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The frontage I have calculated for the Roman army at Cannae, which includes the Roman and allied cavalry comes to 1,400 yards. I've followed Polybius' description that the depth of the maniple was greater than its frontage, and I also have managed to keep the continuity of those batches of infantry with the least campaigns being stationed at the back of the maniple, and those infantry with the most campaigns, stationed at the front of the maniples. Here I am applying Polybius' description of the levy in which he mentions the infantry being levied in batches of four men, which I have found out, are campaign batches, which is obvious, because if the men serve for 16 campaigns and Polybius has batches of four, then 16 divided by four equals four.

The frontage of 1,400 yards allocates the Roman and allied cavalry as having cavalry gaps between the squadrons equal to the frontage of the cavalry as per Polybius' standard description of how the cavalry were arrayed. I cannot see how they could function with no squadron gaps, and they would not even be able to rout successfully with no gaps. I think Livy means the space for the cavalry to operate was small, so restricted manoeuvre space, which does not mean no space to manoeuvre.

The 14 legions that faced Hannibal's army at Cannae conform to the Pythagorean ratio of 4/3, that is 8 legions to 6 legions. Following Livy that 2/3 of the Roman army were raw recruits, this would indicate that the Romans are going to take those men with the most campaign experiences and place them into eight legions (2 consular armies), leaving the six remaining legions as flanking legions (3 per flank). The more I examine the Cannae deployment, the more I am certain that the Roman strategy has been influenced by the Trebbia.

I also believe Hannibal had predicted the Roman strategy and formed a wedge to blunt those eight legions.

I am confused by your reference to fourteen legions.  There were eight at Cannae, plus, it is presumed, eight allied alae, so Pythagorean ratios seem wholly irrelevant.  What are these six "flank" legions to which you refer? I would further observe that Polybius states that the eight legions were deliberately raised overstrength, 5000 infantry each rather than 4000.  Whilst the speech that Polybius credits to Aemilius Paulus is doubtless less than verbatim, it is interesting that he supposedly blames Trebbia and Trasimene on lack of training/experience of the legions, with the implication that the Romans are not going to make that mistake again in 216. 

Interesting, this will I expect continue to be discussed for many years yet but I heartily approve of folks doing their own estimations. Did you see the videos posted a little while ago by Chuck, I think the link here should work.

https://soa.org.uk/sm/index.php?topic=8786.msg112025#msg112025

Quote from: DBS on February 03, 2025, 09:04:53 AMI am confused by your reference to fourteen legions.  There were eight at Cannae, plus, it is presumed, eight allied alae, so Pythagorean ratios seem wholly irrelevant.

During the battle, two legions were involved in the attack on Hannibal's camp. Polybius' has 70,000 infantry killed and when divided by 14 legions results in each legion having 5,000 men. Polybius also has 10,000 infantry captured in the camps and another 3,000 escape. Therefore, Polybius has presumed that everyone in the 14 legions was eliminated.

Quote from: DBS on February 03, 2025, 09:04:53 AMWhat are these six "flank" legions to which you refer?

Part of the 14 legions that faced Hannibal's army. I have eight legions as being the driving force, or the force allocated to break through Hannibal's lines. Therefore, the more experienced troops were placed here.

Quote from: DBS on February 03, 2025, 09:04:53 AMWhilst the speech that Polybius credits to Aemilius Paulus is doubtless less than verbatim, it is interesting that he supposedly blames Trebbia and Trasimene on lack of training/experience of the legions, with the implication that the Romans are not going to make that mistake again in 216

Well, according to Livy, the Romans did make the same mistake. Livy claims that at Cannae two-thirds of the Roman army were raw recruits.

https://www.academia.edu/52383876/A_Breakdown_of_the_Roman_Army_at_Cannae_216_BC

I am sorry, you have not answered the question of how you come up with fourteen legions.  The sources are consistent in saying eight.  "Roman" casualties would come from those eight, plus the eight allied alae, which would have numbered, if Polybius is right about overstrength recruiting, up to 80,000 infantry and up to 12000 cavalry. So Polybius' figures, whilst undoubtedly guesstimates to some degree, are perfectly plausible.

Livy is probably exaggerating "raw" recruits to explain away the disaster.  Apart from teenagers just coming of age and mostly serving as velites or hastati, there probably were not that many who had not racked up a few campaigns before being levied in 216.  The key point is that they would likely be rusty compared to the Carthaginians.

Edit: I should have said up to 9600 cavalry, not up to 12000.

