Centers of gravity and war outcomes

Abstract

Bargaining models argue that wars usually terminate when the information gap closes enough to create a bargaining range. Although this convergence is assumed to be straightforward, factors that identify the information regarding the likely military outcome to the belligerents have not been identified. One of Clausewitz’s main ideas was that states can win wars by attacking the enemy’s centers of gravity, which I argue provide an important way through which information convergence is achieved. I examine the importance of three centers of gravity—capturing the enemy’s capital, destroying the enemy’s military forces, and eliminating enemy allies from the war—on war outcomes through a quantitative analysis of wars from 1816 to 2007.

Keywords

Capturing capitals Clausewitz information convergence war outcomes

Understanding the factors driving war outcomes is a vital element of understanding international conflict more generally (Biddle, 2007; Stoll, 1995). Although the causes of war have been studied far more extensively, bargaining models of war make it clear that war outcomes are important for understanding the causes of war (Filson and Werner, 2002). Since war has tremendous consequences for international relations and the nature of those consequences is driven in large part by who wins and loses, explaining war outcomes is important in its own right. In a broad empirical analysis of war outcomes, Stam (1996) finds that military strategy is the most important determinant, contrary to the previous conventional wisdom focusing on power.

In this article, I test Clausewitz’s claims regarding the importance of centers of gravity through a quantitative analysis of war outcomes from 1816 to 2007. I focus on three centers of gravity identified by Clausewitz: capture of the enemy’s capital, destruction of the enemy’s military forces, and elimination of enemy allies from the war. I also examine the timing of capital captures in order to shed light on their ability to achieve information convergence. I begin by reviewing the bargaining literature and the empirical literature on military victory. I then examine the importance of centers of gravity, lay out the hypotheses to be tested, and present the research design used as well as the empirical results.

Bargaining, absolute victory, and war outcomes

Bargaining models of war have been a prevalent part of the international conflict literature since Fearon (1995) used a bargaining model to examine rationalist explanations of the causes of war. Bargaining models argue that war can result from three sources: incomplete information, commitment problems, and indivisible issues. Fearon (1995) highlights the importance of incomplete information with incentives to misrepresent, generally stemming from uncertainty about either the likelihood of victory or the costs of fighting.

Bargaining models have also been developed to explain war outcomes and termination, and they have generally focused on the role of information (Leventoglu and Slantchev, 2007; Reiter, 2009: 8–21). The basic logic is that war terminates when the information gap between the two sides closes enough to create a bargaining range (Filson and Werner, 2002; Powell, 2004; Smith, 1998; Wagner, 2000). Slantchev (2003) labels this the principle of convergence. One of the strengths of the bargaining model of war is that it allows explanations of war onset, duration, outcome and termination all in one integrated theoretical model (Filson and Werner, 2002).

Yet what produces this convergence, or closing of the information gap? Although most models assume that the information is revealed through outcomes of battles during the course of the war (e.g. Smith, 1998), others (e.g. Slantchev, 2003) also focus on information revealed by competing offers during intrawar negotiations. Slantchev (2003: 629) argues that “war results in a relatively quick disclosure of information”. However, Langlois and Langlois (2009: 1052) demonstrate that states often “delay negotiations in the hope that the other side will give in to outstanding demands instead of attempting to bargain”. Furthermore, while Slantchev and others portray a world in which information is automatically revealed in war, the “fog of war” (Clausewitz, 1976) makes this convergence of information substantially more difficult.

The fog of war is part of the broader concept of friction (Brodie, 1976), which refers “to the factors that distinguish real war from war on paper” (Clausewitz, 1976: 119). The key feature of the fog of war is that uncertainty pervades warfare, making it difficult for leaders—military and civilian—to assess the outcomes of battles, the status of the enemy, and progress in the war. “This difficulty of accurate recognition constitutes one of the most serious sources of friction in war” (Clausewitz, 1976: 117, emphasis in original). Because of the fog of war, information convergence is not always a straightforward process as it is assumed to be in bargaining models (Kirshner, 2000; Rosen, 2005). However, information convergence is not impossible; I argue that centers of gravity are one of the key ways through which information convergence is achieved.

Furthermore, information convergence does not completely explain war termination. Reiter (2009) shows that commitment problems can lead states to pursue absolute victory. If a belligerent doubts its opponent’s ability to credibly commit to a negotiated settlement, the state will push on to pursue decisive victory to increase the stability of the settlement. This can prove to be effective, as imposed settlements (Quackenbush and Venteicher, 2008; Senese and Quackenbush, 2003) and foreign-imposed regime changes (Lo et al., 2008) significantly increase durations of peace following conflict. Wolford et al. (2011) present a bargaining model that incorporates both commitment problems and asymmetric information, and show that convergence can lead to war continuation rather than termination.

The fog of war and commitment problems interfere with the principle of convergence. The presence of commitment problems can lead states to pursue military victory rather than negotiating a settlement when information has converged. The fog of war creates difficulty in interpreting battlefield outcomes, indicating that the process of information convergence during war is not as straightforward as formal bargaining models typically assume it to be. Thus, the fog of war and commitment problems both raise the question of what factors lead to military victory. Warfare is sometimes seen as involving either the pursuit of absolute victory or bargaining. For example, Sullivan (2007, 2012) argues that states can achieve brute force objectives through military victory but can only achieve coercive objectives through bargaining. However, this distinction is overstated. While brute force objectives do not necessarily require target compliance and coercive objectives do, states need to pursue military victory or other success in order to achieve either information convergence (in an advantageous position) or absolute victory.¹ Thus, the important question is what factors identify information regarding the likely military outcome revealed to belligerents during the course of the war?

