Wednesday, April 20, 2022

Modeling Accuracy of Napoleonic Musketry

While reading David Chandler's The Campaigns of Napoleon, Chandler reports some findings determined by the Prussian military near the end of the 18th century. Apparently the Prussian military determined the accuracy of muskets at various distances using sheets (and careful counting). As I understand it, the target was a sheet of cloth roughly a man's height, though a battalion's width. The numbers reported:

  • At 75 yards, 60% of the shots fired hit the sheet
  • At 150 yards, 40% hit
  • At 225 yards, 25% hit

We can actually come up with an equation describing the proportion of shots hit as a function of distance. The trick is not to consider the proportion p = hit/(hit + miss), but instead the logarithm of the proportion p/(1 − p) = hit/miss. Why? Well, this is what we do with the logistic regression. Taking the linear regression ln(p/(1 − p)) = a + b x (where x is distance in yards) gives us coefficients:

  • a = 1.1378733 with a standard error of 0.0734506
  • b = −0.0100272 with a standard error of 0.0004533

This regression has an adjusted R-squared value of 0.9959, an F-statistic: 489.2 on 1 and 1 DF, p-value: it is statistically significant at the conventional alpha=0.05 levels.

Reworking this model, we can explicitly write the proportion of shots hitting their target as:

  • [Full model] p(x) = 1/(1 + exp(−1.1378733 + 0.0100272x))

This is approximately linear until 200 yards away:

  • [Linear approximation] plin(x) = 0.7954567260747398 − 0.0029452336313330117x

For example, the linear approximation would give plin(250) = 0.0708341 (i.e., 7% of shots hit) but the full model gives a more optimistic p(250) = 0.202793 (i.e., 20% of shots hit). For "small x", the two models agree to within a few percent. (The linear approximation will be more optimistic by at most 3.8168%.)

I'm not sure about the accuracy of the "large distance" predictions of the full model; for example, 10% of shots fired 332 yards away will hit, while 5% of shots fired 407 yards away will hit, and 1% of shots fired 571.75 yards away will hit. Perhaps this is true, and it's just the degree of informality when people say, "It is completely inaccurate after 250 yards."

One concluding remark: if you were to use this in a model, I would also add a term for morale. Presumably a soldier on the target range shoots more accurately than after receiving a devestating volley on the battle field; consequently, one would also have to add a term to reflect this.

Friday, March 25, 2022

Clausewitz Quotes

These are a bunch of random quotes which I have tried to use to guide my reading of military history. I've mentioned Clausewitz on examples before. This post is just quotes from several books Clausewitz wrote.

The Campaign of 1815 in France

These quotes are from Hofschroer's translation of On Welligton: A Critique of Waterloo, and the page numbers refer to the hardcover copy.

"After all, the main point of all criticisms of strategy, difficult though this may be, is to put oneself in the position of the decision-maker. If writers were to consider all eventualities, the great majority of criticisms of strategy would be totally without substance or diminish into minute distinctions of reasoning" (§4, pg 38).

"In strategy, nothing is more important than to avoid wasting the forces that one intends to use to make an attack by striking against thin air" (§6, pg 42).

"In war, action is like swimming against the tide, when normal attributes are insufficient to achieve even mediocre results. That is the case particularly when examining the subject of war: the object of criticism is to establish the facts and not to sit in judgment" (§34, pg 105).

On War

These quotes are from the Howard–Paret translation, published by Princeton University Press (1976).

Theory will have fulfilled its main task when it is used to analyze the constituent elements of war, to distinguish precisely what at first sight seems fused, to explain in full the properties of the means employed and to show their probable effects, to define clearly the nature of the ends in view, and to illuminate all phases of warfare in a thorough critical inquiry. Theory then becomes a guide to anyone who wants to learn about war from books; it will light his way, ease his progress, train his judgment, and help him to avoid pitfalls. (Book 2, Ch 2, pg 141)

A specialist who has spent half his life trying to master every aspect of some obscure subject is surely more likely to make headway than a man who is trying to master it in a short time. Theory exists so that one need not start fresh each time sorting out the material and plowing through it, but will find it ready to hand and in good order. It is meant to educate the mind of the future commander, or, more accurately, to guide him in his self-education, not to accompany him to the battlefield; just as a wise teacher guides and stimulates a young man's intellectual development, but is careful not to lead him by the hand for the rest of his life. (Book 2, Ch 2, pg 141)

There are certain constant factors in any engagement that will affect it to some extent; we must allow for them in our use of armed forces. These factors are the locality or terrain, the time of day, and the weather. (Book 2, Ch 2, pg 142)

Three different intellectual activities may be contained in the critical approach.

First, the discovery and interpretation of equivocal facts. This is historical research proper, and has nothing in common with theory.

Second, the tracing of effects back to their causes. This is critical analysis proper. It is essential for theory; for whatever in theory is to be defined, supported, or simply described by reference to experience can only be dealt with in this manner.

Third, the investigation and evaluation of means employed. This last is criticism proper, involving praise and censure. Here theory serves history, or rather the lessons to be drawn from history. (Book 2, Ch. 5, pg 156)

The critic's task of investigating the relation of cause and effect and the appropriateness of means to ends will be easy when cause and effect, means and ends, are closely linked. (Book 2, Ch.5, pg.158)

But in war, as in life generally, all parts of a whole are interconnected and thus the effects produced, however small their cause, must influence all subsequent military operations and modify their final outcome to some degree, however slight. In the same way, every means must influence even the ultimate purpose. (Book 2, Ch.5, pg.158)

In a critical analysis of the action, the search for the causes of phenomena and the testing of means in relation to ends always go hand in hand, for only the search for a cause will reveal the questions that need to be studied. (Book 2, Ch.5, pg.159)

Critical analysis is not just an evaluation of the means actually employed, but of all possible means—which first have to be formulated, that is, invented. One can, after all, not condemn a method without being able to suggest a better alternative. No matter how small the range of possible combinations may be in most cases, it cannot be denied that listing those that have not been used is not a mere analysis of existing things but an achievement that cannot be performed to order since it depends on the creativity of the intellect. (Book 2, Ch.5, pg.161)

The need for suggesting a better method than the one that is condemned has created the type of criticism wh.ich is used almost exclusively: the critic thinks he must only indicate the method which he considers to be better, without having to furnish proof. In consequence not everyone is convinced; others follow the same procedure, and a controversy starts without anv basis for discussion. The whole literature on war is full of this kind of thing.

