Escalation dynamics and the severity of wars

Abstract

Although very large wars remain an enduring threat in global politics, we lack a clear understanding of how some wars become large and costly, while most do not. There are three possibilities: Large conflicts begin with intense fighting, accumulate severity over a long duration, or escalate in intensity over time. Using detailed within-conflict data on civil and interstate wars (1946–2008), we show that escalation dynamics—variations in fighting intensity within an armed conflict—are the primary mechanism for producing large conflicts. Civil wars, however, tend to deescalate once they become very large, limiting their overall severity, while interstate wars exhibit a persistent risk of continual escalation. Simple models of within-conflict severity dynamics show that this distinction compactly explains the historical size distributions of civil and interstate wars, and unconditioned escalation is a plausible mechanism for Richardson’s law—the power law pattern in the frequency and severity of interstate conflicts. The dynamics of escalation within conflicts have broad implications for conflict theory and risk assessment.

The likelihood of a large war is driven by war’s internal escalation dynamics, rather than its scale when shots are first fired.

INTRODUCTION

After two relatively quiet decades, with fewer and less deadly civil wars (1), the number and intensity of armed conflicts have risen sharply since about 2015, especially intrastate and internationalized civil wars. Wars between states, long dormant since the end of the Cold War, have also increased, with the 2022 Russian invasion of Ukraine and the 2026 war on Iran by Israel and the United States standing out. As of 2026, interstate wars are at their highest level since the late 1980s. Today’s conflicts are more numerous, more internationalized, and more lethal than at any point since the Second World War.

In these circumstances, a very large war seems increasingly possible (think China versus the United States, an expanded conflict between the United States and Iran, etc.) (2–6). However, we do not have a way to estimate the likelihood that a new war will become large and highly destructive. If a war were to occur between the United States and China, for example, then we have few tools to determine whether it would be small, medium, or large. This article reveals how some wars become large-scale slaughters, while most stay relatively limited. For instance, do large wars begin with already intense fighting? Does a conflict become large by simply lasting longer, giving more time to accumulate casualties? Or does a war become large by escalating to more intense fighting?

Most scholarly work has focused on understanding war onset and termination without considering its size (7–11). However, if we understood how wars grow or shrink once they begin (what we call conflict “dynamics”), then we would get better at predicting which conflicts are likely to explode and which are likely to fade. This understanding would also sharpen our theories about why wars start (2, 4), improve how we assess the risks of going to war, and help us estimate the odds of a major war in the next century (3, 12).

The size of a war matters. Big wars not only kill more people, but are also much more costly to a country’s economy, government, and society. A single war that kills 500,000 people has far more devastating effects than 10 smaller ones that each kill 5000 and not only in death toll but also in the broader effects that follow (13). That is why size is a better measure of a war’s true cost than simply counting how many conflicts occur (14, 15). However, despite its importance, war size is still largely overlooked. Scholars know far more about how wars start (7, 10, 11) and how they end (8, 9). However, without understanding what makes some wars so much larger and more destructive than others, we are missing a key part of the puzzle.

There are two reasons why the field struggles to answer the question of why some wars grow massive, while others remain contained. One problem is theoretical: Existing theories tend to focus on how armed conflict begins and how it ends, rather than on how its intensity unfolds in between. When past work has considered escalation within a conflict, it has tended to focus on its strategic calculations and risks—viewed, for instance, through the lens of bargaining models (16, 17). In other contexts, fighting is relegated to the military domain of tactics, terrain, and weaponry or treated as an aggregate measure of political cost. We complement these strategic perspectives (described in more detail in text SA) by operationalizing escalation as a continuous process of varying fighting intensity, providing a bridge between within-conflict dynamics and a conflict’s total severity.

Furthermore, civil wars and interstate wars are commonly treated as separate phenomena—the former between states and rebels and the latter between sovereign governments. However, we do not know whether wars escalate differently depending on which type they are or whether they follow a common pattern. For instance, do ethnic civil wars grow similarly to separatist conflicts? Do interstate wars follow a different growth trajectory than insurgencies? On average, civil and interstate conflicts do appear to be different (see text SB). Since 1946, the authoritative Correlates of War (CoW) dataset (18) has recorded 38 interstate wars, accumulating, on average, 93,000 battle deaths over 2.1 years. Civil wars are far more common (191 over the same period), but they are smaller (about 21,000 deaths) and longer (3.5 years). Civil wars are also less likely to end in negotiated settlements (19–21). However, even with all these differences, the real question remains: Are there common dynamics that explain how any war, regardless of type, becomes large?

A second challenge is empirical. Most studies use cumulative battle (military) deaths—defined as direct fatalities among combatants—to measure war severity (2, 6, 18). Cumulative deaths is a useful starting point, but it flattens everything: A long, slow-burning war and a short, explosive war can look the same through this lens. Battle deaths capture only part of the picture. While civilian casualties, displacement, and long-term economic fallout are critical dimensions of a war’s true cost, we lack consistent and reliable data to evaluate them. Military deaths remain the most reliable record of conflict intensity. Although this focus excludes substantial noncombatant harm, scholarship suggests that battle deaths are a robust proxy for overall conflict scale (22, 23). Still, the real limitation is that most data aggregate across the whole conflict, making it hard to track when and how violence escalates. Without data on year-to-year intensity, we cannot study how wars evolve. That is why this article turns to the PRIO Battle Deaths (PBD) dataset (24) to understand within-conflict dynamics, which gives annual death estimates for civil and interstate wars from 1946 to 2008. Disaggregated counts (25) allow us to look inside both types of war to study how conflict severity rises, falls, or stays the same over time and how these variations shape the likelihood of very large conflicts.