Explaining military victory

Traditional explanations of war outcomes focus on relative power of the combatants as the primary explanatory variable. A number of studies have argued that the larger side wins wars (e.g. Henderson and Bayer, 2013; Kugler and Domke, 1986; Organski and Kugler, 1980; Rosen, 1972). However, the stronger side wins only about 60% of the time, depending on what measure of strength is used (Biddle, 2004). Some studies have endeavored to explain why weaker states emerge victorious in war as often as they have (e.g. Arreguin-Toft, 2005; Mack, 1975; Maoz, 1989; Sullivan, 2007). While power is relevant to explaining war outcomes, so are other factors. Furthermore, since these measures of power are taken from the beginning of the war, they are unable to identify information revealed to belligerents during the course of the war.

Stam (1996) greatly advanced the study of war outcomes in political science by analyzing outcomes theoretically and empirically. Unlike previous studies, which typically focused exclusively on power as a determinant of war outcomes (e.g. Kugler and Domke, 1986), Stam accounts for a wide range of material and nonmaterial factors at both the international and domestic levels. In particular, Stam (1996) highlights the importance of military strategy, as represented in a simple classification of maneuver, attrition, and punishment strategies. His results indicate that strategy is of crucial importance for explaining war outcomes.

Others have examined the relationship between regime type and war outcomes. Several studies show that democracies are more likely to win wars than are nondemocracies (e.g. Lake, 1992; Reiter and Stam, 2002). Initiators are also generally expected to be more likely to win because they have can dictate events early in the war and they only initiate when their expected utility for doing so is beneficial (Bueno de Mesquita, 1981; Morrow, 1985).

Ex-ante factors such as power, strategy, regime type, and initiation are undoubtedly important in explaining war outcomes. However, they are unable to explain how the actual conduct of war affects outcomes. Thus, they have limited utility for uncovering the revelation of information that is fundamental to the principle of convergence. Other studies focus on the level of individual battles, rather than the war as a whole. Since battles are expected to be the principal means through which information is revealed in war (Smith, 1998), this seems appropriate.

Biddle (2004) focuses on explaining battle outcomes and argues that the key to victory in modern warfare is modern system force employment because it dampens the effects of technological change and insulates its users from the full lethality of their opponents’ weapons. Grauer and Horowitz (2012) conduct a quantitative test and find evidence supporting Biddle’s theory. However, there is not a direct relation between battle and war outcomes. For example, Biddle’s case studies highlight the excellent performance of German forces in Operation Michael in the First World War and Operation Goodwood during the Second World War, leading to German victories in each case. However, we also know that Germany lost each war less than a year after the battles.

Ramsay (2008) goes a step further by employing a quantitative analysis of battle data to test hypotheses regarding the impact of information convergence on war termination. Although the CDB90 battle data have a variety of limitations, Ramsay is nonetheless able to uncover important findings regarding the role of information. Unfortunately for our present purposes, Ramsay is focused on war termination rather than outcome.

Although these studies build on Clausewitz’s (1976) ideas in various ways, none of them have sought to test any aspects of his theory of war. I argue that Clausewitz provides us with an important explanation of war outcomes that has been previously unexplored in the political science literature. Furthermore, I argue that centers of gravity provide an important way through which information convergence is achieved. Accordingly, I now turn to examining Clausewitz.

Clausewitz and centers of gravity

Carl von Clausewitz was a Prussian officer who fought against France during the Napoleonic Wars. Following Napoleon’s defeat, he served as director of the Prussian War College in Berlin and began writing about strategy and warfare (Howard, 2002). His primary work, On War (Clausewitz, 1976), was published posthumously in 1832 and remains very relevant to strategy and warfare (Brodie, 1976). Among other things, Clausewitz’s (1976: 87) argument that “war is merely the continuation of policy by other means” is fundamental to the bargaining model of war (Wagner, 2000). Although some of his discussions are no longer relevant, Clausewitz provides important insights about friction, absolute vs limited war, war as an instrument of policy, and other topics (Brodie, 1976; Echevarria, 2007; Howard, 1976; Paret, 1976).

Clausewitz argued that the key to victory in war is attacking the enemy’s center of gravity, “the point against which all our energies should be directed” (Clausewitz, 1976: 595–596). Clausewitz identifies three as the most important:

the acts we consider most important for the defeat of the enemy are the following:

1. Destruction of his army, if it is at all significant

2. Seizure of his capital if it is not only the center of administration but also that of social, professional, and political activity

3. Delivery of an effective blow against his principal ally if that ally is more powerful than he. (Clausewitz, 1976: 596)

I begin by examining the importance of the second center of gravity Clausewitz identifies, the enemy’s capital. The capital city of a country is important for many reasons, not only because it is the center of government. It is also usually a primary financial, transportation, manufacturing and cultural center of the state, as well being of great symbolic importance. Hall (2006) categorizes capital cities into different types. Multifunction capitals, such as London and Tokyo, combine “all or most of the highest national-level functions” (Hall, 2006: 8). Other capitals, such as Washington and Brasilia, are political capitals “created as seats of government, and often lacking other functions which remain in older-established commercial cities” (Hall, 2006: 8). Clearly, capture of a multifunction capital represents a larger influence than capture of a political capital. Nonetheless, the capital city—regardless of its type—is generally a nationalist symbol representing the nation itself (Eldredge, 1975; Gordon, 2006).