The proof that we demand is needed whenever the advantage of the means suggested is not plain enough to rule out all doubts; it consists in taking each of the means and assessing and comparing the particular merits of each in relation to the objective. Once the matter has thus been reduced to simple truths, the controversy must either stop, or at least lead to new results. By the other method, the pros and cons simply cancel out. (Book II, Ch.5, pg.163)

In the study of means, the critic must naturally frequently refer to military history, for in the art of war experience counts more than any amount of abstract truths. Historical proof is subject to conditions of its own, which will be dealt with in a separate chapter; but unfortunately these conditions are so seldom met with that historical references usually only confuse matters more. (Book II, Ch.5, pg.164)

Military history in all its aspects is itself a source of instruction for the critic, and it is only natural that he should look at all particular events in the light of the whole. (Book II, Ch.5, pg.165)

A critic should therefore not check a great commander's solution to a problem as if it were a sum in arithmetic. Rather, he must recognize with admiration the commander's success, the smooth unfolding of events, the higher workings of his genius. The essential interconnections that genius had divined, the critic has to reduce to factual knowledge. (Book II, Ch.5, pg.165) Bold added.

A closer look at the use of historical examples will enable us to distinguish four points of view.

First, a historical example may simply be used as an explanation of an idea. Abstract discussion, after all, is very easily misunderstood, or not understood at all. When an author fears that this might happen, he may use a historical example to throw the necessary light on his idea and to ensure that the reader and the writer will remain in touch.

Second, it may serve to show the application of an idea. An example gives one the opportunity of demonstrating the operation of all those minor circumstances which could not be included in a general formulation of the idea. Indeed, this is the difference between theory and experience. Both the foregoing cases concerned true examples; the two that follow concern historical proof.

Third, one can appeal to historical fact to support a statement. This will suffice wherever one merely wants to prove the possibility of some phenomenon or effect.

Fourth and last, the detailed presentation of a historical event, and the combination of several events, make it possible to deduce a doctrine: the proof is in the evidence itself. (Book II, Ch.6, pg.171)

To teach the art of war entirely by historical examples, which is what Feuquières tried to do, would be an achievement of the utmost value; but it would be more than the work of a lifetime: anyone who set out to do it would first have to equip himself with a thorough personal experience of war.

Anyone who feels the urge to undertake such a task must dedicate himself for his labors as he would prepare for a pilgrimage to distant lands. He must spare no time or effort, fear no earthly power or rank, and rise above his own vanity or false modesty in order to tell, in accordance with the expression of the Code Napoleon, the truth, the whole truth, and nothing but the truth. (Book II, Ch.5, pg.174)

Saturday, March 19, 2022

DBMM Scales are all wrong

When thinking about the battle of Granicus, my inclination as a mathematical physicist was to first simulate different configurations. Wargames were developed for this purpose (in addition to training, etc.). After a brief search, it appeared the best rule set for ancient and medieval battles is "De Bellis Magistrorum Militum" (referred to by its acronym, DBMM, by the wargaming community).

DBMM uses miniatures and its unit of length is a "pace". The height of an adult human is given as 1.83 meters or 6 feet, and a pace is 0.75 meters or 2.5 feet (so a Roman mile would be 2000 paces, allegedly). Let us stipulate this all as true. Then the height of an adult human would be between 2.4 paces and 2.44 paces (take the height of a human in meters, then divide by the length of a human in meters; or take the ratio of the figures in feet).

We are also told if we use 15mm miniatures (i.e., the adult human is represented by a figure of height 15mm), then 1 pace is between 6.1475mm and 6.25mm. A syntagmata would then be roughly 16 yards by 16 yards, or 21.33 paces by 21.33 paces. This would be a base between 131.15mm and 133mm wide and long.

But the rules clearly specify the syntagmata would be 15mm, which makes no sense: it's 9-times too small. The alternative would be to scale things so the "element" [base consisting of 4 figures in 15mm] really represents only 4 soldiers, which would require 8-by-8 elements to represent a syntagmata (which is too huge).

I could do these calculations for any suggested scale, and we get similar errors in scale: with 2mm miniatures, we would need 17.5mm-by-17.5mm for a syntagmata but the rules state it needs to be 10mm; for 20mm or larger scale, we get another 9-times too small layout.

The distances provided by the rules are equally erroneous: 80 paces in 15mm scale would be between 491.8mm and 500mm (the rules state it would be 40mm, a 12-fold error), and 80 paces in 2mm scale would be between 65.5mm and 66.67mm (the rules state it would be 30mm, a 2-fold error).

To put this in context, the battle of Granicus requires at least 1346 yards for the Macedonian deployment, or the height of 673 adults stacked atop each other. This would be 10095mm at the 15mm scale (or about 10.1 meters, i.e., 33.12 feet) and 1.346 meters at the 2mm scale (i.e., 4.4 feet).

I'm still experimenting with DBMM rules to simulate a few of the ancient battles of Alexander the Great, but the distances given by the rules are entirely wrong. Worse, the rules use internally inconsistent distances, so it's impossible to use multiples of paces (or ratios of measurements) in a coherent manner unless you recalculate everything from scratch.

Friday, March 18, 2022

Battle of Granicus


Alexander the Great started his great endeavour either the last week of March or the first week of April 334BC.1Donald Engels's Alexander the Great and the Logistics of the Macedonian Army discusses the reasons for this, namely: it would coincide with arriving in Persian lands when rations ran out, but crops were harvested. The Macedonian army arrived at Sestus (a city on the Greek side of the Dardanelles) 20 days later, Arrian (I.11.3–5) reports and Donald Engels justifies in his book.