This article does three things. First, it introduces a new framework for thinking about how wars grow. Second, it uses disaggregated data to identify robust patterns in how real wars change in intensity over time and to develop a simple stochastic model of conflict escalation that connects fighting intensity, conflict duration, and cumulative conflict size or severity. Third, it compares civil and interstate wars to see whether escalation follows a shared logic, whether the biggest wars start off with intensity, last longer, or escalate, and whether escalation is a plausible explanation for the origin of Richardson’s law—the power law distribution in the sizes of interstate wars. The goal is to go beyond predicting how wars start or end to assess how severe they are likely to become once they begin.

Some readers might expect us to identify which conflict-level features correlate with fighting intensity. However, our goal in this article is different. We are interested in how wars become more intense over time, not in which types of wars are intense. This focus allows us to characterize escalation as a process rather than a static outcome. That distinction matters. Our findings show that escalation is remarkably common, suggesting that any factors driving conflicts toward greater intensity are unlikely to be neatly concentrated in a small set of preexisting conflict attributes. Instead, the fact that escalation is so ubiquitous and occurs in such a wide range of wars implies that greater fighting intensity may emerge from decentralized, context-specific dynamics that only become visible once conflict is underway. By disaggregating violence over time, we are able to observe patterns that would otherwise be obscured in aggregate analyses. This kind of within-conflict characterization complements structural explanations and offers a more precise foundation for future work that wants to ask not only why wars become more intense but also how.

MATERIALS AND METHODS

War severity and duration

Our analysis focuses narrowly on how conflict size or severity accumulates over a conflict’s duration. We do not consider the declared reasons for conflict or its political context, including the manner or locus of fighting, geography, military capacity or strategy, or relationships with other conflicts, past or future. Nor do we consider how these additional dimensions of a conflict may themselves evolve over time. This simple focus on severity dynamics within a conflict allows us to develop a generic model that can potentially be adapted to account for conflict-specific factors. Consistent with the PBD data, we define war severity specifically through direct combatant fatalities, which provides a conservative but consistent estimate of conflict intensity and ensures that our longitudinal analysis is not confounded by nonstandardized reporting of civilian or indirect “excess” deaths. To motivate this model, we contrast civil and interstate wars across three primary dimensions: magnitude, duration, and velocity.

Interstate war severity is well known to exhibit a strongly right-skewed pattern (3), such that the largest interstate wars are many orders of magnitude more severe and less frequent than a “typical war” (Fig. 1, A and C). For instance, the CoW data on wars since 1823 records 16,634,907 battle deaths for the Second World War, while the median size of an interstate war is only 7900 battle deaths (18). Since Richardson’s seminal work on conflict sizes in the mid-20th century (6), this broad variance in war sizes has often been described by a stationary power law distribution—called “Richardson’s law”—which implies a small but enduring risk of large conflicts over the next century (3).

Fig. 1. Conflict severity and duration.

Conflict severities (battle deaths) by year of onset for (A) the 95 interstate wars 1823–2003 in the CoW interstate war data (18) and (B) 264 civil wars and internationalized civil wars 1946–2008 in the PBD data (24) (omitting conflicts ongoing in 2008). The solid horizontal line in the top panel highlights the range of time covered in the bottom panel. (C) Severity distributions for the same conflicts, along with the maximum likelihood power law model for the largest-severity interstate wars [solid line; $\hat{\mathrm{\alpha }}=1.53\pm 0.07$ for $x\ge 7061$ (3)]. Inset: Distributions of conflict durations in years, showing civil wars’ much longer durations despite their statistically lower severity. However, conflict severity only weakly correlates with conflict duration (all conflicts: $r^2=0.15$).

Civil war severity also exhibits a highly right-skewed pattern (Fig. 1, B and C), albeit one that is shifted “down” in overall magnitude and with fewer very large civil wars compared to the interstate pattern. At the same time, the largest civil war was about 1000 times larger than the smallest recorded interstate conflict, meaning that their respective size ranges overlap considerably. The PBD data records the Chinese civil war as causing more than 1 million battle deaths (from 1946 onward). In contrast, the median for civil and internationalized civil wars in the postwar period is only 684 deaths (24). The CoW data have a minimum recording threshold of 1000 battle deaths. Beyond magnitude, civil wars often differ in their duration, lasting far longer than interstate wars: Although about half of interstate conflicts since 1823 and slightly more than half of civil wars since 1946 lasted no more than 2 years, the longest interstate war lasted 11 years, while the longest civil war has lasted at least 63 years. Finally, these conflict types likely differ in their escalation velocity. Interstate wars more typically involve “total war” dynamics—state-on-state contests where standing bureaucracies and industrial bases allow for rapid and large-scale mobilization, enabling step function–like increases (or decreases) in intensity. In contrast, civil wars often follow the slower-burn logistics of insurgency. Even when states have significant resources, the asymmetric nature of internal combat—including clandestine rebel movements and the need for localized control—likely imposes a structural limit on how quickly fighting intensity can pivot compared to interstate wars.

The substantial body of research on civil wars and how they may differ from interstate wars (26) says little about war severity. Past studies have shown a poor correlation between factors associated with civil war onset and subsequent severity (27). Formal models of war between rational actors tend to focus on initial outbreaks and highlight how war can occur if bargaining breaks down because of private information and incentives to misrepresent or because of commitment problems arising from shifting power or weak enforcement (28, 29). Theoretical models of conflict dynamics such as contest success functions or war-of-attrition models have not been applied to or used to guide empirical research on variations in conflict severity (30). Empirical studies have examined escalation in militarized disputes in terms of whether hostile actions are reciprocated or reach the threshold of war with more than 1000 casualties but not variation in war sizes (31). Research on conflict duration and termination has noted clear differences between interstate and civil wars. Some have suggested that problems of credible commitment are more intractable in conflicts between states and nonstate actors, causing civil conflicts to be longer than interstate wars, which tend to be more amenable to negotiated settlements once battlefield performance is revealed after conflict onset (19–21). However, these models do not address how or when escalation might occur within a conflict. Incomplete information arguments would, if anything, suggest that deescalation should be the norm due to the information gained from engagement. Fighting reveals who can do what, uncertainty shrinks, and agreement should become easier to reach over time (28, 32). For all formal accounts, rising costs of conflict should make a settlement more attractive.