Thus, the loss of the capital is not only a tremendous physical loss, it is a psychological blow as well. Rosen (2005) provides a neuropsychological argument as to why losing a decisive battle undermines the will to continue fighting, leading to loss in war; losing one’s capital city is usually the ultimate indicator of decisive loss in battle. While Rosen (2005) presents his argument as a counter to rational choice arguments, I argue that we can incorporate his basic insights into a rational choice perspective.² Through censorship and other means, the government can continue to maintain an optimistic outlook (even if only publicly), maintaining hope for eventual victory even in the face of battlefield setbacks. However, the capture of the capital by the enemy dramatically reveals the dismal chances of success for the state’s war effort. Reiter (2009) shows that states will lower their war aims (leading to war termination and defeat) even when faced with serious commitment concerns if they have no hope of ultimate victory.

In an absolute war, where annexation of the country or removing the regime from power is the goal, capturing the enemy’s capital is of obvious importance. However, even when the war is limited, capturing the enemy’s capital provides a clear revelation of information, leading to important bargaining leverage. The Mexican–American War provides a useful example. The war began in April 1846 with fighting along the Rio Grande. Despite a series of American victories as American forces pushed deep into Mexico—with armies pushing down the coast of California, south from Texas and taking Monterey, and across New Mexico—through the rest of 1846, Mexico refused to accede to American demands. In order to convince Mexico otherwise, President Polk decided to launch an invasion of Vera Cruz to enable a march on Mexico City (Clary, 2009; Wheelan, 2007). Once the USA captured Mexico City, Mexico finally agreed to cede California and the rest of what is now the southwestern USA—nearly half of Mexico’s pre-war territory—for the sum of US$15 million (Goldstein, 1992; Wheelan, 2007).

Stolfi (1991) argues that Germany could have captured Moscow if Army Group Center was not diverted to the south in August 1941, and if Moscow had been taken, the Soviet Union almost surely would have been defeated. Thus, Stolfi argues that Hitler’s crucial mistake was diverting focus away from the key center of gravity: capturing the Soviet capital. While Stolfi’s argument that a continued push on Moscow in August 1941 would have been successful is controversial among military historians (e.g. Stahel, 2011), his insistence that capturing Moscow would have been a key enabler of Germany victory is not (e.g. Glantz and House, 1998). Capturing the enemy’s capital is both a clear revelation of information regarding the course of the war and an important step in achieving military victory.³ Accordingly, the first hypothesis is:

Hypothesis 1: Capturing the enemy’s capital city makes victory in war significantly more likely.

One might question how a state can possibly avoid defeat after having its capital captured by the enemy. One possibility is for the military and political leadership of a country to relocate and continue fighting. However, the capital is frequently the largest city in the country, containing a large and probably immovable chunk of the population and economy. The capital is also the transportation nexus of the country, making it easier to control the rest of the country if you control the capital. Further, the cultural/symbolic importance of the capital does not simply transfer to a new city even if the other obstacles are surmounted. This is a tremendous undertaking at any time, but particularly in the midst of war. For example, Brazil’s relocation of the capital to Brasilia was complex, controversial, and difficult even in the absence of war (Scott, 1998). Nonetheless, it is possible, and if a country is able to successfully relocate its capital, then that provides a path to changing the course of the war.

Another possibility for avoiding defeat is if the state can quickly recapture its capital. Recapturing the capital would provide a positive boost to offset the negative of losing it in the first place. A final path to avoiding defeat is if the state has a powerful ally that provides hope of eventually turning the tide of the war. If a state is unable to either retake or relocate its capital after it has been captured, a decisive blow has been dealt. Accordingly, the second hypothesis is:

Hypothesis 2: A state whose capital is captured by the enemy is only able to avoid defeat if it is able to quickly recapture the capital, successfully relocate government functions to a new capital, or has a strong ally on its side.

The first center of gravity that Clausewitz (1976) argues is important is the enemy’s army. However, how does one know when an army is destroyed? By destruction of an army, Clausewitz means that the army ceases to be an effective fighting force. US Army doctrine considers four stages detailing the impact of losses on a unit’s combat effectiveness. These stages are indicated by color codes, where “green” indicates that the unit is combat capable (at least 85% strength); “amber” indicates that the unit is combat capable with minor deficiencies (at 70–84% strength); “red” indicates that the unit is combat ineffective (50–69% strength); and “black” indicates that the unit requires reconstitution before its next mission (<50% strength; Department of the Army, 1997: C-1).

Thus, as casualties increase, combat effectiveness decreases. While the color codes are focused on the combat effectiveness of particular units and Clausewitz is focused on the army as a whole, the same principle applies. Accordingly, I focus on battle deaths as a percentage of total military personnel strength to indicate destruction of the enemy army. However, as enemy losses mount, friendly casualties are likely to increase as well. Therefore, when destroying the enemy’s army, one must be sure to not destroy one’s own in the process. Destruction of the enemy’s army has clear importance as an enabler of military victory. While estimates are imprecise, the general trend of casualties during war is fairly well known. Thus, destruction of the enemy’s army provides an important revelation of information as well. Accordingly, the third hypothesis is:

Hypothesis 3: Ceteris paribus, as the casualties inflicted on the enemy’s army increase, victory in war becomes more likely.

