A post by Sean Manning on numbers in barbarian armies. It's another post Patrick would have enjoyed responding to, and includes a tribute to him by Sean.
https://bookandsword.com/2020/03/28/some-terrifying-numbers/
very interesting but then Sean manning often is. I think we should say at this point that Herodotus justifies his numbers for Xerxes invasion from a count and even tells us how it was counted. Doesn't make the figures accurate but he had clearly asked "And how do you know the army was so big"?
There is another interesting factor which is are smaller numbers more accurate? Is the traditional figure for the size of Xerxes fleet (1207) more accurate because someone might be considered more capable of counting 1200 large objects rather than a crowd of 20,000? And is accuracy dependent on the perceived significance of what you are counting? In the Middle Ages we have plenty of counts of hundreds or low thousands of knights alongside very large numbers of common foot. Are both figures equally accurate or even arrived at in the same way?
thanks for the link Aaron. Good summary I thought
Is Herodotus account of the numbering of the Persian host believable or does it make his eventual number more believable? Many of these troops had marched some thousands of kilometres and must have been fed on the way. That would mean someone going ahead of the contingent to requisition the appropriate number of rations. If that is so then at the very least each contingent leader must know his troop numbers. The Persians had plenty of scribes and no doubt grain had to be accounted for. When the units reached the muster, again they would have to be fed. Even at the low numbers that many of us believe for Xerxes army it will likely take more than one beach to feed the army so someone has to balance the numbers being fed from each point. That again means counting.
Creating an enclosure for 10,000 men and having it repeatedly filled is pointless, a waste of time when the numbers already exist and just need to be aggregated.
As to barbarian armies, it beggars belief that they could deploy 90-100,000 men with their primitive commissariat.
Roy
Roy
Yes SM is always interesting. I look forward to seeing his book (presumably on Achaemenid armies).
Numbers are a strange thing. I've been inclined of late to go a bit meta and wonder about why numbers matter, and why people now are so interested in them. Some articles on ancient battles largely come down to working out how big each army was and what size all its contingents were, but in many ways that is the least interesting question to ask about an ancient battle or an ancient army. People tend to like quantifiable things like numbers but they aren't necessarily very important, in practice. Either Xerxes' army was millions strong, in which case being so large didn't help, so numbers don't matter; or it was some much smaller but now unknowable size, in which case there wasn't a great size discrepancy v. Greeks, so numbers don't matter.
I think it's interesting to think about why modern commentators are so often obsessed with numbers; and why and in what circumstances ancient authors quoted numbers and knew numbers, and why and in what ways they distorted numbers, and whether they even knew they were distorting them, assuming they were. Mythologised versions of more recent conflicts invariably see the good guys (us) standing up against and overcoming enormous odds (them). Which is strange in a way, because saying the enemy were numerous and lost anyway also means saying they were a bit rubbish, which in a sense lessens the achievement of beating them. But the desire to be seen as (or to see oneself as) the underdog seems to be a very common human trait.
And also to add that if you do accept 1200 ships you must also accept 200,000 or more rowers to move them.
QuoteAnd also to add that if you do accept 1200 ships you must also accept 200,000 or more rowers to move them.
Yes. You don't have to accept this number of course but, even if rejecting it, it is hard to cut it back too much, if we accept the Greek figures for their own fleet (in the 370s). This fleet must have taken a considerable effort to keep in action - just finding beaching spots with sufficient water would be hard work, let alone resupply tasks (rowers consume a lot of calories).
I believe that the focus on numbers and contingents is part of the historians' rejection of the 'battle-porn' school of history ( bows are bent saddles empty, steel rings against steel) which led to a dominance of logistical studies because administrative history was without the taint of triumphalism.
I was recently re reading Philip Rance's article on Taginae, it has a substantial section on numbers, fully referenced and demonstrating that its a branch of history with its own historiography, mostly traced back to the challenging ideas of Delbruck.
Numbers, of course are an important component reconstructing a battle. Issus is a very different battle if the Persians only just outnumber Alexander overall as opposed to having say twice as many men. Gaugamela is an example where the sheer size of the outnumbering army hinders it, but to understand the respective tactics it is necessary to know the numbers and the frontage that the various bodies occupy.