Arrian claims Alexander went to Troy whereas Parmenion took the army across the Dardenelles then to Arisbe; Diodorus agrees, but notes 60 triremes accompanied Alexander (XVII.17.2).

If organized well, it is entirely feasible the crossing took a few hours in the morning, which allows Parmenion to reach Arisbe by midday of the 22nd days of the expedition. Parmenion had to transport his men across about 2 kilometers of the Dardanelles with 160 triremes and "numerous other ships", which should take no more than a day. However, upon arriving at Sestos, it is likely the army rested a day, since horses need to rest one day every six days of marching. The alternative would be crossing the Dardanelles, and then resting, which would expose the army for a day (giving more time for Persians to organize an army to challenge the expeditionary force), which seems doubtful.

The Persian garrison of Arisbe may or may not have offered resistance, but it is likely they were able to send the message that some Greek invaders have arrived. Diodorus (XVII.18.2–4) reports the Persians did not act quickly enough to prevent the crossing but quickly organized a council of war.

The Greek mercenary general Memnon suggested to avoid fighting the invaders, and instead the Persians should destroy all crops within 30 miles. With the benefit of hindsight, we can see this plan would have complicated Alexander's plans greatly. But at the time, it sounded suicidal. Consequently, the council of war adopted the exact opposite plan: directly engage with Alexander's army at a favorable location — at Granicus river. Such, at least, is what Diodorus reports.

Diodorus tell us (XVII.19.1) Alexander learned of this then marched directly to Granicus. Arrian provides a more complete picture:

[I.12.6] From Ilium [Troy] Alexander came to Arisbe, where his entire force had encamped after crossing the Hellespont; and on the following day he came to Percote. On the next, passing by Lampsacus, he encamped near the river Practius, which flows from the Idaean mountains and discharges itself into the sea between the Hellespont and the Euxine Sea. Thence passing by the city of Colonae, he arrived at Hermotus. [7] He now sent scouts before the army under the command of Arayntas, son of Arrhabaeus, who had the squadron of the Companion cavalry which came from Apollonia, under the captain Socrates, son of Sathon, and four squadrons of what were called Prodromi (runners forward). In the march he despatched Panegorus, son of Lycagoras, one of the Companions, to take possession of the city of Priapus, which was surrendered by the inhabitants.

[8] The Persian generals were Arsames, Rheomithres, Petines, Niphates, and with them Spithridates, viceroy of Lydia and Ionia, and Arsites, governor of the Phrygia near the Hellespont. These had encamped near the city of Zeleia with the Persian cavalry and the Grecian mercenaries. [9] When they were holding a council about the state of affairs, it was reported to them that Alexander had crossed (the Hellespont). Memnon, the Rhodian, advised them not to risk a conflict with the Macedonians, since they were far superior to them in infantry, and Alexander was there in person; whereas Darius was not with them. He advised them to advance and destroy the fodder, by trampling it down under their horses' hoofs, to burn the crops of the country, and not even to spare the very cities. "For then Alexander," said he, "will not be able to stay in the land from lack of provisions." [10] It is said that in the Persian conference Arsites asserted that he would not allow a single house belonging to the people placed under his rule to be burned, and that the other Persians agreed with Arsites, because they had a suspicion that Memnon was deliberately contriving to protract the war for the purpose of obtaining honour from the king.

[I.13.1] Meantime Alexander was advancing to the river Granicus, with his army arranged for battle, having drawn up his heavy-armed troops in a double phalanx, leading the cavalry on the wings, and having ordered that the baggage should follow in the rear. And Hegelochus at the head of the cavalry, who were armed with the long pike, and about 500 of the light-armed troops, was sent by him to reconnoitre the proceedings of the enemy. [2] When Alexander was not far from the river Granicus, some of his scouts rode up to him at full speed and announced that the Persians had taken up their position on the other side of the Granicus, drawn up ready for battle. Thereupon Alexander arranged all his army with the intention of fighting.

Engels computes the time it would take for Alexander's army to march along Arrian's route would take 4 days to arrive at Hermotus from Arisbe, which would be 5 days of marching since the army had rested. Remember, horses need rest every seventh day. It is one day of marching to arrive at Granicus from Hermotus.

This would make the battle of Granicus occur in early May 334 BC.

Where is Granicus, anyways?

The only river matching the classical description would be the Biga river. However, as Hammond noted in 1980, the course of the river was quite different 2300 years ago, probably a couple miles off. I'm not an expert on rivers, and at first this sounded insane. However, ancient historians noted severe earthquakes in the middle of the 5th century BC shifted the river's course, and there have been more earthquakes over the years, in addition to man-made pumps and dams. Consequently, the exact location is not the current location of the Biga river.

Archaelogists have used radio technology to confirm Hammond's claims, but this occurred between 2005–2007. If memory serves, the course of the river c.335BC is a couple miles from the current location of the river. The best estimates I have found is that it is somewhere between Çeşmealtı, Biga and Gümüşçay (the distance between these two towns is about 2.5 miles walking, so sayeth Google maps). There is a 2000 foot long ridge along the way, which is almost certainly where the battle was fought (approximately 40.304059N, 27.300118E).

Consequently, we do not know exactly the measurements of the river (its depth, width, steepness of banks) which are critical for analyzing the battle of Granicus. We are at the mercy of the ancient authorities.

When was the battle fought

Our two authorities disagree with the timing of the battle. Arrian claims Alexander marched to the river, then fought the battle on the same day. Diodorus claims Alexander marched to the river, then camped, and the next day fought the battle.

We can make an observation: astronomically speaking, the location of the Earth in the solar system would be the same in 334BC as in 2018AD. This is important because the first week of May would have sunset about 5:05–5:15pm and a waning moon: it would be too dark to fight a night battle.2The skeptical reader may hesitate to accept this argument on grounds that we don't know exactly where the battle took place. But we know where it took place somewhere within 1 degree of latitude and longitude (which is approximately 69 miles from the location proposed). This would change the time of sunset by less than a couple minutes, which doesn't change my underlying argument.

