The Arcane Art of the Statistical Analysis of Battle

There are “lies, damned lies, and statistics,” according to the former British Prime Minister Benjamin Disraeli. Christopher A. Lawrence’s War by Numbers continues that truth with an analysis of how the Dupuy Institute’s selectively collected database of military battles conforms with commonly held beliefs about warfare, and examines how statistics do or don’t support what might or might not be lies. As he does so, Lawrence, who is the Executive Director of the Dupuy Institute, updates Trevor N. Dupuy’s venerable Understanding War, the perhaps more dense Numbers, Predictions and War, and their related publications, in this recent contribution to the quantitative historical study of warfare. He presents a comprehensive methodology and transparency to an otherwise arcane mathematical topic, with short historical narratives, but including appendices of Dupuy excerpts for useful reference and summary. Although familiarity with terms like “combat effectiveness value” and “operational lethality index” would be helpful, War by Numbers is a readable discourse on the statistical analysis of military battles.

Lawrence states up front that he leaves conclusions to the readers, and that he mainly asks for further research and data collection, so that more complete and accurate analysis can be made. And while Lawrence peppers this with references to other studies which actually do offer conclusions, he emphasizes the weaknesses of available databases and the need to better quantify the difficult-to-quantify “Human Factors” of warfare, if we are to advance this field of statistical study. Lawrence spends particular effort to discuss the difficulties of Human Factors, mainly with examples from the Second World War in Italy, the Ardennes, and Kursk; plus post-Second World War modern conflicts.

By Lawrence’s own honest admission, even the impressive database he uses is still narrow, selective (partly presented in the many tables throughout the book), and hampered by the available historical record’s lack of accurate details. This contrasts to how we, in our computerized networked era, so often presumptively assume sufficient information. Not only is the database from mostly a small portion of the First and Second World Wars (only land battles mainly in the European Theatre, otherwise mostly recent Arab-Israeli and Iraqi), and usually limited by the available numeric details of even the well-known battles; caveats such as the different scale of battles (data is usually less complete for smaller engagements), and the refereed subjective quantification of terms, such as “mission outcomes” or “casualties”, all naturally hamper the analysis. What is meant by “mission” depends somewhat on interpretation, and what is meant by “casualties” can change over time by nation and even branch of service. Just settling on the definition of a “battle”, which was once at most a three day event at a specific location, but in the modern era has become continuous on a broad and often ill-defined front, requires careful massaging before including battles into the usable dataset. With those caveats, Lawrence discusses how the statistics of known factors support or don’t support common warfare presumptions, including those on: battle outcomes, exchange ratios, combat value of situational awareness and surprise, and lower levels of combat. Yet even with Lawrence’s caveats, some observations rise for discussion.

One observation is that apparently fewer casualties and no greater expenditure of resources are associated with urban combat compared to non-urban combat, despite urban combat having long been considered an operation of particular brutality and intensity. Another observation is that despite the modern increase in weapon lethality, loss rates from combat have generally declined. It also appears that an attacker never “wins” when the defender has more “knowledge” of the situation. In fact, the level of the defender’s knowledge appears far more relevant to battle outcomes than any level of the attacker’s knowledge. In contrast, force ratios appear irrelevant to the rates of advance. Perhaps surprisingly, the patterns of modern combat, despite the constant hype of technology “revolutions”, apparently have not changed much since the Second World War. As he promised, Lawrence does not state broader conclusions from the results of the statistical analysis, which might be unsatisfying to readers; but his approach does offer them an opening to draw their own conclusions with less preconceptions.

However, inherent with statistical analysis is that statistics are merely statistics, and do not and will not substitute for a specific known result of whatever is being considered. Statistics can offer a likely result, and even suggest when any other result is highly unlikely; but statistics do not, and indeed cannot, specifically guarantee a prediction. Statistically, a roll of two six-sided dice might be predicted most likely to be a “7”, and if more factors are known, such as the balance of the dice, the friction of the table, and the angle of the toss, then the better the prediction. However, there can be no guarantee, short of cheating or an absolute and precise certainty on all relevant factors, that the next roll will not be a “2”. And in fact, nowhere in Lawrence’s database structure, at least currently, will there be the calculation of an unexpected Panzer Division resting near a bridge too far at Arnhem, or the fortuitous breakdown of an M5 tank overlooking an amphibious invasion site at Kinmen Island, not to mention an Audie Murphy who jumps on top of a burning M10 to use its machine gun, or a John R. Fox who deliberately calls artillery onto his own position to trade his life for a large number of enemies. Our computers after the fact can crunch all the numbers for what we think we know of force structures and amounts; but random chance, the fog of war, and individual courage will conspire to obscure precise predictions by an algorithmic model.

On top of such uncertainties there are many the definitional vagaries, which because of the natural limitations of the available data, by necessity also must be subjectively explained and formatted. For a quantitative analysis, factors must be assigned numeric values, somewhat subjectively, given the ambiguity, for example, of what is the actual “mission” and what is a “win”. But even with clear and accurate assignment of numeric values, what happens when a battle which normally would be considered a military “loss”, results in a political or strategic victory? Do we tinker with redefining the original “mission” to achieve the proper “result” in our history? Do we consider the 1968 Tet Offensive a Vietnamese strategic victory despite losing every tactical engagement? Do we consider the 1932 Battle of Shanghai a Japanese diplomatic loss despite winning all tactical objectives? Lawrence controls this problem through focusing, as he must, only on the purely military results of the battles in the dataset, despite his being well aware of Carl von Clausewitz’ admonition that "War is the continuation of politics by other means."

And therein lays a major limitation inherent in prospectively applying quantified history whenever we attempt to shoehorn subjective terms such as “victory” into outwardly neat numeric quantities. Lawrence does not deny this difficulty, but neither does this difficulty deny the value of such statistical analysis. As Lawrence rightly points out, the ever-increasing costs of preparing for military conflicts in the modern age, and the costs of the conflicts themselves, dictate that we must seek better methods of deciding expensive policy decisions, whether in the procurement of military equipment, or in the commitment to war, rather than trust the unchallenged memes of warfare derived from fallible wargames and confirmation bias. Even if we never precisely predict the outcome of future battles, we likely would be better off knowing what and how factors affect battles so that we might make more rational policy choices.

War by Numbers is a relatively dry if still, at least for some, a very fascinating read, despite much of its space occupied by tables and graphs. It reminds us that trusted statistics can be easily manipulated by tailoring definitions and cherry-picking data. War by Numbers is not intended to relate the glorious mechanical details of any iconic military equipment, or parse the actions of any particular famous battle, or the brilliant plays of any daring commander; but it does challenge readers to consider whether their beloved truths can withstand mathematical scrutiny, perhaps even off the military battlefield.