Data and statistical models

The dynamics of fighting intensity over the course of an armed conflict can be represented as a time series of annual severities $x_1,x_2,\dots ,x_T$, where $x_t$ is the severity (battle deaths) in year t, T is the conflict’s total duration in years, and $X={\sum }_t{x}_t$ is the conflict’s cumulative size (Fig. 2A). Equivalently, the same conflict can be represented by the severity of the first year of fighting $x_1$ and a sequence of “escalation factors” defined as

$${\mathrm{\lambda }}_t=x_{t+1}/x_t$$ (1)

Fig. 2. Civil war severity dynamics.

(A) Severity time series $x_t$ for five selected civil war conflicts, showing highly variable periods of escalation and deescalation in annual battle deaths $x_t$ over time. PKK, Kurdistan Workers’ Party. (B) Distribution of escalation factors $\text{Pr}\left(\mathrm{\lambda }\right)$, where ${\mathrm{\lambda }}_t=x_{t+1}/x_t$, which defines the likelihood of a conflict increasing or decreasing its annual severity by a factor λ in the next year, for both civil wars (circles; $n_{\mathrm{\lambda }}=1415$, from 188 conflicts with $T>1$) and interstate wars (triangles; $n_{\mathrm{\lambda }}=97$, from 18 conflicts with $T>1$) since 1946, along with a double Pareto distribution with parameter $\hat{\mathrm{\alpha }}=2.1\pm 0.1$. (C) Joint distribution $\text{Pr}(\mathrm{\lambda }\mid x_t)$ of civil war escalation factors ${\mathrm{\lambda }}_t$ versus current annual conflict severity $x_t$, showing a systematic correlation between escalation and severity, in which conflicts below (above) $x_t=500$ tend to escalate (deescalate) in the next year. Shaded regions indicate “forbidden” factors due to minimum measurable severity.

Each such factor denotes a proportional increase (escalation, λ > 1) or decrease (deescalation, λ < 1) in annual severity as a conflict moves from year t to $t+1$. Escalation factors measure the relative changes in levels of fighting, rather than their absolute value, highlighting the conflict’s dynamics and allowing us to treat a conflict time series as generated by a first-order stochastic process. Each conflict year’s severity $x_{t+1}$ can be redefined as a product of the previous year’s severity and some level of escalation in that year: $x_{t+1}={\mathrm{\lambda }}_t x_t$, where ${\mathrm{\lambda }}_t$ is a random variable with distribution $\text{Pr}\left(\mathrm{\lambda }\right)$. Consecutive years of ${\mathrm{\lambda }}_t>1$ indicate a period of repeated escalation, driving a conflict toward larger sizes, while consecutive years of ${\mathrm{\lambda }}_t<1$ has the reverse effect (deescalation). Moreover, the distribution of empirical escalation factors across conflicts $\text{Pr}\left(\mathrm{\lambda }\right)$ will reveal any systematic tendency toward escalation or deescalation, allowing us to quantify the ex ante likelihood of different levels of escalation and deescalation and to develop a generic model of escalation dynamics over a conflict.

When characterizing within-conflict patterns of escalation, we use time series for all conflicts worldwide from 1946 to 2008 contained in the PBD data v3.1 (24). We consider all years of armed violence for (i) civil wars and internationalized civil wars, of which n = 299 meet our inclusion criteria (see text SC), resulting in 1714 conflict years, and separately (ii) interstate wars and extrastate wars, of which n = 22 meet our inclusion criteria, resulting in 119 conflict years. We omit conflicts coded as extrasystemic (conflicts in colonies, outside independent states), and we split each included conflict into time series of continuous armed fighting with no more than 1 year of below-threshold severity. The resulting dataset is disaggregated below the level of entire conflicts but remains aggregated at the level of entire years. Hence, annual severity $x_t$ may not be an accurate measure of typical conflict severity at the level of weeks or days, across space, or within individual battles.

When modeling the severity dynamics of civil wars, we rely entirely on the PBD data on civil and internationalized civil war durations, initial sizes, and escalations. In contrast, when modeling the total severity of interstate wars and, in particular, the relationship between escalation dynamics and global historical patterns such as Richardson’s law, we rely on the 95 wars over 1823–2003 contained in the CoW v4 interstate conflict dataset (18, 33) as a reference. CoW data provide comprehensive coverage in this period, are widely understood and well-scrutinized, and are the most common reference set for claims about the sizes of interstate wars.

RESULTS

We first analyze the statistical patterns of escalation factors in both civil and interstate wars. We use the resulting insights to develop a simple model of within-conflict severity dynamics that derives a conflict’s total severity from variations in fighting intensity, a conflict’s initial severity, and its total duration. We then use that model to assess the role of escalation dynamics in shaping the sizes of civil and interstate wars, whether large conflicts become large because they start with intense fighting, last longer, or escalate and whether escalation dynamics can explain the existence of Richardson’s law for interstate war sizes.

Escalation dynamics in armed conflicts

Substantial conflict escalation is likely to require a ratcheting-up in conflict-waging effort. Repeated escalation over multiple years should thus pose significant political and logistical difficulties from repeatedly building new capacity or continually reallocating resources away from civilian needs. Distinct difficulties are likely to apply to repeated conflict deescalation. Thus, substantial escalation or deescalation in fighting should be punctuated or occasional phenomena rather than continuous, and we should expect empirical escalation factors to cluster around λ = 1 (no change).