Further, there is a 28-year cycle to our calendar. That is to say, every 28 years, the calendar has the same sunrises and sunsets. More precisely, it's subdivided into 11 years, 11 years, 6 years sub-cycles. So 334 BC has the same calendar and sunrises and sunsets as 26 BC, or 3 AD, 1798 AD, 2018 AD.

This makes Arrian's description less plausible, but not implausible. Arrian does not tell us where Alexander was when his scouts informed him of the Persian army's location. If Alexander took a more leisurely march, say camping a half-day's march away from Granicus, then it is plausible to march to Granicus and then fighting the battle. But this raises the question: why was Alexander's army marching as if to battle before learning of the position of the persian army?

Also worth mentioning, if Alexander's army marched directly to Granicus, then it's getting alarmingly close to the point of exhausting the horses. Since cavalry plays a critical role in the Macedonian hammer-and-anvil, it seems likely Alexander rested an extra day along the march Arrian describes.

Army Strength

We have discussed Alexander's army before. Let's first analyze Persian army organization, estimate its size, then return to examine the Macedonian army's strength.

"Lost in translation" hypthesis

Classical authorities disagree drastically about the size of the Persian force. I have not seen any adequate explanation, but here's what makes sense to me. The old Persian word for "regiment" is Hazabaram [literally, "thousands"] which is a composite of hazara [the number 1000] and -bam turning the number into a noun (Sekunda and Chew's The Persian Army: 560–330BC point this out on page 5). When Diodorus (XVII.19.4) tell us about the thousand Bactrian cavalry, I interpret this as something lost in translation: it's really a regiment of Bactrian cavalry.

If this hypothesis is correct, then what seems most likely is Diodorus was correct in reporting 10 cavalry regiments (XVII.19.5) but incorrect in reporting "not fewer" than 100 regiments of infantry if by "infantry regiment" Diodorus meant something like a Taxeis. Arrian reports (I.14.4) the Persian force consisted of 20,000 cavalry and "slightly less" than 20,000 infantry, which would correspond to slightly less than 20 infantry regiments.

Is it feasible the Persians could have mustered 10,000 cavalry? Well, as Michael Taylor points out in his book Antiochus the Great, 10,000 cavalry is an enormous force by ancient standards (pg.80).

If both Diodorus and Arrian err in mistranslating "regiment" because they are taking a stab (and failing) at translating the same source, then 2 of Arrian's regiment corresponds to 1 of Diodorus's regiment. This raises questions about how to reconcile the drastically different estimate of infantry. We could point out Diodorus has erred in calculations before. Another possibility is misidentification of tactical units as "regiment". A third possibility is these exaggerated numbers were in their original source, and it originally was a crude form of propaganda.

But if the mistranslation hypothesis is accurate, and relying on Arrian's estimate (I.16.2) that approximately 1 regiment of Persian cavalry fell, and further relying on the fact that Achaemenid cavalry were armored, then we should interpret Arrian's statement (I.16.7) that 300 suits of Persian armor were sent to Athen's acropylis reflects the estimate of slightly less than 300 horse in a Persian cavalry regiment. This corresponds to the Greek organization of a squadron of cavalry. (Coincidentally, Diodorus reports (XVII.21.6) 2,000 Persian cavalry dead; this is consistent with the mistranslation and misidentification hypothesis: Diodorus is working with a tactical unit half the size of Arrian's tactical unit.)

Then we have between 2,000 to 3,000 Persian cavalry at the Battle of Granicus. This matches our intuitive expectations of a hastily assembled army.

Diodorus reports (XVII.21.6) 20,000 were taken alive; Arrian reports (I.16.6) 1,000 were taken alive. I admit I am at a loss for interpreting this vast discrepency; the best I could offer is that Diodorus's tactical unit for infantry is the Sataba (a "company", 10 of them formed a regiment) whereas Arrian uses hazarabam, and the hazarabam slowly changed its effective size over the course of 170 years.3There is weak archaelogical evidence supporting this hypothesis. Sekunda and Chew cite an article by one A.N. Temerevin published in the Soviet journal Vestnik Drevnei Istorii 151 (1980,1) p.131, but I am unable to locate this journal and have no access to a university library which would contain it. For more on this, see Sekunda and Chew, pages 5–6. This still doesn't explain the anomalous factor of 2 in Diodorus's report, for which I can offer no explanation.

Remark. I do not claim this interpretation is original, and strongly suspect it's somewhere in the literature (e.g., Murray Dahm's Macedonian Phalangite Vs Persian Warrior: Alexander Confronts the Achaemenids, 334–331 BC may have made this point, or I may have "read it into" the text). In any event, I would cede credit to anyone who has thought of this before, as I am convinced this is not an original thought. (End of Remark)

Persian Army Strength

I would estimate the Persian army consists of 10 squadrons of about 250 cavalry apiece, and 20 units of 300 infantry apiece.4Postulating there were 100 "companies" of infantry (following Diodorus) forming 20 regiments (following Arrian), that would be 5 companies per regiment. The estimated number of infantry per regiment ranges from 256 in a syntagmata, or 72 in a "company" [pentekostys] around this time which yields 360 infantry in a regiment. Taking their geometric mean yields a better order-of-magnitude estimate of 300 infantry in a regiment. The composition of the infantry consists of Greek mercenaries (presumably peltasts), but also Persian infantry.

If a Persian cavalry squadron formed a wedge, the squadron would consist of 22 rows. If placed next to each other without overlap, this would be no less than 220 yards wide. If there was sufficient space for another squadron between each one deployed (think: squadron, absence, squadron, absence, etc.), then this would be 462 yards wide. I mention this because the Macedonian army should have a comparable "width", or else there would be an obvious flanking problem which is not reported in any ancient text.