Roy
Quote from: aligern on March 28, 2020, 07:52:30 PM
Numbers, of course are an important component reconstructing a battle. Issus is a very different battle if the Persians only just outnumber Alexander overall as opposed to having say twice as many men. Gaugamela is an example where the sheer size of the outnumbering army hinders it, but to understand the respective tactics it is necessary to know the numbers and the frontage that the various bodies occupy.
Roy
Yes true, but trouble is, we don't. We don't know the numbers of the Persian army, and we can only guess at their frontages. Intervals of Persians - unknown; depth of Persians - unknown; gaps between units of Persians - unknown; numbers of Persians - unknown. We can make intelligent guesses, but reconstructions in the strict, detailed sense are out of the question.
We can make some sensible deductions . However, there is almost always one or more links in the chain that lack sufficient support to fall definitely one side or the other. I am happy that Persians had a decimal structure and fought ten deep on foot , so a unit of 1000 would have a frontage of 100 men and assuming a width of a yard per-man then that unit has a frontage of 100 yards. That sort of logic , agreed with assumptions, can lead to a frontage for Darius' army at Gaugamela. We can make assumptions about where the wings stop because when Alexander rides off there is a point at which Bessas has to follow so that gives a terminus to the left hand deployment and the right of the line is likely to project beyond Parmenio, but how far. I recall Tarn did the work and gets to a number. Now that could be a wrong number but it should not be that far wrong because it relates to Alexander's frontage and we have a good idea of Macedonian numbers and depths. That should enable us to get to an estimate of Persian numbers that is there or there abouts. I suggest that the same chains of logic, can be built for many classical battles. One can get a fair idea of numbers and balance of forces for Taginae abd Ad Decimum and for tge Hannibalic and Sucdessor battles. Of course, where we have little help in battles in The Heptarchy or Europe in the Early Middle Ages, but then isn't chewing over such imponderables a part of the remit of a Society such as ours.
Roy
I don't disagree with you Roy, but the assumptions are at every point of the chain - ten deep for Persians, one metre frontage for Persians - and that's just infantry. Even the Macedonians require a lot of guesses - how deep was the phalanx, how strong was the phalanx, where did the Greek allies form up, were the flank guards at 90 degrees or some other angle, what was the frontage of the Companions etc etc. Bold efforts have been made to calculate Macedonian frontage very precisely (eg Marsden); but even to take that as a starting point for guessing Persian numbers, we might easily be out by 100 percent either way.
I agree that it's possible to make intelligent surmises about all this stuff - we all do - but I also suspect that trying to quantify everything may be a dead end, and just gives a spurious sense of exactness. It might be better to accept that numbers are an unknown (outside of very broad generalisations such as that the Persians outnumbered the Macedonians, if even that is a safe assumption) and try to understand other aspects of battle instead (eg 'face of battle').
Now I worry about the 'Face of Battle ' approach. It revived historians interest in warfare, avoided the pornography of war and gave the study of battle a revived respectability. However, it is based upon assumptions about men's mental states that may or not be accurate. Certainly Ancients are a long way from the modern military experience for which we have live or at least recent witness. My grandfather described assaukting out of a trench in WW1. Before the whistle went men were throwing up and literally shitting themselves. Once he climbed out of the trench he felt calm and just walked forward whilst the bullets and shells whizzed overhead. I do not know if the experience of others was similar or whether this was something particular to that generation or to the peculiar circumstances of the trenches, the waiting, the building tension, the invisible enemy and most of all the expectation of severe casualties. Descriptions of battles with Dervishes , Zulus and Tibetans show similar behaviours under fire. troops get to a certain distance and halt under fire Their officers cannot motivate them to go forward. Eventually they retire, but in a slow dignified fashion.
Do these paradigms work for Ancients ? They do not advance into such an intense missile storm, the volume of casualties is much less. Do we know how the individual perceived the risks involved or reacted to the close physical proximity of comrades. The WW1 soldier experienced combat individually because his safety did not directly depend upon those around him in the way a medieval or ancient soldier acted as part of a team. Even the Napoleonic soldier is is only individually involved even though his comrades are close to him. So I suspect that the FoB approach is too liable to the notions of the historian who can elaborate the military experience from his own thoughts.
