Operation Reinhard (1942–1943) was the largest single murder campaign of the Holocaust, during which some 1.7 million Jews from German-occupied Poland were murdered by the Nazis. Most perished in gas chambers at the death camps Belzec, Sobibor, and Treblinka. However, the tempo, kill rates, and spatial dynamics of these events were poorly documented. Using an unusual dataset originating from railway transportation records, this study identifies an extreme phase of hyperintense killing when >1.47 million Jews—more than 25% of the Jews killed in all 6 years of World War II—were murdered by the Nazis in an intense,100-day (~3-month) surge. Operation Reinhard is shown to be an extreme event, based on kill rate, number, and proportion (>99.9%) of the population murdered in camps, highlighting its singularly violent character, even compared to other more recent genocides. The Holocaust kill rate is some 10 times higher than estimates suggested by authorities on comparative genocide.

INTRODUCTION

The Holocaust, the Nazi-German annihilation of European Jewry during World War II (1939–1945), is unarguably one of the most destructive and murderous events in the history of human civilization (1–17). However, over the last 70 years, genocides and mass killing events have continued to occur and they are not diminishing in frequency (18, 19). Bosnia, Rwanda, Darfur, Burundi, Syria, and Myanmar have all experienced large-scale murder operations in the last 25 years, some of which may have been preventable (20, 21). Developing a deeper understanding of genocides and mass killing events, including their causes, common characteristics, predictability, and mitigation, is thus considered by some as “the most important goal of social science” (18). In this respect, lessons learned from the Holocaust continue to play a vital role, and the topic remains as timely as ever.

One of the aims of this paper is to demonstrate the importance of “quantifying” warfare and conflicts by taking the Holocaust as a particular case study. An attempt is made to go beyond conventional questions, such as “How many victims perished?”, which has been the main data focus until now. Instead, we quantify how the Nazi war against the Jews evolved in time over an important period during the Holocaust and the rate at which the genocide proceeded. Consider, for example, the recent estimate that 5.4 million to 5.8 million Jews were murdered in the Holocaust in the course of World War II, mostly in the 4 years of mass killings of 1941–1945 [(9); breakdown in section S1]. Statements of this nature have limited explanatory power because, in the end, we are left with a single aggregate number that is bewilderingly large and difficult for the human mind to relate to. We gain no insights as to whether the victims were murdered uniformly in the 4 years of mass killings (i.e., 1.5 million per year), as might hypothetically be speculated, or whether there were other patterns or phases in the years of genocidal killing. Even researchers who have studied the Holocaust in detail, and who have some reasonable grasp of the historical timeline, can struggle to provide a simple clear picture of the changing kill rates over extended periods of time. Neither is this information easily found in specialist textbooks, given that they are not particularly specific and offer only limited characterization. However, this is not unexpected since the Holocaust was, after all, a highly complex and chaotic period in history. At various times over the war, the Nazis activated major genocidal death camps and controlled >40,000 Jewish ghettos and concentration camps across Europe [even going back to 1933 when the first camp at Dachau was opened (17)], all of which eventually had to be organized for implementing the Nazi leaders’ vision for the “Final Solution to the Jewish question.” With all this complexity, here we ask, Are there any simple definitive killing patterns that can be distilled from this period that can shed better light on the large-scale dynamics of the Nazi operation? To help answer this question, basic time series tools and spatiotemporal mappings are used to study an unusual dataset collected by Professor Yitzhak Arad (2) and to provide a different outlook on the Holocaust that focuses on its dynamically changing character. In the process, we identify kill rates of extreme magnitude that are almost twice as high as the Rwanda genocide and roughly 10 times higher than commonly believed.

