory in the southern part of the peninsula over a period of 82 days. According to the TFR method, we can deduce:

CE_{DPRK - ROK(Jun.25-Sep.15,1950)}=93Gsqm/1968h=47.26Msqm/h

From September 15 to October 25, 1950—a period spanning from the Incheon Landing to the intervention of the People's Republic of China in the war—there was a noticeable reversal in combat effectiveness between the conflicting parties. U.S. forces regained the lost territory in the southern peninsula and seized control of approximately 77,000 square kilometers of territory in the northern peninsula within 40 days. According to the TFR method, we can deduce:

CE_{DPRK - US&ROK(Sep.15-Oct.25,1950)}=(-93Gsqm-77Gsqm)/960h=-177.08Msqm/h

Based on the above two measurements of average combat effectiveness, we can approximate the contribution of the Incheon Landing to the combat effectiveness of both parties using Formula (3):

CFCE_{DPRK - US&ROK(Sep.15-Oct.25,1950)}=-CFCE_{US&ROK- DPRK (Sep.15-Oct.25,1950)}

=2×(CE_{DPRK -US&ROK (Sep.15-Oct.25,1950)}-CE _{DPRK- ROK(Jun.25-Sep.15,1950)})/t_{Jun.25-Oct.25,1950}

=2×(-177.08Msqm/h-47.26Msqm/h))/(1968h+960h)=-153.24ksqm/h²

The Incheon Landing is a complex composite of multiple contributing factors to combat effectiveness, as it directly triggered changes in combat effectiveness across various levels:

The DPRK benefited substantially from Soviet aid at the war's outset, including military hardware such as tanks, artillery, and military advisors. These contributing factors were part of the basis for North Korea's superior combat effectiveness. However, following the Incheon Landing, the direct intervention of the United States introduced a significant influx of advanced weaponry and equipment to the South Korean side. The formidable aerial capabilities of U.S. forces quickly secured air dominance over the Korean Peninsula, effectively neutralizing the contribution of Soviet support to North Korea.

In the early stages of the war, North Korea's combat effectiveness was further bolstered by its flexible tactics—namely, concentrating forces to assault enemy transportation and communication lines and making key breakthroughs at these hubs, rather than engaging in positional confrontations with the main South Korean force. This caught the South Korean forces by surprise. Coupled with the Republic of Korea’s (ROK) cumbersome decision-making process, this strategy led to a disorganized and haphazard response to the initial North Korean offensive. However, the "element of surprise," which had been a contributing factor to North Korea's initial success, became a factor that increased the combat effectiveness of the United States after the Incheon Landing. The surprise nature of the landing caught the North Korean forces off guard, causing significant disruption to their logistical lines and leading to the fragmentation of their forces, creating a situation where the North Korean army was attacked from both fronts.

These factors encompass a wide range of complex and multidimensional elements, many of which contain an infinite number of immeasurable subjective sub-factors. This complexity makes it infeasible to achieve a comprehensive quantification of all contributing factors through a single factor analysis. Moreover, an even more intricate situation arises, as there are contributing factors to the changes in North Korean combat effectiveness before and after the Incheon Landing that are unrelated to the landing itself. For instance, the initial combat effectiveness advantage of the DPRK also stemmed from their active ideological propaganda, wherein they twisted liberalism into a hypothetical enemy and reframed their expansionist war against South Korea as a patriotic defense to boost military morale. However, by the time of the Incheon Landing, the relentless combat engagement had inflicted considerable fatigue on North Korean forces, leading to a marked decline in individual combat morale compared to the previous phase.

The result we obtain, "-153.24 ksqm/h²," not only encompasses the new CFCE brought about by the Incheon Landing but also includes CFCE factors unrelated to the landing, representing the overall cumulative result of all CFCEs.

From October 25, 1950, to January 8, 1951 — the period from PRC's entry into the war to the US-ROK forces' counteroffensive from the 37th parallel — the second reversal in combat effectiveness among the conflicting parties was observed. Under the attack of the allied forces of China and North Korea, the United States and South Korea retreated to the south continuously for 75 days until the 37th parallel. It means that in addition to the previously occupied land in the north, the US-South Korea Coalition forces also lost control of the approximate 23,000 square kilometers of land between the 37th and 38th parallel. Thus, the combat effectiveness for this period is computed as follows:

CE_{PRC&DPRK-US&ROK(Oct.25,1950-Jan.8,1951)}=(77Gsqm+23Gsqm)/1800h=55.56Msqm/h

By substituting the above result and the previously obtained CE_{DPRK -US&ROK (Sep.15-Oct.25,1950)} values into Formula (3), we obtain:

CFCE_{PRC&DPRK-US&ROK(Oct.25,1950-Jan.8,1951)}=-CFCE_{PRC&DPRK - US&ROK(Oct.25,1950-Jan.8,1951)}

=2×(CE_{PRC&DPRK-US&ROK(Oct.25,1950-Jan.8,1951)}-CE_{DPRK -US&ROK (Sep.15-Oct.25,1950)})/t_{Sep.15,1950-Jan.8,1951}