Livy affirms, with cautious circumspection, that 16 legions were raised and the number of men in each legion was augmented by 1000, raising the legion's strength to 5000. That means a total of 80,000 men, or two double-consular armies.

QuoteThe armies also were augmented. But how large were the additions of infantry and cavalry I should hardly venture to declare with any certainty —so greatly do historians differ in regard to the numbers and kinds of troops. Some say that ten thousand new soldiers were enlisted as replacements; others that four new legions were enrolled, so that they took the field with eight. Some assert that the legions were also increased in the numbers of their infantry and cavalry, and that each received an additional thousand foot and a hundred horse, bringing up the total of every one to five thousand foot and three hundred horse; and that double the number of horse and an equal number of foot were furnished by the allies. - History of Rome, 22:36

Polybius confirms this:

QuoteFor the Romans, as I have stated before, habitually enrol four legions each year, each consisting of about four thousand foot and two hundred horse; and when any unusual necessity arises, they raise the number of foot to five thousand and of the horse to three hundred. Of allies, the number in each legion is the same as that of the citizens, but of the horse three times as great. Of the four legions thus composed, they assign two to each of the Consuls for whatever service is going on. Most of their wars are decided by one Consul and two legions, with their quota of allies; and they rarely employ all four at one time and on service. But on this occasion, so great was the alarm and terror of what would happen, they resolved to bring not only four but eight legions into the field [and an equal number of allied legions]. - Histories, 3:107

The 70,000 Roman dead were the infantry on the eastern bank of the Aufidus. The 10,000 men on the western bank managed to retreat to their camp where some later escaped and the rest surrendered to the Carthaginians.

QuoteOf the infantry ten thousand were taken prisoners in fair fight, but were not actually engaged in the battle: of those who were actually engaged only about three thousand perhaps escaped to the towns of the surrounding district; all the rest died nobly, to the number of seventy thousand - Histories, 3:117

Edit: OK, I see the confusion. Monad is talking about the 14 legions on the east bank of the Aufidus, with the implication that the 10,000 men on the west bank were the remaining two legions.

Quote from: Monad on February 03, 2025, 09:28:02 AMPart of the 14 legions that faced Hannibal's army. I have eight legions as being the driving force, or the force allocated to break through Hannibal's lines. Therefore, the more experienced troops were placed here.

According to Livy, the Roman legions on the east bank of the Aufidus were deployed in the right half of the line whilst the allied legions were deployed in the left half. No mention of better legions deployed in the centre. The uniform extreme depth of the Roman deployment suggests the Romans intended simply to steamroll over the Carthaginians in front of them.

QuoteOnce across, they joined to their own the forces which they had kept in the smaller camp, and marshalled their battle-line as follows: on the right wing —the one nearer the river —they placed the Roman cavalry, and next them the Roman foot; the left wing had on the outside the cavalry of the allies; and nearer the centre, in contact with the Roman legions, the infantry of the allies. The slingers and other light-armed auxiliaries were formed up in front. - History, 22:45

My take on the wedge (FWIW) is that it was a delaying tactic. The whole point of a wedge is that you concentrate your best troops at the tip. These are the first to engage the enemy and hopefully will have enough time to shatter the centre of the enemy line and then begin to roll up both halves before the enemy has time to engage and break the rest of the wedge. The wedge at Cannae was defensive rather than offensive and was crescent-shaped, i.e. its tip was flattened. My surmise is that the best Gallic and Hispanic troops were stationed there, delaying the Roman infantry advance whilst the cavalry did its work on the flanks.

The wedge eventually broke and fell back to the second line at its rear (Livy is clear there was a second line). That second line began to give way in its centre whilst standing firm at its flanks because the Libyan infantry on the flanks had wrapped around the Romans' own flanks, stopping their advance. The Romans between the flanks and the centre needed to stay connected and not create breaks the Carthaginians could exploit, so - a bow-shaped line.

Just to clarify things in my mind:

What was the make up of the two legions that end up in the camp? Two Roman, two allied or one of each?  Did they keep their integral cavalry?

How many cavalry were there in total? I have a vague recollection that allied legions had more cavalry than Romans normally but  don't know what the boosted numbers do to this equation.

Quote from: Erpingham on February 03, 2025, 11:44:46 AMJust to clarify things in my mind:

What was the make up of the two legions that end up in the camp? Two Roman, two allied or one of each?  Did they keep their integral cavalry?

How many cavalry were there in total? I have a vague recollection that allied legions had more cavalry than Romans normally but  don't know what the boosted numbers do to this equation.