For instance, in the Afghanistan conflict (Fig. 2A), annual severity was high and relatively steady before 1990, when the government supported by the Soviet Union was fighting rebels heavily armed and trained by the United States, killing around 30,000 per year. From 1990, after Soviet forces withdrew, annual severity fell to a substantially lower level, around 5000 per year, reflecting the lessened direct foreign state support to both the government and the nonstate actors. In contrast, conflict severity in the Guatemalan civil war (1963–1995) was relatively stable over most of its duration, with around 2000 deaths per year, except for a brief period in the early 1980s where fighting spiked to 10,000 deaths per year before returning to its previous level.

For civil wars with durations $T>1$ year, empirical escalation factors across all conflict years exhibit a highly symmetric distribution that is peaked at λ = 1 (Fig. 2B), and we find no evidence of a systematic tendency to escalate or deescalate. Instead, (i) the most commonly observed change in severity within a conflict (44% of all escalation factors) is no change, i.e., fighting holds steady, and (ii) the likelihood that a conflict’s annual severity may increase to be 10 or even 100 times larger in the next year closely follows the likelihood of a concomitant decrease in severity. This unconditional distribution ignores any correlations among escalation factors or correlations with conflict covariates or the conflict’s current severity, a point we return to below. We note that the abundance of λ = 1 escalation factors is likely an artifact of the PBD’s construction: For many multiyear periods within conflicts or for some entire conflicts, the annual severities simply equal the period’s total divided by its length. However, there is no reason to expect that correcting this artifact would alter the shape of the distribution’s tails, i.e., the tendency to escalate or deescalate, and we find that removing the excess of λ = 1 factors does not substantially influence our modeling results (see text SD).

We characterize the shape of the distribution of escalation factors using a piecewise model, in which with probability q, there is no change in severity this year (${\mathrm{\lambda }}_t=1$) and, otherwise, ${\mathrm{\lambda }}_t$ is drawn from a double Pareto distribution, which has symmetric power law tails above and below the modal value. Using standard statistical techniques (34), we find that the maximum likelihood power law tail parameter is $\hat{\mathrm{\alpha }}=2.1\pm 0.1$, indicating an extremely high variance distribution (35). Furthermore, we cannot reject the Pareto distribution as a data generating process for the tails of the escalation factor distribution $(p_{\text{KS}}=0.31\pm 0.03)$. That is, the observed escalation factors are, as a group, statistically indistinguishable from an independent and identically distributed (iid) draw from the fitted double Pareto distribution.

Interstate wars do not permit an independent characterization of their escalation factors because of their smaller number in the PBD period (1945–2008) and shorter durations. However, we find that interstate war escalation factors (excluding λ = 1) are statistically indistinguishable from the empirical distribution of civil war factors [two-tailed Kolmogorov-Smirnov (KS) test, P = 0.16] and are a plausible iid draw from the estimated model of civil war factors ($p_{\text{KS}}=0.61\pm 0.03$). That is, we find no evidence that empirical escalation dynamics differ significantly between civil and interstate wars, even as the cumulative sizes and durations of these conflicts differ substantially (Fig. 1C). This statistical equivalence suggests that high-variance escalation dynamics are a generic feature of armed conflict.

Within civil wars, the escalation factors correlate slightly with annual severity, such that “hot” conflicts tend to deescalate in the next year, while “cold” conflicts tend to escalate (Fig. 2C). The effect at the lower end is attributable to left censoring because small conflicts can only become so much smaller before their severity falls below a measurable threshold (in the PBD, $x_{\text{min}}=25$). Hence, conditioned on conflict continuing for another year at measurable severities, an otherwise symmetric distribution of conflict escalation factors (Fig. 2A) would be truncated on the left side, shifting the average escalation factor to be $\langle \mathrm{\lambda }\rangle >1$ (escalation). Although there is no such constraint on the upper end, we nevertheless observe a symmetric tendency toward deescalation among large civil wars, i.e., $\langle \mathrm{\lambda }\rangle <1$ (but no such tendency among large interstate wars; fig. S2). The cross-over point between these two regimes occurs at about $x_t=500$. Hence, civil wars will tend to regress, over time, toward this “warm” value of severity, although the broad variance of escalation factors will tend to obscure that pattern in any particular conflict. An important direction of future work is to understand the causes of this systematic tendency for large civil wars to deescalate, which could be related to fundamental constraints arising from population, military capabilities, recruitment, bargaining, war fatigue, or even international pressure.

The severity of civil wars

Escalation dynamics highlight how fighting intensity often changes over the course of a conflict, and our results indicate that escalation is a common pattern in armed conflicts. However, a high-variance pattern in escalation factors does not itself indicate whether repeated escalation is required to explain the cumulative sizes of conflicts. To resolve that question, we develop a generic dynamical model that allows us to characterize whether escalation dynamics explain the cumulative sizes of civil wars (Fig. 1C). We assess the goodness of fit of the model’s output on two dimensions: the predicted war size distribution $\text{Pr}\left(X\right)$ and its corresponding size duration function X(T), which characterizes how the average size of a war varies with its duration.

The escalation model generates a conflict time series $x_1,x_2,\dots ,x_T$ in three parts: conflict duration, initial severity, and escalation dynamics. We define these model components in a nonparametric way, which leverages the PBD’s rich data on civil wars and minimizes assumptions about underlying distributional forms.

First, we draw the conflict duration T uniformly at random from the empirical distribution of civil war durations $\text{Pr}\left(T\right)$ (Fig. 1C, inset). Second, we draw the severity in the first year of fighting $x_1$ uniformly at random from the empirical distribution of initial severities $\text{Pr}\left(x_1\right)$. Third, for each year $1\le t<T$, we draw an escalation factor λ_t uniformly at random from the distribution of civil war escalation factors, conditioned on the conflict’s current severity $\text{Pr}(\mathrm{\lambda }\mid x_t)$ (see text SD), and we record $x_{t+1}={\mathrm{\lambda }}_t x_t$. The simulated conflict’s total severity is the sum of these simulated annual severities $X={\sum }_t{x}_t$.