=2×(55.56Msqm/h-(-177.08Msqm/h))/2760h=168.58ksqm/h²

From January 8 to April 10, 1951 — the period spanning the US-ROK forces' northward counteroffensive until crossing the 38th parallel again — a third reversal of combat effectiveness between the belligerents was observed. On April 10, 1951, the US-ROK forces pushed the front northward to the 38th parallel within approximately 92 days. Thus, the combat effectiveness of the belligerent forces during this period can be calculated as follows:

CE_{PRC&DPRK-US&ROK(Jan.8-Apr.10,1951)}=-23Gsqm/2208h=-10.42Msqm/h

By substituting the above result and the previously obtained CE_{PRC&DPRK-US&ROK(Oct.25,1950-Jan.8,1951)} values into Formula (3), we obtain:

CFCE_{PRC&DPRK-US&ROK(Jan.8-Apr.10,1951)}=-CFCE_{US&ROK-PRC&DPRK (Jan.8-Apr.10,1951)}

=2×(CE_{PRC&DPRK-US&ROK(Jan.8-Apr.10,1951)}-CE_{PRC&DPRK-US&ROK(Oct.25,1950-Jan.8,1951)})/t_{Oct.25-Apr.10,1951}

=2×(-10.42Msqm/h-55.56Msqm/h)/4008h=-32.92ksqm/h²

The two opposing values, "168.58ksqm/h²" and "-32.92ksqm/h²," together illustrate a more complex situation in the contributing factors to combat effectiveness—namely, the interaction of contributing factors. Specifically, this is the result of the complex interplay between the factor of China's intervention and other contributing factors:

1.In the northern part of the Korean Peninsula, the uneven mountainous terrain significantly limits the line of sight and mobility of U.S. mechanized forces. On the other hand, the southern part of the Korean Peninsula, with its vast plains, provides an ideal platform for U.S. mechanized forces to demonstrate their potent offensive capabilities and maneuverability. The terrain factors lead to stark differences in the CFCE brought about by China's intervention at different stages of the conflict. Specifically, the complex terrain of the northern Korean Peninsula, marked by towering mountains and narrow valleys, favored the Chinese and North Korean forces, who employed highly effective ambush tactics, nocturnal raids, and infiltration strategies. Conversely, the mechanized equipment of the U.S.-ROK alliance struggled to execute standard offensive maneuvers in this difficult terrain. On one hand, the elevated ridgelines provided optimal cover to avoid the parabolic trajectories of incoming artillery. On the other hand, compared to the lighter equipment of the PRC-DPRK forces, the heavier weapons of the U.S.-ROK alliance became a burden for mountain marches. It is akin to walking being slower than driving on a highway, but faster than driving on an unmodified mountain road. In contrast, as the battlefield shifted south of the 38th parallel, the proportion of plains terrain increased significantly. As the battlefront moved into the Han River Plain region, the mechanized units of the U.S.-ROK forces began to fully utilize their combat effectiveness. Conversely, the advantages gained by the PRC-DPRK forces from their mountain warfare tactics no longer held the same efficacy.

2.In addition to terrain factors, other variables, such as the length of supply lines, also contribute to the uncertainty in the CFCE values triggered by China's intervention. At the onset of China's involvement, the battlefield was close to northeastern China, allowing the Sino-Korean forces to easily obtain supplies and personnel from China and the Soviet Union. However, as the battlefront shifted further south, the supply lines for the Sino-Korean forces lengthened, increasingly complicating their logistics and making them more susceptible to disruption. In contrast, given the proximity of the southern Korean Peninsula to U.S.-occupied Japan, a steady stream of logistical supplies was provided to the U.S.-ROK forces, facilitated by the U.S.'s robust sea and air transport capabilities.

3.The aforementioned factors can be analyzed qualitatively, allowing us to assess their varying effects on China's intervention during different periods, either strengthening or weakening its impact. However, some variables, such as the "snow-earth" factor, cannot be evaluated for their specific impact, as they have both strengthening and weakening effects. On the one hand, the combination of mountainous terrain and snow further intensified the difficulties in the mobility of mechanized units and increased fuel requirements (extra fuel consumption for uphill movements and heating). On the other hand, the snowy terrain also led to numerous cases of frostbite among the Chinese troops, who lacked proper cold protection equipment, thus reducing their human resources. Clearly, the impact of the snow variable on China's intervention is difficult to determine, as it has dual effects.

It is clear that after 1951, the most crucial contributing factor was China’s intervention. However, with the 38th parallel as a dividing line, other factors such as terrain and logistics had a significant and divergent impact on the CFCE brought about by China’s intervention. These factors could either amplify the changes in combat effectiveness to over 150 or diminish them to below zero. The two data points we obtained clearly capture the complex interplay between these combat effectiveness contributing factors.

Table 1. Qualitative and Quantitative Results of CFCE during the Stalemate Stage of the Korean War.