Macedonian Army Strength

Arrian is our only source for the deployment of the Macedonian army (I.14.1-3):

[1] Having spoken thus, he [Alexander] sent Parmenio to command upon the left wing, while he led in person on the right. And at the head of the right wing he placed the following officers:—Philotas, son of Parmenio, with the cavalry Companions, the archers, and the Agrianian javelin-men; and Amyntas, son of Arrhabaeus, with the cavalry carrying the long pike, the Paeonians, and the squadron of Socrates, was posted near Philotas. [2] Close to these were posted the Companions who were shield-bearing infantry under the command of Nicanor, son of Parmenio. Next to these the brigade of Perdiccas, son of Orontes, then that of Coenus, son of Polemocrates; then that of Craterus, son of Alexander, and that of Amyntas, son of Andromenes; finally, the men commanded by Philip, son of Amyntas. [3] The first on the left wing were the Thessalian cavalry, commanded by Calas, son of Harpalus; next to these, the cavalry of the Grecian allies, commanded by Philip, son of Menelaus; next to these the Thracians, commanded by Agatho. Close to these were the infantry, the brigades of Craterus, Meleager, and Philip, reaching as far as the centre of the entire line.

I won't bore you with the calculations, but this would describe a battle line about 1346 yards wide (i.e., several times longer than the Persian army, and roughly twice the length of the high ground on the battle field).

For the sake of discussion, we will stipulate this deployment is accurate, and see how far we can go under this (possibly wrong) assumption.


Arrian provides the greatest detail concerning the Macedonian deployment, Diodorus provides the Persian deployment. Arrian (I.14.4) says the Persian infantry was posted along a ride, and the Persian cavalry opposite the Macedonian cavalry. We can draw a map, to scale:

The Order of Battle

The battle of Granicus opens with Alexander leading the cavalry within the right wing of the Macedonian army across the river. The Persian cavalry engages with Alexander (Diodorus XVII.19.5, Arrian I.14). Simultaneously, Parmenion leads the Macedonian cavalry from the left, and engages the cavalry directly opposing him.

The Persian cavalry prevented Alexander's wing from leaving the river, but it's unclear the depth of the river and the steepness of the banks. We are not informed about the Persian cavalry opposing Parmenion's crossing, presumably they likewise tried to prevent Parmenion's crossing.

Persian missile infantry focus on firing upon Alexander's wing of cavalry (Arrian I.15.1).

Independent of all this, the Macedonian infantry crossed the river unimpeded and unopposed. Arrian does not tell us their objective or destination, but did not engage the Persian cavalry (either because they were trying to engage the Persian infantry, or else arrived after the Persian cavalry routed).

The opening movements of the battle could be summed up as:

After fierce fighting, Arrian reports (I.16.1) and Diodorus agrees (XVII.21.4) the death of the Persian satrap ["governor"] and several other [Persian] commanders on the Persian left wing started a route. Then the Persian center routed, followed by the Persian cavalry on the right routed. Last the Persian infantry routed.

The Persian's Greek mercenaries appeared to try a tactical withdrawal, whereas the other infantry broke and fled. The Greek mercenaries were surrounded, fought valiantly, and lost. The surviving Greek mercenaries fighting with the Persians were sent back to Macedonia as slaves.

Why didn't the Macedonians pursue?

The battle thus described raises the obvious question: why didn't Alexander's cavalry pursue the Persian forces?

This is where Arrian's narrative makes more sense. If the battle was fought at the end of the day, then it would be too dark to adequately pursue. However, if this battle was fought in the morning (as Diodorus suggested), then Alexander seems naive.

I've been waffling on which authority is correct regarding the time of the battle, and the more I think about it, the more Arrian's narrative makes military sense.


Could the Persians have done anything to avoid (or, at least, improve) their outcome?

Presumably, the Persians were aware that Alexander had a sizeable force, and that they were badly outnumbered. This would be the basis of their strategy to fight at the river, where the Persians believed they would both have the literal high-ground and be able to challenge Macedonian cavalry when the Persians have the advantage [i.e., when the Macedonians are in the river and the Persian cavalry has the relative high ground]. This plan has merit, taking the high ground is always a good heuristic.

But the Macedonians outnumbered the Persians by a factor of 5. It is unclear (and impossible to know) if the Persians were aware of this. Nevertheless, this is the main obstacle the critic needs to confront.

Initially, I thought the Persians should have used chevaux de frise, but this would be anachronistic: they couldn't use something which won't be invented for a millenium.

The next alternative would be to find a superior place to challenge the Macedonians where the terrain will negate any numeric advantages. Sadly, I do not know the area as well as Memnon, so I am forced to assume this is the best feasible location for the battle.

Having made these stipulations, we are left with only one variable left: different deployments. The tactical objective would remain the same (i.e., kill Alexander the Great as quickly as possible). I think if the mercenary hoplites lay on the ground behind the Persian left cavalry, the Persian left cavalry feigned a retreat (and avoided stomping on the mercenary hoplites), the Macedonians would have pursued and found themselves in a tight spot. This is more complicated to execute, far easier to say from the comfort of an armchair.

The only alternatives besides this would be to have a unit or two of the Persian right cavalry be deployed on the left instead, or to deploy mercenary Peltasts on the Persian left. But this is all said with the benefit of hindsight, I know the Persians failed. If I were planning before the battle, would this recommendation still make sense? Probably not the cavalry redeployment, but perhaps the light infantry.

Concluding Remarks

Just from the numbers alone (6000 Persian infantry against 32000 Macedonian infantry, 2500 Persian cavalry against roughly 5000 Macedonian cavalry) it is clear the Persians are at a disadvantage.

A lingering question remains, why does anyone care about this battle that amounted to little more than a cavalry skirmish? I think the answer is two-fold: (a) it is the first battle Alexander the Great fought against Persian forces; and (b) it is a form of ancient propaganda. After carefully studying the literature on this battle, I don't think it's worth the ink spilled over its details.

But it is important because later generals may refer back to this battle in their thinking.