If large conflicts become large without escalation, then they must either begin at a high initial severity or simply last long enough to accumulate a large severity. Both of these possibilities can be modeled by a “no escalation” version of the model, which includes the effects of duration and initial severity but omits any effect from escalation. In this no-escalation model, for each simulated conflict, we draw a duration T and initial severity $x_1$ and then set its total severity $X=T\times x_1$, which is equivalent to setting ${\mathrm{\lambda }}_t=1$ for all t. Both escalation and no-escalation models are fully nonparametric, with no fitted parameters; they either fit the data, or they do not.

Empirically, we find that civil war severity is only mildly correlated with conflict duration ($\text{log}X$ versus T, $r^2=0.30$, $P<{10}^{-20}$; fig. S1 and text SB), and there are many examples of large civil wars that are short and long civil wars that are not particularly large. For example, as of 2008, the civil war between the Ethiopian government and the Oromi Liberation Front had been ongoing for 25 years but with only 650 estimated total deaths, while the Chinese civil war saw an extreme death toll over only 4 years (1946–1949).

The no-escalation model poorly reproduces the observed variation in civil war size over the period 1946–2008 (Fig. 3A) but does so in a way that highlights the role of escalation dynamics. Specifically, the model produces too few conflicts of intermediate size (those between 1000 and 100,000 battle deaths), and its conflicts are systematically smaller in size X for their given duration T than in the empirical data (Fig. 3A, inset). Although the no-escalation model produces large conflicts at about the right frequency, this apparent agreement is misleading because its large civil wars have no tendency to deescalate: Each additional year of fighting increases a conflict’s severity by a fixed amount, regardless of current size; hence, the simulated X(T) grows proportionally with duration T. In contrast, the empirical function grows more quickly through the middle severity range and then levels off (or perhaps even decreases), reflecting the empirical tendency for large civil wars to deescalate (Fig. 2C). Adjusting the simulation to make conflict sizes scale up more quickly with T would improve the agreement in the middle severity range but would also create far more large conflicts than observed.

Fig. 3. Simulating civil war severities.

(A) Total severities (battle deaths) for civil wars 1946–2008, along with conflict initial severities $x_1$ and 50 simulations of total severity, with effects from initial severity and duration but without escalation. (B) Total severities for civil wars, along with simulated severities from the nonparametric escalation model (see “The severity of civil wars” subsection of Results), showing close agreement. Insets: Mean conflict severity $\langle X\rangle$ as a function of conflict duration T (years) for civil wars and the corresponding simulations, showing closer agreement under the escalation model.

In contrast, the escalation model produces conflict sizes that closely match the entire historical distribution of civil war sizes $\text{Pr}\left(X\right)$, without fitting any parameters. Allowing conflict severity to vary each year and including the empirical tendency for large civil wars to deescalate reproduces the overall shape of the size distribution, the frequency of intermediate-sized conflicts, and the frequency of the very largest conflicts (Fig. 3B). Including escalation dynamics also reproduces the observed pattern in how conflict size X tends to increase with conflict duration T (Fig. 3B, inset), both in the middle range of severity and in the upper range. These results indicate that within our modeling framework, escalation is a necessary component to explain the frequency and severity of civil wars across multiple scales and that distribution cannot be explained through duration and initial severity alone.

In principle, escalation dynamics could also be used to make a model-based forecast of a current or potential future conflict’s size. In text SE, we consider two such forecasting tasks for civil wars. In the first, we consider hypothetical civil wars in four large states (the United States, China, India, and Nigeria). Briefly, using initial severity based on estimated future population and a randomly drawn initial intensity factor, we forecast the cumulative size of the hypothetical conflict. In the second, we consider three civil wars that were ongoing in 2008 (the last year of the PBD data) in Turkey, Ethiopia, and Myanmar, and we forecast their eventual total duration and cumulative severity. The forecasts in both cases have a very broad distribution of sizes spanning more than an order of magnitude in total battle deaths (fig. S5, A and C). This variation highlights how escalation dynamics amplify uncertainty in future severity. This uncertainty is not consistent with the assumption that decision makers can accurately anticipate the likely size of a conflict at its outset but resembles the emphasis on uncertainty in warfare stressed by von Clausewitz (36).

The severity of interstate wars

We now consider the question of whether escalation dynamics can also explain the cumulative sizes of interstate wars and, in particular, their role in Richardson’s law and the enduring risk of a large conflict. However, testing the ability of escalation dynamics to explain the sizes of interstate wars requires a different approach than we used for civil wars.

A conflict-level comparison of PBD and the CoW data (33) reveals structural incompatibilities that illustrate how the “size” and duration of an interstate war can differ depending on procedural measurement choices and categorical judgments.

First, differences in procedures and thresholds can create a systematic magnitude gap. The CoW’s minimum threshold of 1000 battle deaths excludes over half of the interstate episodes listed in the PBD, which has a lower threshold of 25 annual deaths. The reported battle deaths also differ in ways that cannot be attributed to differences in stated procedures. In practice, CoW total figures appear to be notably higher: the post-1946 CoW median (5304 deaths) is nearly seven times higher than the PBD interstate median (794 deaths). PBD includes high and low and “best” estimates for each conflict, while CoW reports a single estimate, with no uncertainty. Using the best estimates when available (and the geometric mean of high and low when not) might account for the more conservative estimates in PBD compared to CoW, and the PBD may be more careful in ensuring that estimates do not include civilian deaths.

Second, classifications of wars into mutually exclusive types can be sensitive to subjective judgments, e.g., in events with elements of both domestic conflict and external intervention. Notably, CoW reclassifies the Vietnam War as interstate after 1965, arguing that increased US intervention transformed the civil war in South Vietnam, which itself followed an extrasystemic French Indochina war from 1946 until independence in 1954. Reclassification makes each episode appear as a separate conflict, even if they are arguably phases of the same conflict, involving many of the same actors. Both the Vietnam War after 1965 and the war in Afghanistan after 1979 could instead be considered continued civil wars with foreign intervention. In CoW, Kosovo becomes an interstate war with NATO intervention in March 1999, while it is considered an internationalized civil war in PBD.