The third center of gravity that Clausewitz identifies is the principal ally of the enemy. He restricts the importance of allies to only those that are stronger than the state in question. At first glance, this seems to be a useful distinction. For example, Germany and Italy were allies in the Second World War, but Germany was much stronger, and Germany was certainly a more vital ally to Italy’s war effort than Italy was to Germany’s. Thus, it is much harder to imagine Italy fighting on after the elimination of Germany from the war than vice versa. However, all allies contribute something to the coalition war effort even though they do not contribute equally. In the Second World War, the Allies’ knocking Italy, Romania, and Finland from the war certainly aided their campaign against Germany, even though they were not nearly as powerful as Germany.

Gartner and Siverson (1996) demonstrate that wars usually remain bilateral because, if potential initiators expect additional states to join the war on the side of the target, they will often be deterred from initiating. Just as states prefer to enter a war against fewer states, they prefer fighting against a smaller coalition once the war begins. Eliminating states from the opposing coalition increases one’s chances of victory. Given that, it is better to eliminate the largest allies possible from the enemy coalition. In contrast to Clausewitz, I argue that eliminating any allies from the war increases the chances of victory. This leads to the fourth hypothesis:

Hypothesis 4: As more countries are eliminated from the enemy’s coalition, victory in war becomes more likely.

Research design

To test these hypotheses, I examine employ two different units of analysis: directed war dyads and war sides. To identify wars and war participants, I use version 4 of the Correlates of War (COW) interstate war data (Sarkees and Wayman, 2010), which covers the time period 1816–2007. The COW project defines war as fighting between the regular military forces of two or more countries, directed and approved of by central authorities, with at least 1000 battle deaths.

My analysis of directed war dyads is inspired by previous analyses of war outcomes (e.g. Henderson and Bayer, 2013; Stam, 1996).⁴ Following Stam (1996: 75–77) and Reiter and Stam (2002: 52–57), as well as historical sources (Clodfelter, 2008; Dupuy and Dupuy, 1986), I modify the COW list of wars in several ways: I break up the First World War into multiple wars, dividing them by front; break up the Second World War into multiple wars, dividing them by campaign/theater; split the Vietnam War into 1965–1973 and 1975 wars; and split the Gulf War into two parts.⁵ I also delete minor allies from the Seven Weeks, Franco-Prussian, Korean, Vietnam, Kosovo, Afghanistan, and Iraq wars. Table 1 provides a list of the wars that have been split into multiple parts.

Table 1.

Wars that are split into multiple parts

Modified war	Modified actors
WWI: Belgian Campaign	Germany vs Belgium
WWI: Western Front	Germany vs France, UK, US
WWI: Eastern Front	Germany, Austria–Hungary vs Russia
WWI: Italian Front	Germany, Austria–Hungary vs Italy
WWI: Balkan Front	Germany, Austria–Hungary, Bulgaria vs Serbia, Greece, France, UK
WWI: Romanian Front	Germany, Austria–Hungary, Bulgaria, Ottoman Empire vs Romania
WWI: Turkish Front	Ottoman Empire vs UK, France, Russia
WWII: Germany–Poland	Germany vs Poland
WWII: Germany–Belgium	Germany vs Belgium
WWII: Germany–Netherlands	Germany vs Netherlands
WWII: Germany–Norway	Germany vs Norway
WWII: Germany–France	Germany vs France
WWII: Germany–UK/USA	Germany, Italy vs UK, USA
WWII: Germany–USSR	Germany vs Soviet Union
WWII: Germany–Yugoslavia	Germany vs Yugoslavia
WWII: Germany–Greece	Germany vs Greece
WWII: Japan–USA	Japan vs USA, UK
WWII: Italy–Greece	Italy vs Greece
Vietnam 1965–1973	North Vietnam vs USA, South Vietnam
Vietnam 1975	North Vietnam vs South Vietnam
Gulf War: Iraq–Kuwait	Iraq vs Kuwait
Gulf War: USA–Iraq	USA vs Iraq

For the dyadic analysis, I utilize one observation per directed-war-dyad. Because the dataset has multiple observations of each war, these observations are not independent as is assumed in standard statistical models. This nonindependence between multiple observations of the same war is dealt with using robust standard errors adjusted for clustering by war.

The second unit of analysis I employ is a side vs side analysis. This enables examination of the war as a whole rather than decomposing it into dyads or fronts. In multilateral wars, the likelihood of winning the war is a function of how your ally does on other fronts. Although Austria–Hungary had many difficulties in the First World War, the ultimate reason it lost is because Germany lost. At the same time, Germany’s need to come to Austria–Hungary’s rescue at several points during the war drained forces from the main German effort on other fronts (Wawro, 2014).

This side vs side analysis provides a k-adic analysis that overcomes limitations of dyadic analyses in dealing with multilateral wars. Poast (2010) identifies a number of limitations in using dyadic data to analyze multilateral events and recommends analyzing k-adic data to solve them.⁶ These analyses also enable the testing of hypothesis 4 regarding allies.