  • Murray Dahm, Macedonian Phalangite Vs Persian Warrior: Alexander Confronts the Achaemenids, 334–331 BC. Osprey, 2019.
  • Donald W. Engels, Alexander the Great and the Logistics of the Macedonian Army. University of California Press, 1980.
  • N. G. L. Hammond, "The Battle of the Granicus River". The Journal of Hellenic Studies 100 (1980) pp.73-88, doi:10.2307/630733
  • Nick Sekunda and Simon Chew, The Persian Army: 560–330B.C. Osprey, 1992.
  • Michael Taylor, Antiochus the Great. Pen and Sword Military, 2013.
  • Kathleen Toohey, The Battle Tactics of Alexander the Great. Ch.2 The Battle of the Granicus, PhD thesis.

Wednesday, March 16, 2022

Army of Alexander the Great

Alexander's Army

Our only source for Alexander's army organization is Diodorus (XVII.17.3-5):

There were found to be, of infantry, twelve thousand Macedonians, seven thousand allies, and five thousand mercenaries, all of whom were under the command of Parmenion. [4] Odrysians, Triballians, and Illyrians accompanied him to the number of seven thousand; and of archers and the so-called Agrianians one thousand, making up a total of thirty-two thousand foot soldiers. Of cavalry there were eighteen hundred Macedonians, commanded by Philotas son of Parmenion; eighteen hundred Thessalians, commanded by Callas son of Harpalus; six hundred from the rest of Greece under the command of Erigyius; and nine hundred Thracian and Paeonian scouts with Cassander in command, making a total of forty-five hundred cavalry. These were the men who crossed with Alexander to Asia.

To tally this in a more succinct fashion:

  • Heavy Infantry (24,000)
    • 12,000 Macedonian phalangites
    • 7,000 Greek ally hoplites
    • 5,000 mercenary hoplites
  • Light Infantry (8,000)
    • 7,000 Odrysians, Triballians, and Illyrians
    • 1,000 Agrianians and archers
  • Heavy Cavalry (3,600)
    • 1,800 Macedonian cavalry
    • 1,800 Thessalian cavalry
  • Light Cavalry (1,500)
    • 600 Greek Ally cavalry
    • 900 Thracian and Paeonian scouts

I'm a little confused by Diodorus's arithmetical error with tabulating the cavalry; I guess there's a reason Diodorus became a historian and not a mathematician.

The questions we will try to answer here are: how were these units organized? What formation did they take on the battle field? How were they armed? What tactical roles did they play? How much "space" did they take up? (This last question will be useful when trying to double check ancient estimates of army sizes.)


Heavy Infantry

The role heavy infantry played at this time in history is to provide a "solid center". This distinguishes heavy from light infantry, as light infantry plays a complementary role in battle.

When estimating the battle front, we should approximate one heavy infantrymen to be approximately 1 yard per man [0.91 meter]. Marsden's Gaugamela (pg.66) makes this approximation, citing Polybius (XVIII.29.2); Kathleen Toohey's Battle Tactics ch.2 (pg.41) acknowledges this as reasonable.

Macedonian Phalangites

We have discussed Macedonian phalangites before. (Note: the technically correct term would be "pezhetairoi", not phalangite.)

Unlike the Greek hoplite, the phalangite had no breastplate and a smaller shield.

Phalangites were organized into 16-by-16 squares called syntagmata (sometimes translated as "battalion"). Then 6 syntagmata form a taxeis consisting of 1536 infantry, and a variable number of taxeis form a phalanx.

As discussed before, the surissa was much longer than the Greek spear, and as far as using it in combat. Well, Kathleen Toohey refers to this YouTube clip showing what seems like a reasonable deployment (around minute 2 until the end):

Greek Hoplites

We have discussed hoplites before. The critical aspect of a hoplite unit was working as a team, forming a shield line.

The Spartan army had the following organization: A column (literally, a line) of 8 soldiers forms a file, and 4 files form a enomotia ("platoon"). Then 4 enomotiai form a pentekostys ("company"). Then 4 pentekostys form a lochos. There were 7 lochoi in the army. That is to say,

  • 1 file = 8 soldiers (highlighted in red below)
  • 1 enomotia = 4 files = 32 soldiers (highlighted in blue below)
  • 1 pentekostys = 4 enomotiai = 128 soldiers (one group of 4 black rectangles below)
  • 1 lochos = 4 pentekostys = 512 soldiers

I think the pentekostys is analogous (in its tactical role) to a phalangite syntagmata, and a lochos is analogous to a taxeis.

Caution: the term "lochos" is used at different times in Ancient Greece for different organizational units (e.g., other ancient authors use it to refer to a "file" in other armies), but Spartan organization has been fairly consistent about consisting of 4 pentekostys. The reader is urged to take care when reading ancient sources if this term appears.

Light Infantry

Light infantry had a variety of roles, usually skirmishing or screening. Unlike heavy infantry, the light infantry were not drawn up in rows and columns: light infantry form a "loose mob", not a rectangle.

The role of ancient light infantry includes protecting the flanks and rear of heavy infantry, as well as using their projectiles either to wound advancing heavy infantry or else get lodged into the shields of heavy infantry (which would be forced to discard the shield or hinder the fighter).


The term "peltast" seems to refer to javelin-armed light infantry, Xenophon explicitly distinguishes Thracian peltasts from Greek peltasts. Their pelte shield carried was smaller than the Hoplite's shield. But the weapons given to peltasts do not seem to be standardized: some carried 2 javelins, others carried spears.

Peltasts defended the flanks and rear of heavy infantry, particular from enemy cavalry. For this reason, mobility is the crucial quality of peltasts in battle.


Remember: stirrups have not yet been invented. All cavalry at this time lacked stirrups.

The roles heavy and light cavalry played, at this time, are just beginning to be distinguished from each other. Thus speaking of "light" or "heavy" cavalry is slightly anachronistic. Squadrons [Gk: ila singular, ilai plural] of companion cavalry were used for scouting, and Thessalian cavalry functioned as shock troops in several battles.

If estimating the dimensions of a horse, Google claims the length of a horse is 8 feet (or, rounding up, 3 yards). The width that should be used for a horse is 3 feet, as Kathleen Toohey points out in her discussion of the battle of Granicus [The front occupied by an individual cavalryman should therefore be taken to have been only three feet]. For our metric friends, that's a 3 meters length and a 1 meter width.