The impact of these divergent classifications is evident in the resulting conflict profiles. In the 1967 Six-Day War, CoW records a total of 19,600 deaths, while the PBD’s dyad-focused coding captures only 1349 deaths for the primary Israel-Jordan dyad. Even the aggregated severity (≈2076) of PBD’s dyadic entries for 1967 is nearly an order of magnitude lower than CoW’s estimate. Discrepancies also appear in temporal anchoring: CoW records the Sino-Vietnamese conflict as two discrete wars of 1 year in 1979 and 1987 totaling 25,000 deaths, while the PBD codes a single 11-year episode (1978–1988) with continued conflict and 49,300 deaths. In general, PBD interstate conflicts are substantially longer in duration than CoW conflicts ($\langle T\rangle =5.4$ versus 2.1 years, respectively), reflecting a systematic tendency for PBD to bridge years of low-level military engagement into single continuous episodes, compared to CoW only recording the spikes.

Measures of escalation such as λ_t are less susceptible to procedural and threshold differences because they quantify proportional changes within a consistently coded conflict. However, the PBD provides annual severity estimates for only 18 interstate wars since 1946. Their lower frequency and shorter duration compared to PBD’s civil wars produce only 97 interstate escalation factors (compared to 1415 factors for civil wars), 69% of which are λ = 1. This limited empirical sample provides a poor estimate of the variance of interstate escalation. Subsampling experiments using the more abundant civil war factors (see text SD) indicate that approximately 500 empirical factors would be needed to produce stable estimates of maximum war sizes in a nonparametric model. We estimate that achieving this number of factors would require coding 91 additional interstate conflicts using PBD’s methodology; for reference, CoW includes only 57 interstate conflicts over the 1823–1945 period.

For these reasons, PBD interstate war data cannot be used to evaluate the role of escalation in producing a CoW-style pattern such as Richardson’s law or its role in shaping the likelihood of the largest interstate conflicts.

We answer these questions by instead using the CoW data as a reference and systematically investigating a fully parametric model of conflict dynamics to understand how the distribution of cumulative war sizes $\text{Pr}\left(X\right)$ depends on (i) initial conflict size, (ii) conflict duration, and (iii) the possibility of escalation. As before, a simulated conflict is specified by an initial size $x_1$ and a conflict duration T. We then consider two conditions for its severity dynamics: (model 1) no escalation, in which λ_t = 1 always and hence $X=x_1\times T$ (as in the civil war model); and (model 2) with escalation, where each year’s λ_t is drawn from a distribution. Hence, the only difference between these two conditions is whether escalation factors can vary over time, allowing increases in severity to compound.

Initial conflict sizes $x_1$ are drawn from a power law distribution with parameter η, which controls their variance. In the extreme case of η = 1.5, initial severities $\text{Pr}\left(x_1\right)$ are just as heavy-tailed as Richardson’s law for total severity (see Fig. 1C) (3). As η increases, initial sizes are smaller and have lower variance, and a conflict can only become large by either lasting substantially longer or through escalation. Conflict durations T are drawn from a geometric distribution with parameter q, which closely approximates the empirical distribution (Fig. 1C, inset) and where q can be interpreted as the annual hazard rate for war termination. Empirically, $\hat{q}=0.47$ for CoW interstate wars, which have a mean duration of $\langle T\rangle =2.1$ years.

Under the escalation condition (model 2), escalation factors λ_t are drawn from a double Pareto distribution with parameter α = 2.1, which models the unconditioned distribution of escalation factors observed in PBD conflicts and eliminates its excess λ = 1 factors (Fig. 2B and fig. S2A). This choice reflects an assumption that interstate conflict poses an unconditioned risk of escalation, i.e., that belligerents are less subject to the self-limiting tendencies observed in civil wars (Fig. 2C), being able to mobilize resources via taxation and conscription, and that conflicts may expand via alliances or geographic proximity (37, 38). Last, we enforce CoW’s minimum threshold throughout, requiring that $x_t\ge x_{\text{min}}=1000$.

The interstate war simulation is thus specified by

$$\begin{array}{c}{x}_1\sim \text{PowerLaw}\left(\mathrm{\eta }\right),\text{where} \mathrm{\eta }>1\hfill \\ T\sim \text{Geometric}\left(q\right),\text{where} q\in [0,1]\hfill \\ {\mathrm{\lambda }}_t\sim \{\begin{array}{c}\text{DoublePareto}(\mathrm{\alpha }=2.1) \text{with escalation}\hfill \\ 1 \text{no escalation}\hfill \end{array}\hfill \end{array}$$ (2)

We assess this model’s behavior using systematic parameter sweeps of η and q under each of the two conditions. For a given choice of parameters, we simulate 10⁵ conflicts, compute the simulated cumulative severity distribution $\text{Pr}\left(X\right)$, and measure its distributional distance from the empirical severities of interstate wars in CoW. Here, we use the Anderson-Darling distance, which is sensitive to deviations in both distribution body and tail; the KS distance yields similar results (see fig. S3). If large interstate conflicts can generally become large without escalation, then we expect the no-escalation condition to broadly produce Richardson-like severity distributions across the parameter space, indicated by large regions of the parameter space with small distributional distances.