Dependent variable: war outcome

I consider three possible war outcomes—win, lose, or draw—and follow conventional wisdom in defining these. An initiator wins if it achieves its primary war aims and loses if it fails to do so. A target state wins if it prevents the initiator from achieving its war aims and loses otherwise. I generally follow the COW codings: wins and losses are coded accordingly, whereas compromise (“a solution is reached in which both sides gain something”; Sarkees and Wayman, 2010: 61) and stalemate (“fighting ceases without a satisfactory agreement”; Sarkees and Wayman, 2010: 61) outcomes are coded as draws. However, the COW codings are modified in two scenarios. First, for wars that have been split into parts, the outcome is coded following historical sources (Clodfelter, 2008; Dupuy and Dupuy, 1986). Second, several wars are coded by COW with an outcome of “4”, indicating that the interstate war was immediately followed by an extrastate or intrastate war. Following historical sources (Clodfelter, 2008; Dupuy and Dupuy, 1986; Goldstein, 1992), I recoded these to give the outcome of the interstate war. Several were recoded as decisive outcomes (Franco-Mexican, Angola, Second Ogaden, Bosnian Independence, Afghanistan, and Iraq wars), whereas one was recoded as a draw (War of the Communist Coalition). Because my hypotheses regard the likelihood of winning, rather than losing, the regression analyses below use only a binary dependent variable (win/lose), ignoring draws.⁷

Explanatory variables

Enemy’s capital captured

I coded capture of enemy capitals (including dates of capture) for all interstate wars from 1816 to 2007 using a variety of general histories of warfare (Clodfelter, 2008; Dupuy and Dupuy, 1986; Goldstein, 1992; Sarkees and Wayman, 2010) and histories of specific wars (Blair, 1987; Breuilly, 2002; Hart, 2013; Hastings, 1987; Powaski, 2003). For the dyadic analyses, I use a dichotomous variable, enemy capital captured, where 1 indicates that the enemy capital was captured, and 0 indicates otherwise.⁸ For the side vs side analyses, I use a dichotomous variable, any capital captured, where 1 indicates that one or more enemy capitals were captured, and 0 indicates otherwise.

Destruction of enemy’s army

To measure destruction of the enemy’s army, I focus on the battle deaths inflicted on the enemy divided by the enemy’s peak military personnel strength during the war.⁹ This is a conservative measure because it ignores captured and wounded enemy soldiers. For most wars, I use the battle deaths as coded by the COW data. For wars that have been split into parts, I code casualties using Clodfelter (2008). The military personnel strength is taken from the COW Composite Indicator of National Capabilities (CINC) data (Singer et al., 1972).¹⁰ I measure destruction of the friendly army in the same manner, except that I divide state A’s battle deaths by state A’s peak military personnel strength during the war. From these intermediate variables, I create casualty ratio, which equals the enemy casualty ratio divided by the sum of the enemy and friendly casualty ratios and varies from 0 to 1.¹¹ For the dyadic analyses, this is calculated in terms of state A and state B. For the side vs side analyses, the casualty ratio is calculated using the total casualties and personnel of side A and side B. Values from 0.5 to 1 indicate that the enemy casualty ratio is greater than the friendly casualty by an increasing margin, while values less than 0.5 indicate that the friendly casualty ratio is higher. The observed values range from 0 to 1, with a mean of 0.5 and a standard deviation of 0.36.

Control variables

Relative power

To measure states’ base level of power, I use CINC scores (Singer et al., 1972). Boulding (1962) argues that states suffer a loss of strength gradient when they project power over distances. To account for this effect of distance on power, I utilize the technique developed by Bueno de Mesquita (1981: 104–105).¹² I use the measure of distance from EUGene (Bennett and Stam, 2000), which measures the distance between capital cities adjusted for the USSR, USA, and contiguity. To calculate adjusted relative power, I divide state A’s adjusted power by the sum of the adjusted power of states A and B. For the side vs side analyses, I do not adjust power for distance given the difficulties with computing distances between sides of multiple states rather than pairs of states. I simply use relative power, which equals total of side A’s power divided by the sum of the total power of sides A and B.

Initiator

To identify initiators, I rely on the COW war data codings for initiation. In cases where wars have been split into multiple parts, the initiator of that part of the war is identified from historical sources. For the dyadic analyses, the initiator variable is coded 1 for initiating states and 0 for noninitiating states. For the side vs side analyses, the initiator variable is coded 1 for initiating sides and 0 for noninitiating sides.

Democracy

To measure democracy, I use the Polity2 variable, which ranges from −10 to 10, of the Polity IV data (Marshall et al., 2013). I use a dichotomous measure, where states with a Polity2 score greater than 5 are coded as democracies, and other states are coded as nondemocracies. For the dyadic analyses, I include variables for both states, democracy A and democracy B. For the side vs side analyses, I include the variables Average democracy A and Average democracy B, which are the average polity scores for the states on each side.

Strategic advantage

Stam (1996) developed a typology of maneuver, attrition, and punishment strategies. Coupling this with whether the states are on the strategic offensive or defensive results in 18 strategy combinations. For example, OMDA indicates offense maneuver vs defense attrition; state A is on the offensive with a maneuver strategy against state B, on the defense with an attrition strategy. Following Reiter and Stam (2002), I collapse these into a dichotomous variable that indicates if state A has a strategic advantage. The combinations OMDA, OPDM, OPDA, DPOA, DPOM, and DMOA provide an advantage and are coded 1; others are coded 0. This variable is not available for all cases, so it is not used in all models.

Number of states

For the side vs side analyses, it is important to control for the size of the opposing coalitions. Whether a side has 1, 2, or 10 states determines how many capitals are available to capture and how many states it is possible to eliminate from the war. Accordingly, I include control variables in the side vs side analyses for the Number of states A and Number of states B, each of which is a count of the number of states actively involved (according to the COW data) in the war on side A and B, respectively.

Empirical results

To test these hypotheses regarding the effect of centers of gravity on war outcomes, I conduct a series of empirical analyses. I discuss the dyadic analyses and side vs side analyses, and then examine how quickly war ends once the capital is captured.