Table 1. Qualitative and Quantitative Results of CFCE during the Stalemate Stage of the Korean War.

Period	Major Contributing Factors	CE	CFCE
Jun.25-Sep.15,1950	Soviet support, South Korea caught off guard	47.26Msqm/h	——
Sep.15-Oct.25,1950	Incheon Landing, North Korean troop fatigue	-177.08Msqm/h	-153.24ksqm/h2
Oct.25,1950- Jan.8,1951	China’s intervention, battlefield environment favorable for China (mountainous terrain favored guerrilla warfare, supply lines shorter for China, longer for the US)	55.56Msqm/h	168.58ksqm/h2
Jan.8-Apr.10,1951	China’s intervention, battlefield environment unfavorable for China (plains favored advanced weapons, supply lines shorter for the US, longer for China)	-10.42Msqm/h	-32.92ksqm/h2

Note: In this table, CE refers to CE _{PRC & DPRK-US & ROK} and CFCE refers to CFCE _{PRC & DPRK-US & ROK}.

Case Analysis V&VI: The Current and Future Wars

Case Analysis VI: Future Wars

As Harold Laswell said, “Modern war must be conducted on three fronts: the military front, the economic front, and the propaganda front. The military front is a mere consequence of the other two. The economic blockade will be the decisive factor in the war, and the propaganda that precedes and accompanies it will serve to confuse and demoralize the enemy”(Lasswell 1927,p.208). This trend will only become more pronounced in future warfare. It implies that one of our tasks is to extend the formula for measuring combat effectiveness in the military domain to encompass the economic and propaganda domains. The TFR method proposed by Sun and Wang (2025) uses the two-dimensional frontline advancement rate as a measure of military combat effectiveness. We can extend this method by employing a two-dimensional market share advancement rate to measure economic combat effectiveness (treating market boundaries as frontlines and calculating the area enclosed by the old and new market boundaries over a unit of time), and a two-dimensional ideological advancement rate to measure propaganda combat effectiveness (treating ideological boundaries as frontlines and calculating the area enclosed by the old and new ideological boundaries over a unit of time).

Due to the independence between the three types of combat effectiveness, as exemplified by the statement from Mrs. Thatcher, the former British Prime Minister: “The Soviet Union is a superpower militarily, but it has failed abysmally in economic and moral terms” (delivered by Margaret Thatcher in a speech to the Conservative Party Conference on October 9, 1983), it reflects that high military combat effectiveness does not necessarily imply high effectiveness in other domains. Therefore, the three-dimensional combat effectiveness of a country is not a simple sum of the three types of combat effectiveness. Instead, it is more appropriate to create a Cartesian coordinate system to measure combat effectiveness in military & politics, economy, or propaganda on the x, y, and z axes, respectively. In such a coordinate system, the three-dimensional combat effectiveness of a country, sub-national entity (e.g.; political parties or associations), or a supra-national entity (such as the UN or the EU) can be expressed as A (x_{A(military&politics)}, y_A(economy), z_{A(propaganda)}). The dyadic three-dimensional combat effectiveness between A and B (x_B, y_B, z_B) is calculated as:

and the monadic three-dimensional combat effectiveness of A as:

The unit of measurement for both is still sqm/h or sqkm/a.

When we extend combat effectiveness from one dimension to three dimensions, it means that CFCE can also undergo a similar extension, incorporating the contributing factors of combat effectiveness in the military, economic, and propaganda domains. In the Cartesian coordinate system, we can model three-dimensional CE and three-dimensional CFCE as follows:

In the ideal state P, the three-dimensional combat effectiveness of country P is represented by (x, y, z), which is influenced by a three-dimensional CFCE, capable of simultaneously affecting the military, economic, and propaganda combat effectiveness. When the CFCE value is m, its direction can be represented as (m·cosθ₁·cosθ₂, m·cosθ₁·sinθ₂, m·sinθ₁) with the origin at (0,0,0). Here, θ₁ represents the included angle between the CFCE and the xOy plane, and θ₂ represents the angle between the projection of the CFCE on the xOy plane and the Ox axis. After a period of time (t), the three-dimensional combat effectiveness of Country P becomes (x', y', z'), where

$$\left\{\begin{array}{c}x`=x+\left(\mathrm{m}\bullet {\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\theta }}_1\bullet {\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\theta }}_2\right)\times t\\ y`=y+\left(\mathrm{m}\bullet {\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\theta }}_1\bullet {\mathrm{s}\mathrm{i}\mathrm{n}\mathsf{\theta }}_2\right)\times t\\ z`=z+\left(\mathrm{m}\bullet {\mathrm{s}\mathrm{i}\mathrm{n}\mathsf{\theta }}_1\right)\times t\end{array}\right.$$

Based on the above model, if the initial CE and three-dimensional CFCE are known, it becomes possible to calculate and simulate the comprehensive progression and impact of a war on a country across the political, economic, and cultural dimensions.

Conclusions

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