Under the no-escalation condition (model 1), Richardson-like distributions of interstate war severities are only produced when the initial sizes $x_1$ are already close to Richardson, i.e., when $\mathrm{\eta }\approx 1.5$ (Fig. 4, A and C, and fig. S3B). In this regime, cumulative severity X depends mainly on initial conflict size $x_1$ and not on conflict duration T: Longer durations produce only modest increases in severity compared to the large differences caused by a Richardson-like choice of $x_1$. However, if initial conflict sizes are drawn from even a slightly narrower range (e.g., $\mathrm{\eta }\gtrsim 1.7$), large wars become substantially less likely (Fig. 4B). Longer durations (smaller q) can compensate for smaller initial sizes but only partially, and duration primarily affects the frequency of mid-range conflict severities and not the largest events. Without escalation, Richardson-like distributions are only generated under the extreme circumstances of very large initial severities.

Fig. 4. Simulating interstate war severities.

Heatmap of Anderson-Darling distances between simulated conflict severities and the empirical severity of interstate wars (CoW; 1823–2003), across initial size $x_1$ and duration T parameter choices, under two conditions: (A) without escalation and (D) with escalation (see text for model assumptions). Darker pixels indicate closer agreement with Richardson’s law, and contours indicate isoclines of the surface. (B, C, E, and F) Simulated total severity distributions $\text{Pr}\left(X\right)$ and their initial sizes $\text{Pr}\left(x_1\right)$ for the two parameterizations marked in (A) and (D). Richardson-like severity distributions are only generated without escalation when initial sizes $x_1$ are already heavy-tailed ($\mathrm{\eta }\approx 1.5$). In contrast, models with escalation more broadly produce Richardson-like severity distributions. Moreover, escalation models with longer durations and/or larger initial sizes can produce conflict severities that are more heavy-tailed than Richardson’s law. Additional simulation results are provided in text SD and fig. S3.

With escalation (model 2), conflict dynamics produce Richardson-like distributions across broad regions of the parameter space, even when initial conflict sizes and durations are modest (Fig. 4D and fig. S3D). Escalation has little impact on conflict severity when durations are extremely short ($q\gtrsim 0.65$)—in this regime, total conflict severity is again dominated by initial conflict size because duration sets a ceiling on the number of escalation factors (Fig. 4F). However, once conflict duration increases even modestly (e.g., $q\lesssim 0.5$), escalation dynamics robustly raise the likelihood of very large conflicts, producing Richardson-like severities for a wide range of settings (Fig. 4E). In the regime where conflict durations are large (e.g., $q\lesssim 0.3$), escalation tends to increase the likelihood of large conflicts so much that the distribution of interstate war sizes is more heavy-tailed than Richardson’s law (fig. S3E). These results also suggest a path by which concurrent changes in underlying processes may not lead to noticeable changes in the sizes of war. For example, if advances in technology increase the initial size $x_1$ of conflicts at the same time that changes in the international system reduce the duration T of conflicts, then $\text{Pr}\left(X\right)$ can remain well within the broad Richardson-like zone of conflict dynamics (Fig. 4D).

Within our modeling framework, these results indicate that escalation dynamics are an essential component for explaining the sizes of interstate wars, including the sizes of the very largest conflicts. That is, large wars become large primarily because they escalate, and Richardson’s law for the distribution of sizes for interstate wars can be interpreted as a direct consequence of escalation dynamics within armed conflicts. Moreover, the key difference between the sizes of civil wars and interstate wars is the presence of a systematic tendency for large civil wars to deescalate, implying that civil wars do not follow Richardson’s law.

Modeling limitations and opportunities

An important limitation of our model is that we do not explain the initial sizes of armed conflicts when they first begin. Understanding what factors predict this initial severity for either civil or interstate wars would substantially improve the utility of the escalation model in conflict forecasting tasks (12). Similarly, our analysis relies on data that are aggregated at the yearly level, and, hence, the escalation factors we introduce represent an aggregation of many events and potential escalations that occur at finer timescales. Ideal conflict data would be comprehensive at the level of battles, which would allow an exploration of how escalation dynamics unfold at different levels of temporal aggregation.

Characterizing how a conflict’s covariates shape its potential for escalation and deescalation is an important direction for future work. For instance, are some types of conflict-level incompatibilities more or less likely to produce escalation? A geographic incompatibility (39), in which a separatist group is able to operate in some ways similar to a state, may be inherently more risky for escalation than a failed military coup. Modeling escalation factors as a function of conflict-level covariates such as the type of incompatibility, geography, capabilities, characteristics of the belligerents, characteristics of allies, etc. would shed considerable light on precisely how escalation occurs.

Escalation’s broad tendency to produce Richardson-like distributions in the cumulative sizes of interstate conflicts (Fig. 4D) opens up new opportunities for understanding the origin of Richardson’s law, e.g., by focusing theoretical models on escalation as a mechanism. It also highlights how specific changes to the underlying political processes that generate conflicts would likely filter through to change the distribution of cumulative conflict sizes. For instance, increases in the initial severity of interstate wars have a much more marked impact on the likelihood of a very large war than do increases in conflict duration. However, reducing conflict duration tends to limit escalation’s potential to markedly increase severity. In this way, escalation dynamics provide a useful new lens on understanding whether the so-called “long peace” may persist, by highlighting how shifts in the tendency or likelihood of escalation, once fighting breaks out, may be constrained or amplified by other political institutions or processes. For instance, internationalization of civil wars may tend to suppress escalation, while alliances and commitment problems may tend to amplify them.

Escalation dynamics may also have an endogenous component, in which the potential for escalation depends on the particular way that the fighting unfolds or on feedback between fighting and domestic politics. Untangling the relationship between within-conflict characteristics and within-conflict severity dynamics will likely require developing new theories and new data sets. For interstate wars in particular, it may be important to disaggregate at a finer timescale than yearly since these conflicts tend to have relatively short durations.