Heavy Cavalry

Macedonian Cavalry

The Macedonian heavy cavalry, the famous Companions, acted like heavy cavalry and charged into the enemy at speed. How, exactly, this worked without stirrups ensuring the rider won't be unseated, well, it remains unclear (and probably will remain unclear).

Macedonian heavy cavalry fought in wedge formation (a "triangle" or "arrowhead").

Various sources have suggested 200 Companions in a squadron, which (if in wedge formation) would suggest 20 rows drawn up in a triangle. Mathematicians will recognize this is due to the nature of triangular numbers.

Thessalian Cavalry

The role of Thessalian cavalry seems hotly debated. Kathleen Toohey argues they were light cavalry, other scholars argue they were heavy cavalry.

Scholars debate what formation the Thessalian cavalry employed. Extant text from various histories suggest they formed a Lozenge ("diamond") shape. Some scholars argue this was just for training purposes, other scholars point out a lozenge can change direction quickly while retaining the benefits of a wedge.

If the lozenge formation is used, it is likely to have 15-by-15 horse in a squadron (or 225 horse in a squadron), and 8 Thessalian squadrons joined Alexander's army. On the other hand, in a wedge formation, 21 rows would be used (approximately 231 horse in a squadron).

Scholars also debate whether Thessalians were light cavalry or heavy cavalry. This debate, in my mind, is a bit of a "sideshow" since Alexander the Great really introduced "combined tactics". Before now (e.g., at Leuctria), cavalry only engaged with cavalry, infantry only fought infantry. Alexander's battles are literally the dawn of distinguishing "light cavalry" from "heavy cavalry", and Thessalians played both roles throughout the campaigns.

Light Cavalry

Thracian Cavalry

Thracian cavalry (including Odrysians) fought like javelin-armed skirmishers. Armed with 2 javelins (one for throwing, the other for melee) and a sword, scholars believe the Greek cavalry modeled themselves after the Thracians.

Webber's The Thracians (pg 41) and Ashley's The Macedonian Empire (pg 34) argue the Thracian cavalry were organized into wedge formations.

Ashley argues (pg 34) there were 500 Thracians organized into 4 squadrons, which would roughly correspond to the 15th triangular number (i.e., 120 horse organized into 15 rows). Marsden's Gaugamela (pg.38) argues there were 450 Thracians organized into 3 squadrons of 150 cavalry each, which would correspond to the 17th triangular number (i.e., 153 horse organized into 17 rows).

Greek Ally Cavalry

Kathleen Toohey summarizes allied Greek cavalry as being equipped with a helmet, a breastplate, but no shield. For weapons, two javelins (one for throwing, the other for melee acting as a spear) and a sword attached at the belt.

The standard formation for Greek cavalry was a rectangle, not a wedge (nor the exotic lozenge). The 600 Greek cavalry were organized into 5 squadrons [ilai] of 120 horse each. Connolly's Greece and Rome at War (pg 71) suggests they were organized 8 deep ["rows"] and 16 abreast ["columns"].


  • J.R. Ashley, The Macedonian Empire: The Era of Warfare Under Philip II and Alexander the Great, 359-323 B.C. McFarland, 2004.
  • P. Connolly, Greece and Rome at War. Macdonal Phoebus, 1981.
  • E.W. Marsden, Campaign of Gaugamela. Liverpool University Press, 1964.
  • Rolf Strootman, "Alexander’s Thessalian cavalry". In Proceedings of the Dutch Archaeological Society, 2011. Eprint
  • Kathleen Toohey, "The Battle Tactics of Alexander the Great". PhD thesis, revised in 2018.
    • Light infantry, chapter 1 part 1, eprint.
    • Heavy infantry, chapter 1 part 2, eprint
    • Greek allies and mercenaries, chapter 1 part 3, eprint
    • Light cavalry, chapter 1 part 4, eprint
    • Heavy cavalry, chapter 1 part 6, eprint
  • Christopher Webber, The Thracians: 700BC–AD46. Osprey press, 2001.

Thursday, March 10, 2022

Great Captains of History: A Reading List

Napoleon concludes his Military Maxims with:

Maxim LXXVIII. Peruse again and again the campaigns of Alexander, Hannibal, Caesar, Gustavus Adolphus, Turenne, Engene, and Frederick. Model yourself upon them. This is the only means of becoming a great captain, and of acquiring the secret of the art of war. Your own genius will be enlightened and improved by this study, and you will learn to reject all maxiums foreign to the principles of these great commanders.

Presumably, this is elaborated in The Edinburgh monthly magazine, vol 14, (1823) pg 176. There, the translation is:

Make offensive war like Alexander, Hannibal, Gustavus Adolphus, Turenne, Prince Eugene, and Frederic. Read again and againthe history of their 88 campaigns; model yourself upon them. That is the only way to become a great commander, and to obtain the secrets of their art.


“Alexander conducted eight campaigns—in Asia and India; Hannibal, seventeen—one in Spain, fifteen in Italy, and one in Africa; Caesar, thirteen—eight against the Gauls, and five against Pompey's legions; Gustavus Adolphus, three—one in Livonia against the Russians, and two in Germany against the House of Austria; Turenne, eighteen—nine in France, and nine in Germany; Prince Eugene, thirteen—two against the Turks, five in Italy against France, and six on the Rhine, or in Flanders; Frederic, eleven—in Silesia, Bohemia, and on the Elbe. The history of these 88 campaigns would be a complete treatise on the art of war.”

These 88 campaigns are necessary for a good education, but probably insufficient. That is to say, if we omitted one of these campaigns, we would always have an incomplete education; but if we only studied these 88 campaigns, we probably won't have a complete education, either. After all, what of the 14 campaigns of Napoleon (2 in Italy, 5 in Germany, 2 in Africa and Asia, 2 in Poland and Russia, 1 in Spain, and 2 in France)? Or the undefeated Suvorov? Or the American civil war? Or World War 2?