Dyadic analyses

I begin the empirical analyses with a bivariate look at the effect of capturing the enemy capital on war outcome. The cross-tabulation between them is shown in Table 2. Of the 36 cases where the enemy’s capital was captured, 29 (80.6%) resulted in victory. Six cases resulted in draws, and one case resulted in a loss despite occupying the opponent’s capital. When the capital was not captured, only 41.4% of the cases resulted in victory. Occupying the enemy’s capital has a strong and significant impact on the likelihood of victory, supporting hypothesis 1.

Table 2.

Cross-tabulation of enemy capital captured vs outcome

Enemy capital captured	Outcome
	Lose	Draw	Win	Total
No	175	32	146	353
Yes	1	6	29	36
Total	176	38	175	389

In order to control for the effects of other factors, I turn to maximum likelihood estimation for further analyses. A series of probit models are shown in Table 3. Models 1 and 2 show bivariate regressions of the main independent variables individually. Both capturing the enemy’s capital (model 1) and destroying the enemy’s army (model 2) significantly increase the likelihood of victory.¹³ Thus, these results reaffirm the cross-tabulations above.

Table 3.

Dyadic results for prediction of victory in war, probit models

Variable		Model 1	Model 2	Model 3	Model 4
Enemy capital captured	β	1.951^**		1.774^**	1.519^**
	Se_β	0. 461		0.548	0.566
Casualty ratio			1.530^**	2.124^**	2.347^**
			0.409	0.620	0.631
Adjusted relative power				−1.232	−1.017
				0.675	0.737
Initiator				0.116	0.138
				0.264	0.298
Democracy A				0.766^**	0.629^*
				0.266	0.306
Democracy B				−0.897^**	−0.741^*
				0.292	0.343
Strategic Advantage					1.342^**
					0.426
Constant		−0.117^**	−0.774^**	−0.576^*	−0.914^**
		0.030	0.201	0.242	0.307
Wald χ ²		17.9^**	14.0^**	42.3^**	54.4^**
Log-likelihood		−226.2	−210.1	−174.6	−129.0
N		352	348	348	282

Notes: *p < 0.05, **p < 0.01. Unit of analysis is directed war-dyads. Draws are omitted from the analyses. Standard errors are robust standard errors adjusted for clustering by war.

Model 3 brings in control variables for power, initiation, and democracy. Capturing the enemy’s capital and destroying the enemy’s army have strong, highly significant effects on war outcome. Of the control variables, only the democracy variables exert statistically significant effects on war outcome; the effect of Democracy A is positive, indicating that democracies are more likely to win, whereas the effect of Democracy B is negative, indicating that states facing democratic opponents are less likely to win. Each of these results is as expected given previous research (e.g. Reiter and Stam, 2002). However, the effects of adjusted relative power and initiation are both insignificant. Interestingly, relative power is in the negative direction.¹⁴

Model 4 brings in the strategic advantage variable in addition to the variables in model 3. The results of model 4 show that a strategic advantage for a state makes victory significantly more likely, as one would expect given previous research (e.g. Bennett and Stam, 1998). The findings for all other variables are substantively identical. Most importantly for our present purposes, capturing the enemy’s capital and destroying the enemy’s army still significantly increase the likelihood of victory, even when controlling for strategic advantage.

To examine the substantive significance of these findings, I look at the effect of the key variables on the predicted probability of victory. With all other variables set to their means, when the enemy’s capital is not captured, the predicted probability of winning is 0.47; when the enemy’s capital is captured, the predicted probability increases markedly to 0.93.¹⁵ Thus, the effect of capturing the enemy’s capital has great substantive impact.

The impact of destruction of the enemy’s army is most clearly seen through a graph of the predicted probabilities, shown in Figure 1. Two curves are shown in the figure. The dark, dashed curve is the impact of the casualty ratio on the probability of victory when the enemy’s capital is not captured, while the dark, solid curve shows the impact of casualty ratio on the probability of victory when the enemy’s capital is captured.

Figure 1.

Impact of casualty ratio on probability of victory.

Beginning with the case where the enemy’s capital is captured, one can see that the predicted probability of victory is very high regardless of the casualty ratio. This indicates that capturing the enemy’s capital is a clear revelation of information. However, while the predicted probability is about 0.6 even when the casualty ratio is 0, the confidence interval is very large. As the casualty ratio increases, the confidence interval shrinks, and when the casualty ratio is 0.2—indicating that the enemy casualty ratio is 20% of the total of the two casualty ratios—the lower bound of the confidence interval is above a probability of victory of 0.5. When the casualty ratio is above 0.6, capturing the enemy capital all but guarantees victory in the war.

When the enemy capital is not captured, destruction of the enemy’s army has a clear positive impact on the likelihood of victory, although the predicted probabilities are not as large. When the casualty ratio is less than 0.5—indicating that the friendly casualty ratio is larger than the enemy’s—the likelihood of victory is less than half. However, when the destruction of the enemy’s army outstrips destruction of one’s own (the casualty ratio is greater than 0.5), the probability of victory is greater than 0.5 and grows increasingly large.

One can compare the confidence intervals of the two curves to determine the significance of the difference between capturing the enemy’s capital and not. Comparing the lower bound of the confidence interval around the solid curve with the upper bound of the confidence interval around the dashed curve, one can see that difference in the predicted probability of victory is statistically significant in all but the most extreme values of casualty ratio. Overall, these dyadic analyses provide very strong support for hypotheses 1 and 3, indicating that capturing the enemy capital and destroying the enemy’s army greatly increase the likelihood of victory.