This paper is generally concerned with Operation Reinhard, which has been referred to as “the largest single murder campaign within the Holocaust” (10). The Operation began in March 1942 and lasted 21 months, concluding in November 1943 (2). In this Operation, the three key death camps Belzec, Sobibor, and Treblinka were set up with the intention of eliminating every Jew in German-occupied Poland (1–6)—the region known as the General Government (GG). The three Nazi “death camps” or “killing centers” were infamous for their industrial mass killings and their ability to rapidly liquidate entire Jewish communities with the aid of gas chamber technology, thereby resulting in a large-scale “Holocaust by Gas.” Detailed records of the killings are almost nonexistent because of the Nazis’ tight secrecy around Operation Reinhard. Any information that was recorded was deliberately burnt and destroyed by the Nazis during the war for fear of future incrimination. In addition, a large percentage of murders have to be attributed to widespread shooting, since a “Holocaust by Bullets” took place in parallel both in and outside the GG (6, 11).

Because Auschwitz has long been viewed as the central symbol of the Holocaust, the Reinhard death camps have received relatively less attention for many years (4). While Auschwitz had a reasonable number of survivors to reconstruct the history, very few survived the camps of Operation Reinhard to convey their experiences. Partly for these reasons, Pohl (9) pointed out in 2004 that the three main death camps “Belzec, Sobibor and Treblinka became, from the Spring of 1942, the murder site of almost half of Polish Jewry [i.e., ~1.7 million people], but no scholarly camp monograph has yet been published.” Only recently have historians been able to reconstruct a reasonably accurate picture of the total numbers of victims who perished at the major death camps (7, 8, 12, 13). Although population assessments have been undertaken, the data on human lives are considered so highly sensitive that there have been very few attempts to explore it in any depth beyond coarse-scale summaries. As a result, the literature remains vague on what actually occurred during the chaos of Operation Reinhard, and efforts to address this gap have begun only in recent years (4, 10, 12, 13).

The present study relies on Arad’s (2) carefully compiled dataset of train deportations to the three key death camps. This paper first reconstructs the temporal dynamics of what actually occurred during Operation Reinhard, providing the first aggregated high-frequency time series of killings as the Operation progressed over 1942 and 1943. It uses the time series to expose the unusual speed and kill rate during Operation Reinhard, a characteristic that has been poorly quantified in the past. The rate of killing is found to be an order-of-magnitude larger than the estimates routinely cited by many internationally recognized authorities of comparative genocide (20–28). Furthermore, the paper graphically shows for the first time that the great bulk of the killings occurred in a rapid 3-month pulse during August to October 1942 (see Fig. 1). To support the analyses, this paper also explores the spatial and spatiotemporal dynamics of Operation Reinhard, as it took place in the GG and over the rail network; it presents simple indices for quantifying mass killings, with a particular focus on “kill rate,” and it improves documentation of historical events that took place over the Holocaust with the aid of visual time series, a spatiotemporal video, and basic data analysis.

Fig. 1 Holocaust kill rate. Reconstruction of Holocaust monthly kill rate in units of murders per month, totalled for Belzec, Sobibor, and Treblinka death camps and plotted as a green line from January 1942 to December 1944. The superimposed red line is the total number of murders per month after inclusion of Auschwitz victims and Einsatzgruppen shooting victims (see section S1). The actual Holocaust kill rates for the months of August, September, and October 1942 are highlighted by red dots in the ellipse. The large peak in the year 1944 (red line) represents Auschwitz victims. The thick magenta line indicates the Rwanda kill rate (243,300 murdered per month). The thick yellow box indicates the range of Holocaust kill rates based on recent erroneously published estimates that assume it to be one-third to one-fifth as intense as the Rwanda genocide kill rate.

As indicated, this study also relates to the broader framework that has sprung up in the social sciences over the last two decades, dealing with the patterns and dynamics of warfare, by learning from and by modeling past events (29). It helps set the stage for returning to study individual atrocities and rethinking approaches when discussing genocides other than the Holocaust (18, 19). As the Holocaust is often used as a reference frame when studying modern-day genocides, a quantitative view of the Holocaust is essential for understanding how modern genocides differ or are similar to those of the past. The data-driven results obtained here allow us to revisit past comparisons. For example, textbooks and the literature often state that the kill rate of the Rwanda genocide was three to five times more intense than the Holocaust. Our results allow us to quantitatively show that this claim is incorrect and thereby illustrate the importance of accurately quantifying not only the Holocaust but also modern conflicts in general.