But still, these 88 campaigns are a good starting point. I'd like to write a bibliography surveying these campaigns. (The curious reader may wonder whether Napoleon's recommendations stand up to scrutiny; there is some statistical arguments supporting aspects of the claim.)

I will probably update this with more books as I read them, and link to blog-posts studying these campaigns and battles as I get to them.

Caution: On the term "Campaign"

The word "campaign", classically, refers to one year ending in Winter. Sometimes there was combat in Winter, but usually it was a time of recovery and reorganizing. So the numbers of "[number] N campaigns in [region] Y" should be taken with a gram of salt.

Alexander — 8 campaigns (in Asia and India)

  • Battle of the Granicus River (Asia Minor)
  • Siege of Halicarnassus (Asia Minor)
  • Battle of Issus (Syria)
  • Siege of Tyre (Syria)
  • Siege of Gaza (Egypt)
  • Battle of Gaugamela (Egypt)
  • Siege of the Sogdian Rock (Bactria/Afghanistan)
  • Invasion of India

Primary sources — well, that notion is kind of fuzzy with ancient warfare. Callistenes was the official "court historian" of Alexander, but his work has been lost. The extant ancient sources includes:

  • Arrian
  • Polybius
  • Curtius Historiae Alexandri Magni, presumably based mostly on Cleitarchus
  • Diodorus's Bibliotheca historica Book 17 relates the conquests of Alexander, based almost entirely on Cleitarchus and Hieronymus of Cardia
  • Plutarch, but this should be taken with a ton of salt (I don't even consult it);
  • Justin, which compresses Trogus's lost works on Alexander, focusing more on moralistic points (I don't consult it)

Other resources I've found valuable includes Engel's Alexander the Great and the Logistics of the Macedonian Army, and for the mechanics of pike, the article "Pike Drills" Colburn's United Service Magazine and Naval and Military Journal (1867), pp.536–544, provides useful details.

I would be remiss to omit Kathleen Toohey's Battle Tactics of Alexander the Great.

Hannibal — 17 campaigns (one in Spain, fifteen in Italy, and one in Africa)

The campaign in Spain...refers to Hannibal's early career conquering Iberia?

The 15 campaigns in Italy refer to the Second Punic War. In particular, the battle of Trebia, and the battle of Cannae, are noteworthy.

The African Campaign presumably refers to the Battle of Zama.

Polybius's Histories is the only surviving primary source about the Second Punic war. Although Livy wrote about the war, he is more poet than historian, and shouldn't be relied upon for military history. Hans Delbrück's History of the Art of War (vol I) discusses the Second Punic war in good detail. Cannae has been one of the most studied battles in 19th century (and early 20th century) Prussia.

Caesar — 13 campaigns (eight against the Gauls, five against Pompey’s legions)

Major Douglas C. Sanders, "Julius Caesar and the Gallic Campaign: A Road map to the Use of the Instruments of Power". PDF

Kurt Raaflaub and John Ramsey, "Reconstructing the chronology of Caesar's Gallic Wars". Histos 11 (2017) 1–74, Eprint.

Jameson Minto, Logistics during Caesar’s Campaigns in Gaul.

Gustavus Adolphus — 3 campaigns (one in Livonia against the Russians, two in Germany against the house of Austria)

  • The Livonian campaign almost certainly refers to the Ingrian war (1610-1617)
  • The other two campaigns against Austria (well, the "Holy Roman Empire") probably refer to the Thirty years war

I would think the Swedish-Polish war worth studying, but perhaps not.

Turenne — 18 campaigns (nine in France, nine in Germany)

Also known as Henri de la Tour d'Auvergne.

  • Four "Famous Campaigns" which brought an end to the Thirty Years' Wars in Germany
    • Battle of Freiburg (3, 5, 9 August 1644)
    • Battle of Mergentheim (2 May 1645)
    • Battle of Allerheim (3 August 1645)
    • Battle of Zusmarshausen (17 May 1648)
  • Fronde, a series of Civil Wars in France between 1648-1653
    • Specifically the Second Frond (1650-1653)
    • The Franco-Spanish War (for Turenne, 1653-1659)
  • The Dutch War (presumably constitue the other 5 German campaigns)

Prince Eugene — 13 campaigns (two against the Turks, five in Italy against France, and six on the Rhine or in Flanders)

The two Turkish campaigns appear to refer to the "Great Turkish War" (Eugene was involved in the Battle of Zenta) and the "Austro-Turkish War of 1716-18".

The Italian campaigns, presumably, refer to the early years in the War of Spanish Succession.

The remaining campaigns on the Rhine or in Flanders refers to the later years in the War of Spanish Succession.

Nicholas Henderson, Prince Eugen of Savoy: A Biography. Phoenix publisher, 2002.

Derek McKay, Prince Eugene of Savoy (1977).

Frederick the Great — 11 campaigns (in Silesia, Bohemia, and on the Elbe).

  • The Silesian Wars
    • The War of Austrian Succession (16 December 1740)
  • The Seven Years War
    • Battle of Leuthen
  • War of Bavarian Succession
  • Battle of Mollwitz (Bohemia, 10 April 1741)

Closing Remarks/Apology

I'm working my way through collating my notes on Alexander the Great, so I probably have more references for his campaigns than the more modern generals.

But I would err on the side of studying military history mildly sequentially, since — like philosophy — military endeavours are like on-going philosophical dialogs which builds on the contributions of the past. For example, Napoleon contributed nothing new to military theory, because he merely mastered the techniques of the past and adapted them to his situation.

As old Clausewitz put it, "After all, the main point of all criticisms of strategy, difficult though this may be, is to put oneself in the position of the decision-maker. (Hofschroer [tr.], On Welligton: A Critique of Waterloo, §4, pg 38) And the decision-maker only has prior history to consult.

I hope, next time, to discuss Alexander the Great's first major battle, the battle of Issus. (The battle of Grannicus appears to be more a work of propaganda than an actual battle worth studying.)

Wednesday, March 13, 2013

Book Review of Boot's "Invisible Armies"

A short promotion: I reviewed Max Boot's Invisible Armies. You can read it in full here.