Side vs side analyses

The second set of empirical analyses considers each war in its entirety, rather than splitting wars into dyads. For bilateral wars, the two approaches are the same, but for multilateral wars the differences could be profound. Thus, these analyses allow us to test the robustness of the dyadic findings. They also allow us to test hypothesis 4 regarding the effect of eliminating allies.

The results of the probit models analyzing wars in their entirety are shown in Table 4. I begin with two models isolating the effects of capturing capitals and eliminating allies. In model 5, the effect of capturing any enemy capital is once again positive and significant. In model 6, the percentage of enemy eliminated is also positive and significant, indicating that, when a larger portion of the enemy coalition is eliminated from the war, victory is more likely. These results provide strong support for hypotheses 1 and 4, but they do not include controls for other factors.

Table 4.

Side vs side results for prediction of victory in war, probit models

Variable		Model 5	Model 6	Model 7
Any capital captured	β	1.591^**		1.182^*
	Se_β	0.486		0.586
Percentage enemy eliminated			2.044^*	2.293^*
			0.711	1.036
Casualty ratio				2.597^**
				0.650
Relative power				−1.334^*
				0.677
Initiator				0.587^*
				0.268
Average democracy A				0.983^*
				0.388
Average democracy B				−0.934^*
				0.389
Number of states A		0.102	0.096	0.117
		0.062	0.065	0.099
Number of states B		−0.210^**	−0.196^*	−0.294^*
		0.069	0.084	0.126
Constant		0.035	0.087	−0.799^*
		0.164	0.178	0.327
Wald χ ²		21.9^**	13.4^**	83.6^**
Log-likelihood		−103.4	−107.7	−72.6
N		165	165	165

Notes: *p < 0.05, **p < 0.01. Unit of analysis is war sides. Draws are omitted from the analyses.

A more complete analysis including the various control variables is shown in model 7. Once again, the effects of any capital captured and percentage of enemy eliminated are found to be positive and significant, indicating further support for hypotheses 1 and 4. Furthermore, the effect of the casualty ratio is also found to be positive and significant, supporting hypothesis 3.

The findings for the control variables are also mostly consistent with the dyadic findings. Relative power is again found to have a negative coefficient, although this time the effect is found to be statistically significant.¹⁶ This result is driven in large part by the high correlation between relative power and the casualty ratio. Initiators are more likely to win, and the effect is statistically significant. As for regime type, the more democratic side A is, the more likely it is to win, while the more democratic side B is, the less likely side A is to win. Finally, I control for the number of states in each coalition. A larger coalition for side A has no significant effect on the likelihood that side A wins, but larger opposing coalitions (side B) have a significantly negative effect, reducing the likelihood of victory for side A.

We can again utilize predicted probabilities to examine the substantive significance of the findings. With all other variables at their means, when a capital in the enemy’s coalition is not captured, the predicted probability of winning is 0.44; when an enemy capital is captured, the predicted probability increases markedly to 0.88. Furthermore, when no member of the enemy’s coalition is eliminated from the war, the predicted probability of winning is 0.47; when half of the enemy coalition is eliminated, the predicted probability increases to 0.79.¹⁷ Thus, capturing the enemy’s capital and eliminating enemy allies from the war have great substantive impact.

A closer look at capturing the enemy’s capital

The results above show a very strong effect of capturing the enemy’s capital on the likelihood of victory. Since the analyses are static, questions about the causal relationship between capturing the capital and victory could be raised. If a state captures the enemy’s capital and the war does not end until years later, it is difficult to say that capturing the capital city revealed information that opened up a bargaining range. However, if states tend to win wars quickly after capturing the capital, then this provides stronger evidence of a causal impact. Furthermore, hypothesis 2 lays out expectations for how states can avoid defeat even if their capital is captured, but this hypothesis was not tested by the previous analyses. Accordingly, it is important to take a closer look at the relationship between capturing the enemy’s capital and the timing of war termination.

I begin by examining the distribution of durations following the capture of the enemy’s capital until the end of the war. States have captured the enemy’s capital and held it until the end of the war 32 times. Of these, the war ended within 1 day 14 times (43.8 % of the time) and within 2 weeks six additional times. Thus, 63% of the time that the enemy’s capital is captured, victory quickly follows. Only six cases featured an extended occupation of the capital (greater than 180 days, or 6 months) prior to war termination.

There are only three cases in the data where capturing the enemy’s capital and holding it for the remainder of the war did not result in victory. In the Franco-Turkish War (1919–1921), France only achieved a draw despite capturing the Turkish capital. However, Turkey was able to move its government functions from Constantinople, its prewar capital, to Ankara during the war. Similarly, Japan achieved a draw in the Third Sino-Japanese War (1937–1945) despite capturing the Chinese capital. China was able to shift its capital, first to Hankow and then to Chungking. More importantly, Japanese inability to subdue continued Chinese resistance was intricately related to its preoccupation with fighting the USA in the Pacific and American support of Nationalist Chinese forces. In contrast, France captured Mexico City and still lost the Franco-Mexican War (1862–1867). In that case, American demands for French withdrawal following the end of the American Civil War in 1865 played a vital role.

In four cases, the war ended in a draw after the enemy’s capital was captured and then lost, and each stems from the Korean War (1950–1953). North Korea held Seoul, South Korea’s capital, from 28 June to 27 September 1950. South Korea fought on in hope that the USA would turn the tide of the war, which it did with the Inchon landing on 15 September. The USA and South Korea held Pyongyang, North Korea’s capital, from 19 October to 6 December 1950. North Korea fought on because Chinese intervention offered hope for shifting the course of the war. It did, and China and North Korea held Seoul again from 4 January to 15 March 1951. South Korea once again held on to hope that the USA would reverse this setback after recovering from the surprise of Chinese intervention. In each of these cases, we see that an alliance with a stronger state played an important role in avoiding defeat, and the ability to recapture the capital played an important part in the Korean War. Thus, each of the cases where states were able to avoid defeat despite having their capital captured supports hypothesis 2.