Roy
Interesting thought Roy.
My readings lead me to conclude that there is a huge psychological shift with battlefield gunpowder, and a second with high explosive.
I think it is inadvisable to compare psychology across those two boundaries,
pre gunpowder( which includes medieval as the guns were so rare ), war was basically getting up next to each other ( or damn close if you had a bow), and then hitting the chap you saw over the head until they ran away.
Once gunpowder became common, there was a lot more emphasis on scaring the chap in front of you until he ran away.
And with high explosives, you had no idea who was in front of you, and death seems to come from everywhere, which you had to overcome and hope the other chap ran away.
High explosive is also the first real era where running away was likely to be safer than staying, as it's the first time that pursuit wasn't where the main casualties came from.
Ah we obviously mean slightly different things by FoB - I mean the 'mechanics of combat' aspects of it, not the 'universal soldier' aspects, which I agree are problematic in the extreme (and getting way off the theme of this thread, if that matters). I agree that gunpowder and explosives changed warfare enormously not least in making death random, unforeseeable and inescapable - face to face combat at least offers the illusion, even if it is only an illusion, that if you fight well, you can survive, but industrialised war is a lottery. Plus there are all the cultural and societal differences.
By FoB I mean understanding the nuts and bolts and mechanics of combat, through comparative stuff where appropriate but mainly through ancient accounts. Psychology comes into it, but it should be ancient psychology. My reading of Keegan is that this is what he meant by FoB too - it's interesting that the understanding has become so altered.
While I entirely agree with Richard about the original direction of FoB (I was writing a very similar reply), we do have the usual issue of how much can be recovered of the soldier's eye view of battle in our period of interest. But the part of Keegan's technique - taking battle passages talking of heroic sweeping moves in stirring prose and saying "but how?" - is of value to us. Trying to draw out universals of soldier behaviour is harder, simply because behaviours are frequently culturally derived. I'm sure there are universals (humans get tired, hungry, fearful, enraged etc.) but actually meaningfully interpreting how these came through the cultural filter is tough.
Coming back to the issue of numbers, it continues to me to be of interest, even if I think Richard has a point that in many cases it is not vitally important in the understanding of battle. I've been searching about for online pieces on assessing army numbers, triggered by this discussion, and turned up this article (https://deremilitari.org/2014/06/the-recruitment-of-armies-in-the-early-middle-ages-what-can-we-know/), which contains a section on numbers. This highlights an alternative numbers issue; the size of early medieval armies and the contention between the small army and large army advocates. This has a wider impact beyond military matters into how we view societies. Were, for example, Merovingian and Carolingian armies based round a univeral levy of free warriors or a more select levy of the followers of the nobility? It takes you to the roots of social organisation.
I think that's true and different types of social organisation produce different types of fighting men.
As fighting was, mainly, very close up and personal in our period I'd wonder about the morale of part time fighters when confronted by professionals who were better equipped and more skilled in weapon handling. If they were used to combat and had the numbers they might stand until help arrived. Otherwise I'd imagine they would be strongly tempted to get out the way and leave it to their social superiors.
I'm a little confused by Reuter's argument against armies in the thousands on the grounds they'd leave a wake of destruction. In later medieval and early modern times armies in the thousands or tens of thousands were common enough, and their popularity wasn't appreciably diminished by the fact they did leave wakes of destruction.
(He might object that Europe was richer and more populous in the 15th or 17th century than in the eight or ninth, and therefore better able to afford rampaging armies; but the difference was hardly one of orders of magnitude.)
I thought it had a number of weaknesses. For example, just because small forces operated in certain places and times doesn't mean different levels of warfare didn't exist. And the "small Great Army" arguments alluded to have been rather weakened by recent archaeology of burials and camps.
It's interesting that even for Merovingians and Carolingians, who were pretty well organised, we don't have accurate figures even for their own side.