DISCUSSION

Although large wars are dangerous precisely because of their disproportionate social, economic, and political costs, war size remains understudied both theoretically and empirically. As a result, war size often functions implicitly as a measure of cost within theories of deterrence, war onset, and war termination. Larger wars are assumed to require more extreme conditions to begin and to be more likely to end once underway because fighting is expensive. When war size is considered explicitly, the focus is typically on cumulative battle deaths after the conflict has ended, without attention to how that size was produced or how long it took to accumulate. Without a clearer understanding of how wars become large in the first place, assessments of the risk of highly destructive conflicts remain incomplete.

There are three ways a war can become large: It can begin at high intensity, last long enough to accumulate many casualties, or escalate as fighting intensifies over time. Our analyses show that large wars do not become large because they last especially long or begin with especially intense fighting. Instead, escalation is the primary mechanism by which wars become large. High-variance escalation dynamics—large changes in fighting intensity—appear to be a generic feature of armed conflict (Fig. 2B). While most conflicts exhibit periods of relative stasis, each additional year of fighting carries roughly a 10% ex ante risk of a doubling in severity and about a 1% risk of increasing by an order of magnitude.

Large wars therefore become large primarily through escalation. This finding challenges accounts of war termination that rely primarily on information revelation and instead points to a central role for commitment problems that intensify as conflicts unfold. If war arises as an information problem and states fight because they misjudge each other’s capabilities or resolve, then combat should correct that problem: Continued fighting should reduce disagreement and increase the likelihood of settlement. Our results complicate this logic in two ways. First, we find no tendency toward deescalation as information accumulates. Instead, escalation is about as likely as deescalation from one year to the next, with highly variable changes in severity and rare but extremely large upward jumps (Fig. 2B). Second, escalation is a generic feature of conflict trajectories across war types and is the main way wars become large. If learning dominated within-war dynamics, then (conditioned on a war continuing) fighting should become less intense as uncertainty declines and the range of acceptable bargains grows. Instead, violence does not settle down, and large jumps up in intensity remain just as possible as wars unfold.

Under commitment problems, settlements should be more attractive with escalation, but costs by themselves do not remove the barriers to settlement, and commitment problems do not predict convergence toward deescalation. As violence alters capabilities, territorial control, or domestic political constraints, credible commitment can become harder rather than easier. Continued fighting can therefore remain the best option even if both sides understand the likely battlefield outcome (29).

Our results are consistent with this interpretation. Escalation and deescalation are ex ante equally likely, indicating that conflict severity is not pulled toward stability. Instead, violence often holds steady before spiking suddenly. This pattern is consistent with wars being repeatedly pushed into new bargaining conditions by shifting coalitions, external intervention, alliance activation, leadership turnover, or the collapse of internal restraint. The heavy-tailed distribution of escalation factors further shows that a small number of large shifts account for a disproportionate share of large wars—exactly the kinds of changes most likely to generate or intensify commitment problems.

Standard bargaining models often treat actors as unitary and the bargaining environment as stable. Escalation dynamics suggest otherwise. Even when information about relative capabilities converges, wars can become harder to end if domestic political constraints tighten, new factions gain autonomy, or leaders lose the ability to credibly deliver compliance from their own coalition. These dynamics are especially pronounced in civil wars, where fragmented nonstate actors, shifting coalitions, and weak enforcement institutions make credible commitment particularly difficult (20, 21, 40). The only tendency toward deescalation we observe is in hot civil wars, which tend to cool off over time. This “ceiling” on escalation may reflect the structural limits inherent to internal conflict that are absent in interstate war. As intensity grows, belligerents encounter recruitment plateaus, or the scale of violence triggers international containment and domestic political pressures that constrain or reverse further escalation. In this way, barriers to settlement are not only informational but also organizational and institutional, and these barriers influence not only the end of fighting but also how the fighting intensity evolves over time.

This perspective also clarifies how escalation dynamics can inform debates about war costs and deterrence. In many models, high expected costs deter war by expanding the set of bargains preferable to fighting. Escalation dynamics point to a complementary mechanism: deep uncertainty about how costly a war might ultimately become. Because war size follows a heavy-tailed escalation process that amplifies uncertainty about future size, costs are not only high but also difficult to bound. Before war begins, this uncertainty may strengthen deterrence by making worst-case outcomes harder to insure against. Once a war is underway, the same uncertainty can encourage restraint. Actions such as widening the war, activating alliances, or introducing new capabilities risk pushing the conflict into a far more dangerous phase. Models that treat war costs as predictable or smoothly increasing largely miss this dynamic and are at odds with the emphasis on uncertainty in many classical discussions of warfare, such as by von Clausewitz (36).

Nonunitary actors who stand to benefit from prolonged warfare add another layer of complexity. Leaders may not themselves suffer from the costs of war borne by the general population and may even profit from war (41). Ideologically driven actors, by contrast, can be particularly insensitive to the suffering of followers, pursuing prolonged conflict because it aligns with their goals or beliefs (42, 43). In both cases, escalation may reflect the actors’ strategic or ideological interests rather than commitment problems.

In sum, escalation dynamics show that information problems alone cannot explain how conflict severity evolves once wars begin. Large wars are driven less by misunderstanding than by commitment problems that deepen as war reshapes the bargaining environment. The symmetry of empirical escalation factors shows that any incremental “learning” from the battlefield is effectively neutralized by changes to the commitment dynamics that drive escalation. As combat reveals information about relative capabilities, it simultaneously generates political and strategic shocks—such as shifting internal coalitions or changing stakes—that destabilize the bargaining environment. The path of a war is thus not a steady convergence toward settlement via information revelation but a volatile process where information gains are constantly offset by new barriers to credible commitment. As fighting unfolds, power shifts, enforcement weakens, and leaders become more constrained by domestic politics in ways that make peace harder to sustain. Escalation is not only a cost of war but also a process that changes the conditions of conflict over time. Viewed this way, this research on escalation links war size, war termination, and war onset through a single mechanism: How violence builds and feeds back on itself once war is underway.

Supplementary Materials

This PDF file includes:

Supplementary Text SA to SE

Figs. S1 to S7

References