According to Livy the Roman boosted their cavalry per legion from 200 to 300 whilst the allied boosted their contribution to double that per legion. So 300 x 8 + 600 x 8 = 7200 cavalry.

QuoteSome assert that the legions were also increased in the numbers of their infantry and cavalry, and that each received an additional thousand foot and a hundred horse, bringing up the total of every one to five thousand foot and three hundred horse; and that double the number of horse and an equal number of foot were furnished by the allies.

Nothing is explicitly indicated in the sources, but if one presumes the Romans did their standard 50/50 split, then there were 7 Roman and 7 allied legions with attached cavalry on the east bank and 1 Roman and 1 allied legion with attached cavalry on the west bank. So 70,000 infantry, 2100 Roman cavalry and 4200 allied cavalry on the east bank and 10,000 infantry, 300 Roman cavalry and 600 allied cavalry on the west bank. The numbers of course are susceptible to a little more-or-less.

Quote from: DBS on February 03, 2025, 09:58:24 AMI am sorry, you have not answered the question of how you come up with fourteen legions.

I'm assuming that Steven is simply including the allied contingents as "legions".

Quote from: Justin Swanton on February 03, 2025, 11:23:35 AMNo mention of better legions deployed in the centre.

I have made that interpretation, that is eight legions formed the centre and on each flank of the eight legions were three other legions, of which I have termed the flank guard legions.

Quote from: Justin Swanton on February 03, 2025, 11:23:35 AMThe uniform extreme depth of the Roman deployment suggests the Romans intended simply to steamroll over the Carthaginians in front of them.

And that is why I have arrived at a frontage of 1,400 yards for the whole Roman army, of which the infantry has a very small frontage.

Quote from: Justin Swanton on February 03, 2025, 10:26:46 AMThat means a total of 80,000 men, or two double-consular armies.

I prefer two consular armies and two proconsular armies.

Quote from: Justin Swanton on February 03, 2025, 10:26:46 AMThe armies also were augmented. But how large were the additions of infantry and cavalry I should hardly venture to declare with any certainty —so greatly do historians differ in regard to the numbers and kinds of troops. Some say that ten thousand new soldiers were enlisted as replacements; others that four new legions were enrolled, so that they took the field with eight. Some assert that the legions were also increased in the numbers of their infantry and cavalry, and that each received an additional thousand foot and a hundred horse, bringing up the total of every one to five thousand foot and three hundred horse; and that double the number of horse and an equal number of foot were furnished by the allies. - History of Rome, 22:36

Four new legions would amount to 20,000 men, so the figure of 10,000 men is as Livy mentions "replacements." However, the two consular armies raised by Paulus and Varro had not been on campaign so therefore, being newly raised do not need replacements. This leaves the two proconsular armies already in Apulia that required replacements, and 10,000 replacements (rounded up) is right for two proconsular armies. There is enough data in Livy's later books alone to be able to work out how the replacement system works.

Quote from: Justin Swanton on February 03, 2025, 10:26:46 AMFor the Romans, as I have stated before, habitually enrol four legions each year, each consisting of about four thousand foot and two hundred horse; and when any unusual necessity arises, they raise the number of foot to five thousand and of the horse to three hundred.

Notice how Polybius states "about" 4,000 foot, so let's keep that in perspective before everyone runs about claiming 4,000 infantry increasing to 5,000 infantry.

Quote from: Justin Swanton on February 03, 2025, 10:26:46 AMEdit: OK, I see the confusion. Monad is talking about the 14 legions on the east bank of the Aufidus, with the implication that the 10,000 men on the west bank were the remaining two legions.

You are describing the forces in relation to the rive whereas I am describing those forces (14 legions) that actually engaged Hannibal's main army and those that attacked Hannibal's camp (2 legions).

Quote from: Duncan Head on February 03, 2025, 12:05:05 PMI'm assuming that Steven is simply including the allied contingents as "legions".

Correct.
 

Pardon me for expecting some precision in language, especially when used in connection with a fallacious extrapolation to a supposed Pythagorean ratio.

No mention of "raw recruits" in Livy, given, as I say, that most of the newly levied troops probably had served in past campaigns. Rusty, maybe. Lacking optimum cohesion as a legion, maybe. Raw? Very doubtful.

Quote from: DBS on February 03, 2025, 01:48:16 PMPardon me for expecting some precision in language, especially when used in connection with a fallacious extrapolation to a supposed Pythagorean ratio.