It's hard for people to really get a good feel for numbers, especially large ones. Inspired by the title of this thread, I've been having a look at the cheerful subject of mortality rates. In England and Wales in 2018 (latest full data), 513,936 people died (that's 1,408 every day). Of these, 15,415 died in accidents - mainly not road accidents (just 1,547), the big ones are 'Accidental falls' (6,103) and 'Accidental poisoning' (3,814). An accident that kills 42 people is big news, but every single day of 2018, 42 people were killed in accidents of one sort or another in England and Wales. There were 638 homicides (just under 2 a day - compare with US figures!). Influenza and pneumonia accounted for 29,516 - about 81 per day, every day, for a year. The big ones of course were cancer (146,357), dementia/Alzheimers (69,478) and heart disease (55,995). Of the big killers of the past, tuberculosis killed 225, 'Vaccine-preventable diseases' killed 160 and 'Vector-borne [ie mosquitos etc] diseases and rabies' killed 8.
The relevance of which to army numbers is... I'm not sure, except that any number that isn't derived from detailed accurate records from their own side (as must have been maintained for logistical purposes, in 'civilised' armies at least) is always going to be suspect. So I wonder which large army numbers we have seem to come from those sorts of sources, and which from guesses, traditions etc. What's the largest Ancient/Medieval army whose size seems likely to come from detailed records?
Perception of numbers is an interesting thing. There's quite a bit on risk perception (stemming often from the insurance industry) which shows that humans are pretty poor at assessing risk based on things like accident statistics. Your fall statistics are often from home accidents. But road traffic accidents would probably be seen as much more dangerous. Anyway, the only relevance there is that perception of numbers, rather than actual numbers, can be important.
To help us on our way, here is an example of the scaling details medieval records can provide . This is for the Florentine army at Pistoia in 1302.
Among those paid by Buoninsegna, we find 6,292 effective combatants. These can be subdivided into horsemen and footmen (crossbowman, pavesarii , infantryman).
Belonging to the first category, we find 507 cavalrymen. Belonging to the second category, we find 5,785 footmen. There were within the army a series of auxiliary companies, who could be employed for combat, but generally were relegated to a specific strategic function (i.e. the systematic devastation in the countryside through the employment of sappers, in Latin
guastatores). Belonging to this category, we find 977 auxiliary or support troops. Within the host, Buoninsegna also records the employment by the Commune of 221 men assigned exclusively to non-combat related duties. These included carpenters, tailors, administrative officials, messengers and logistics personnel.
I've taken this from this thesis (https://www.academia.edu/39515324/The_Changing_Army_of_Communal_Florence_around_the_time_of_Montaperti) by Drew Calisle. The full tables are on page 16. I knew this list existed but have only just found it in this thesis, which may be interesting in itself.
We have various records from the Middle Ages we can draw on - English from mid 13th to mid 15th century, Flemish towns militia lists, Italian records, Swiss musters, Burgundian musters and so on.
Looking at Curry et al The Soldier in later Medieval England, the largest number put into the field in the 15th century part of the HYW was about 4,000 men-at-arms and 13,000 archers, divided into several forces, in 1436. The highest numbers in one place never seem to have much exceeded 11,000.
Vaughan shows from records that the Burgundian army of John the Fearless never managed more than 10,000 men and was usually in the 5-7000 range. He notes that chroniclers accounts of numbers in armies for which we have records are often greatly exaggerated.
Is this a good point to introduce Lanchester's Laws (https://en.wikipedia.org/wiki/Lanchester%27s_laws) into the discussion? *
These series of differential equations were developed approximately 100 years ago to assess the power relationship between opposing armies. That is, how much better one side's troops were compared to the other or, looked at another way, how many additional men does the weaker side need to match the stronger side.
Lanchester developed two separate laws for the ancient warfare (Linear Law) where battles are principally decided by hand-to-hand combat and the modern period dominated by long range weapons, such as firearms (Square Law).