Nearly half (14) of the 29 cases where states won when capturing the enemy’s capital ended within 1 day, while an additional six cases ended within 2 weeks. Thus, nearly 70% of the victories following capture of the capital occurred within 2 weeks. All three of the cases with an occupation of capital beyond 180 days but resulting in eventual victory occurred in South America during the 1800s. Brazil and Argentina fought against Paraguay in the Lopez War (1864–1870). After years of fighting they occupied Asuncion, capital of Paraguay, in January 1969. However, Paraguay’s leader Francisco Solano Lopez continued fighting a guerilla war until he was captured and killed in March 1870. In the War of the Pacific (1879–1883), Peru was able to continue fighting after Chile occupied Lima, the Peruvian capital, in January 1881, because they were able to establish a new seat of government at Arequipa and Bolivia continued fighting against Chile. Nonetheless, Peru eventually surrendered to Chile in October 1883.

Table 5 shows the results of a Cox proportional hazards model analyzing the duration of wars ending in victory. The results indicate that capturing the enemy’s capital greatly increases the hazard of war termination (decreasing duration). Furthermore, the hazard ratio indicates that that war termination becomes over 560% more likely once the enemy’s capital is captured. Thus, capturing the capital has a very large substantive impact. None of the control variables have a significant impact, although the initiator variable is close (p-value of 0.062).

Table 5.

Cox model results for duration of war victories

Variable		Coefficient	Hazard ratio
Enemy capital captured	β	1.726^***	5.617
	Se_β	0.258
Casualty ratio		−0.122	0.885
		0.430
Adjusted relative power		0.219	1.245
		0.451
Initiator		0.330	1.391
		0.177
Democracy A		0.151	1.163
		0.177
Democracy B		0.310	1.363
		0.231
Likelihood ratio χ ²		55.3^***
Log-likelihood		−694.4
N		215

Notes: *p < 0.1, **p < 0.05, ***p < 0.01.

These results indicate that there is a strong relationship between capturing the enemy’s capital and the end of a war. This is exactly as expected if capturing the enemy’s capital conveys crucial information leading to convergence. Reiter (2009) shows that states will continue fighting despite negative information flows if they have commitment concerns. However, if states face discouraging information from the battlefield coupled with either almost no hope for ultimate victory or prohibitively high costs of continued warfare, then they lower their war aims even if they have commitment concerns. Having one’s capital captured and held by the enemy is one of surest signals of little hope for ultimate victory, except in the rare cases that the government is able to function with a new administrative center, as in the Franco-Turkish War.

Conclusions

Bargaining models of war termination generally focus on closing the information gap between the two sides enough to create a bargaining range. However, this convergence of information is not as straightforward a process as it is assumed to be. Because empirical studies of war outcomes have focused on ex-ante factors such as power, strategy, regime type, and initiation, they are unable to explain how the actual conduct of war affects war outcomes. Thus, they are unable to shed light on the revelation of information that is fundamental to the principle of convergence.

Carl von Clausewitz (1976) has been very influential in understanding strategy and warfare, but his ideas have not been rigorously tested. One of his main ideas was that states can win wars by attacking their enemies’ centers of gravity. In this article, I argue that centers of gravity provide an important way through which information convergence is achieved and examine their effect on war outcomes through a quantitative analysis of wars from 1816 to 2007. I focus on three centers of gravity identified by Clausewitz—capture of the enemy’s capital, destruction of the enemy’s military forces, and elimination of enemy allies from the war—and find that each makes victory significantly more likely. A further hypothesis regarding how states can avoid defeat despite having their capital captured is also supported. While it is logical that these factors should make victory in war more likely, there has been only anecdotal evidence to support Clausewitz’s claims until now. Furthermore, there have been many cases where certain relationships between variables seemed obvious yet large-n analysis revealed otherwise.

In addition, bargaining models focused on the convergence of information would suggest that wars should not reach the point where one side’s capital is captured because the losing side would make concessions to end the war before it got that far. I argue that we observe differently in actual wars for two reasons. First, because the fog of war creates difficulty interpreting battlefield outcomes, the process of information convergence is not as straightforward as bargaining models assume it to be. Second, the presence of commitment problems leads states to pursue military victory rather than negotiating a settlement when information has converged.

This article also points to several important paths for future research. First, while I focus on establishing that Clausewitz’s centers of gravity are important for explaining war outcomes generally, future research could identify which center of gravity is the most essential in a given war. Second, this article demonstrates the importance of examining the effects that the actual conduct of war has on war outcomes, in contrast with conventional studies that focus solely on ex-ante factors. Finally, future research that can successfully connect battle outcomes with war outcomes would provide a tremendous contribution to our understanding of international conflict.

Footnotes

Acknowledgements

Previous versions of this article were presented at the annual meetings of the International Studies Association, San Diego, California, April 2012, and the Peace Science Society (International), Los Angeles, California, October 2011. I would like to thank Carol Atkinson, Cooper Drury, Matt Knuth, Amanda Murdie, Dan Reiter, and Laron Williams for helpful comments and suggestions.

Funding

This research is supported by a grant from the University of Missouri Center for Arts and Humanities.

Notes

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