No mention of "raw recruits" in Livy, given, as I say, that most of the newly levied troops probably had served in past campaigns. Rusty, maybe. Lacking optimum cohesion as a legion, maybe. Raw? Very doubtful.

Given previous casualties and the sheer size of this army, I do feel that Raw could well be justified. I've not time to check Livy but from memory the last big campaign was Battle of Telamon in 225BC .
Also we do know that the Romans were happy to take volunteers and we also know (from a little later than this) that men do seem to have made a career of military service. So it could well be that the proportion of 'volunteers' was quite high in those legions raised in 'quiet' years. So it could be that a lot of these had been lost in previous battles against Hannibal

Quote from: Monad on February 03, 2025, 12:21:37 PM

Quote from: Justin Swanton on February 03, 2025, 11:23:35 AMNo mention of better legions deployed in the centre.

I have made that interpretation, that is eight legions formed the centre and on each flank of the eight legions were three other legions, of which I have termed the flank guard legions.

Sure, but an interpretation based on what?

Quote from: Monad on February 03, 2025, 12:21:37 PM

Quote from: Justin Swanton on February 03, 2025, 11:23:35 AMThe uniform extreme depth of the Roman deployment suggests the Romans intended simply to steamroll over the Carthaginians in front of them.

And that is why I have arrived at a frontage of 1,400 yards for the whole Roman army, of which the infantry has a very small frontage.

I disagree. A mid-republican legion deployed about 200 yards wide. In this case a legion deployed 100 yards wide, i.e. at twice its habitual depth for half its habitual width. My take is that the frontage of the battlefield at Cannae was a little under 3km, allowing infantry and cavalry to deploy deep, the depth of the latter hopefully negating the Carthaginian numerical superiority in cavalry. But we can argue about this.

Quote from: Monad on February 03, 2025, 12:21:37 PM

Quote from: Justin Swanton on February 03, 2025, 10:26:46 AMThat means a total of 80,000 men, or two double-consular armies.

I prefer two consular armies and two proconsular armies.

If you like. The point is that 4 standard-sized armies each of around 20,000 infantry were combined into a force of about 80,000 infantry.

Quote from: Monad on February 03, 2025, 12:21:37 PM

Quote from: Justin Swanton on February 03, 2025, 10:26:46 AMThe armies also were augmented. But how large were the additions of infantry and cavalry I should hardly venture to declare with any certainty —so greatly do historians differ in regard to the numbers and kinds of troops. Some say that ten thousand new soldiers were enlisted as replacements; others that four new legions were enrolled, so that they took the field with eight. Some assert that the legions were also increased in the numbers of their infantry and cavalry, and that each received an additional thousand foot and a hundred horse, bringing up the total of every one to five thousand foot and three hundred horse; and that double the number of horse and an equal number of foot were furnished by the allies. - History of Rome, 22:36

Four new legions would amount to 20,000 men, so the figure of 10,000 men is as Livy mentions "replacements." However, the two consular armies raised by Paulus and Varro had not been on campaign so therefore, being newly raised do not need replacements. This leaves the two proconsular armies already in Apulia that required replacements, and 10,000 replacements (rounded up) is right for two proconsular armies. There is enough data in Livy's later books alone to be able to work out how the replacement system works.

OK, and we get to 80,000 infantry which is the important number for this battle.

Quote from: Monad on February 03, 2025, 12:21:37 PM

Quote from: Justin Swanton on February 03, 2025, 10:26:46 AMFor the Romans, as I have stated before, habitually enrol four legions each year, each consisting of about four thousand foot and two hundred horse; and when any unusual necessity arises, they raise the number of foot to five thousand and of the horse to three hundred.

Notice how Polybius states "about" 4,000 foot, so let's keep that in perspective before everyone runs about claiming 4,000 infantry increasing to 5,000 infantry.

Nobody is claiming exact numbers. Elsewhere in his History Livy gives numbers for legionary strength as 4,000, 4,200, 5,000, 5,200 and 6,000. About 4,000 means the legions were augmented by about 1,000 men each which is all we need to know.

Quote from: Monad on February 03, 2025, 12:21:37 PM

Quote from: Justin Swanton on February 03, 2025, 10:26:46 AMEdit: OK, I see the confusion. Monad is talking about the 14 legions on the east bank of the Aufidus, with the implication that the 10,000 men on the west bank were the remaining two legions.

You are describing the forces in relation to the river whereas I am describing those forces (14 legions) that actually engaged Hannibal's main army and those that attacked Hannibal's camp (2 legions).

OK. Comes to the same thing.