One of my Ideas For An Article involves an examination of sundry wargames rules using Lanchester's Linear Law. Watch out for it in future Slingshots. 8)
* Nothing to do with the Secretary of the Lance & Longbow Society (https://lanceandlongbow.com/contacts.php)
I shall look forward to that. I've always struggled to see the point or value of Lanchester's Laws. To quote WP:
"For ancient combat, between phalanxes of soldiers with spears, say, one soldier could only ever fight exactly one other soldier at a time. If each soldier kills, and is killed by, exactly one other, then the number of soldiers remaining at the end of the battle is simply the difference between the larger army and the smaller, assuming identical weapons."
It seems to me that every part of those two sentences is wrong in general and in detail, and I can't imagine what useful results could ever be extracted from such a meaningless 'law'. So I'd be happy to be enlightened...
A discretized version of the Square Law is useful for describing many wargames of the chuck dice to score hits variety. A couple of years ago I ran across a guy who'd independently found it as an empirical fact about Axis & Allies.
Some people over at BGG who are more into military modelling than I am tell me that real-world combat, or at least real-world WWII land combat, approximately follows a "Lanchester's logarithmic law" where fighting strength is proportional to the logarithm of numerical strength. Put less mathily, an army twice as numerous is rather less than twice as strong, given that individual prowess is constant.
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Some people over at BGG who are more into military modelling than I am tell me that real-world combat, or at least real-world WWII land combat, approximately follows a "Lanchester's logarithmic law" where fighting strength is proportional to the logarithm of numerical strength. Put less mathily, an army twice as numerous is rather less than twice as strong
Forgive my unmathiness, but isn't "an army twice as numerous is rather less than twice as strong" almost the exact oppposite of what Lanchester says, which is (as I understand it) that an army twice as numerous is much more than twice as strong?
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given that individual prowess is constant
But that isn't given. That's the trouble with such 'laws' - if you could factor out individual prowess, and differences of equipment, and terrain, and weather, and tactical factors, and human factors, and a whole array of other circumstances, then no doubt what was left might be a simple arithmetic relationship between strength in numbers. But you can't, or if you do you have factored out everything that is important and interesting in the study of combat. What could such a model tell us - that the larger force wins, all else being equal? Well, OK. That seems on one level so obvious as to not be worth saying, and on another level so meaningless as to not be worth saying (because all else isn't equal).
I'd be interested in practical applications or predictions that can be made using Lanchester (or equivalent). I know militaries use similar things in OR and such, but I hope their models are more sophisticated than Lanchester.
The WP wording is not the best in the world and could probably be improved. It seems to focus more on highlighting the differences between linear and square model relationships rather than explaining the rationale behind either.
The square law is easiest to understand when considering a group of, say 20 soldiers with muskets shooting at another body containing 40 soldiers. Assuming the weapons and marksmanship to be the same and that all soldiers can find a target amongst the enemy, if the first unit receives 40 shots (2 shots/soldier in the unit), then the second only receives 20 shots (0.5 shots/soldier). In other words, half the strength leads to the unit being four times worse off. Conversely, in order for the lower strength unit to equal the stronger unit, it needs to improve its firing efficiency (ie, shots per firer within a given time) by a factor of 4 rather than 2.
The linear model assumes that, more or less, only the front ranks of each body are able to engage or will be killed. Thus, if one's hoplite in a cuirass is twice as good as a peltast in little more than a t-shirt, a peltast unit will need to be twice a big (ie, deep) as a hoplite unit to achieve a draw.
Note that the above examples bandy about quite large relative effectiveness factors. In real life, such differences tend to be smaller, in the region of 1.1-1.2.
Of course, the points cost of different troops types is meant to reflect in some way the relative effectiveness with respect to other types. Therefore, without wishing to give too much of a spoiler on what might appear in Slingshot, one could always compare troop type effectiveness (as determined from the relevant combat mechanism) to the corresponding points costs to see what transpires.
Interesting point on possible logarithmic relationships. What is the rationale behind it?
Quote from: RichT on April 01, 2020, 02:56:29 PM
Forgive my unmathiness, but isn't "an army twice as numerous is rather less than twice as strong" almost the exact oppposite of what Lanchester says, which is (as I understand it) that an army twice as numerous is much more than twice as strong?
The linear law says that a force twice as big is twice as strong.
The square law says that a force twice as big is four times as strong.
The logarithmic law, which wasn't formulated by Lanchester but derives from similar considerations, says that a force twice as big is less than twice as strong.
It doesn't really make sense to say that "Lanchester says" - you have to specify which law is thought to be (more-or-less approximately) applicable.
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given that individual prowess is constant
But that isn't given.
It's a pedagogically useful assumption to make when explaining the concept.
I mean, if Bob and Alice have individual fighting powers of eight, it's interesting to learn (assuming it to be true) that their combined fighting power is less than sixteen. It's not appreciably more interesting to learn that if their individual fighting powers are eight and seven their combined is less than fifteen.
QuoteI'd be interested in practical applications or predictions that can be made using Lanchester (or equivalent). I know militaries use similar things in OR and such, but I hope their models are more sophisticated than Lanchester.
The only practical application I know are things like the salvo models mentioned in the WP article, where things like morale don't really figure.
ETA: Practical application to warfare that is. Wargames is another thing.
One thing I can say, based on googling the subject since it came up, is there is a huge debate about validating Lanchester's Laws through the use of historical data (primarily 20th century). Numerous studies seem to have been done, often contradictory in conclusion. Very little application seems to have been made to pre-modern warfare. It will be interesting, therefore, what Nick comes up with.
Quote from: NickHarbud on April 01, 2020, 03:11:05 PM
Interesting point on possible logarithmic relationships. What is the rationale behind it?
Basically that the outnumbered force is in a target rich environment. Increasing your numbers makes it harder for your troops to find a meaningful target and easier for the enemy.
Unlike the two original laws, I've never seen a mathematical derivation of it, and a brief google is not helpful on the subject.
Andreas:
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It doesn't really make sense to say that "Lanchester says"
??? It makes sense in this sense:
Andreas:
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The logarithmic law, which wasn't formulated by Lanchester
IIUC, Lanchester proposes the linear law (pre-gunpowder) and the square law (gunpowder). Some people on BGG propose a logarithmic law for WW2. Therefore the people on BGG are proposing something that contradicts what Lanchester says (in his square law, which is the one he would apply to WW2).
Is that fair?
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It's a pedagogically useful assumption to make when explaining the concept.
Yes and I'm not criticising your pedagogy, I'm questioning the value or relevance (to real life) of the concept.
Quote from: RichT on April 01, 2020, 03:56:05 PM
IIUC, Lanchester proposes the linear law (pre-gunpowder) and the square law (gunpowder). Some people on BGG propose a logarithmic law for WW2. Therefore the people on BGG are proposing something that contradicts what Lanchester says (in his square law, which is the one he would apply to WW2).
Is that fair?
Lanchester (writing in 1916) would presumably have expected WWII warfare to approximate the square law, yes. But others have applied his laws differently (e.g. the linear law has been used to model indirect artillery fire in WWII), and I'm used to "Lanchester says" meaning "whichever of Lanchester's laws I think is applicable says" rather than "Lanchester the man said".
QuoteQuote
It's a pedagogically useful assumption to make when explaining the concept.
Yes and I'm not criticising your pedagogy, I'm questioning the value or relevance (to real life) of the concept.
To pre-gunpowder land battles of the kind we typically discuss here, I think the relevance is close to nil. At the most basic level, such battles were not primarily attritional.
I might note that Lanchester's original work is online at Wikisource (https://en.wikisource.org/wiki/Aircraft_in_Warfare_(1916)).
The difficulty is surely Lanchester wrote over 100 years ago. He proposed two laws. Since then there are several other versions (like the logarithmic and the mixed (or asymetric) model where the two sides follow different laws. There follow from these a set of equations in search of a "general" Lanchester equation. So, you really have a family of Lanchester laws through time.
BTW, I particularly liked this article (https://www-users.york.ac.uk/~nm15/BoBtalk.pdf), which gives you lots of lanchester equations to play with and tries to apply Lanchester to the Battle of Britain. Please excuse the inaccuracy of the first page picture. If you look carefully, you will find a Lanchester Ancient Battles equation. :)
The difficulty apparently is that I said "Lanchester says" instead of "Lanchester's Square Law says". In the context of a forum discussion I thought it was clear enough what I meant, but apparently not. Never mind.