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A while back, Amras posted under https://www.planet-tolkien.com/board/13/5140/0/the-rammas-echor a link to another Tolkien related forum site in which a member had analyzed the amount of troops available to Gondor, Isengard, Rohan, and Mordor. These analyses can be found here http://www.middleearthcenter.com/forums/showthread.php?t=19439. The estimated forces were as follows

Gondor 23,000 soldiers, with up to 6,000 freed slaves as reserves

Rohan 11,500 soldiers, almost all of whom were cavalry

Isengard 16,500 soldiers, the majority of whom were uruks or men persuaded to fight by Saruman

Mordor 200,000 Orcs and ~100,000 evil men from Khand, Harad, and Rhun, as well as several assorted trolls, cave trolls, Oliphants, Nazgul, and fell beasts

At Pelennor, there were at least three companies (200-500 soldiers) of upper circle guards, making for a total of 600-1500 (averaging 1,050) elite guards. There is no precise estimate of the lower circle guards, but it makes sense that there would be many more regular guards in the lower circles than the citadel, Dante (the one who gave the average numbers above) estimates between 2,000 and 4,000 of these soldiers, so lets say 3,000 more regular guards. The elite upper level guards would be very well trained and equipped soldiers, and the other 3,000 would still be trained soldiers but there is a notable difference between the two units of soldiers.

From Ithilien there came another company of men used by Faramir to harass the enemy soldiers moving east of the great river. The estimate given by Dante is 300 soldiers, who would be trained in survival and tracking as well as war, as they functioned similarly to the rangers of the north. Their actual training for war is debatable, but I can't see Denethor sending his own son out with soldiers that were not very well trained, and I imagine these soldiers would be trained about as much as the elite guards of Minas Tirith, making for 1,350 elite soldiers so far.

There were also soldiers stationed at Osgiliath, and when Faramir took his company from Ithilien to reinforce them Denethor did not think it a significant increase. I therefore think that Faramir's 300 were only 10-15% of the soldiers stationed there. If the 300 are 12% of the soldiers, then there would be 8.3333… times that many soldiers at Osgiliath in total, making for a total of 2,500 soldiers. However, I think that apart from Faramir's 300 these would be regular soldiers, since it doesn't make sense for there to be more elite guards then regular ones. So now we have 1,350 elite soldiers and 5,500 trained soldiers.

There was also a permanent garrison of soldiers at the island of Cair Andros, however, it didn't put up any significant resistance to the invading orcs and was probably fairly small. Dante estimates 500 soldiers, which seems reasonable as it would probably be manned by a single full company and there were not many chances for the 500 soldiers to die. These soldiers, being a permanent garrison, would be trained but probably not elite, making for a total of 6,000 trained soldiers so far.

From the various fiefdoms we get some exact numbers, adding together all of the soldiers who arrived gives us slightly less than 3,000 soldiers. Reading the descriptions of there arrival it seems the majority of them are trained, there are

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{Forlong's 200} men, well-armed and bearing great battle-axes; grim-faced they were
Tolkien seems to use grim-faced to describe soldiers who have at least seen battle, and they are also well equipped, though that is probably true of the majority of Gondorian soldiers because of their legacy of having a huge empire and because they used to have a much larger population.
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behind the son of their lord, Dervorin striding on foot: three hundreds
again, I can't see a lord sending his son off to battle without giving him good soldiers, so these are probably trained.
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tall Duinhir with his sons, Duilin and Derufin, and five hundred bowmen.
Once more, the nobles don't go running off without good soldiers, and bows are weapons that it takes at least some skill to use, so they are probably trained.
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a long line of men of many sorts, hunters and herdsmen and men of little villages, scantily equipped save for the household of Golasgil their lord.
there is no way to know how many men this "long line" constitutes, but Forlongs 200 were described as only a "dusty line", so perhaps this is somewhat more that 200? There is also no way of knowing how many men were from the household of Golasgil, but if I remember correctly Húrin's household was only fifty strong, so I'd say this unit of men would be somewhere around 200 untrained peasants and fifty trained warriors. Their lack of equipment would probably be remedied at the Gondor armory. There are also
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From Lamedon, a few grim hillmen without a captain. Fisher-folk of the Ethir, some hundred or more spared from the ships.
So perhaps 150 more untrained peasants? Then there is
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Hirluin the Fair of the Green Hills from Pinnath Gelin with three hundreds of gallant green-clad men.
I'd say these were probably trained since they are traveling with their lord and are "gallant".
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last and proudest, Imrahil, Prince of Dol Amroth, kinsman of the Lord, with gilded banners bearing his token of the Ship and the Silver Swan, and a company of knights in full harness riding grey horses; and behind them seven hundreds of men at arms, tall as lords, grey-eyed, dark-haired, singing as they came.
There is no way to know just how big the company here mentioned is, but 200+500=700 and 700/2=350, so 350 mounted knights and 700 more trained soldiers following. This makes for a total of 2,050 trained soldiers, 350 untrained peasants, and 350 heavy cavalry. Adding on to the current estimates, this makes 8,050 trained soldiers, 350 peasants, 1,350 elites, and 300 heavy cavalry led by Imrahil

That is my estimate for the number of soldiers in Minas Tirith for the battle of Pelennor fields. However, there were also at least 6,000 riders from Rohan, Dante estimates 1,440 (12 Eored) of Rohan's forces were permanent soldiers, and only 60% of the soldiers Rohan mustered went to Gondor, if we divide the 1,440 in that way we end up we end up with 846 permanent Rohanian soldiers at Pelennor. I haven't looked through the organization of Rohan's military in a while, so I am not sure how trained the other ~5,154 riders were, but in any case they were mounted and were of fighting age.

Finally, there were the forces Aragorn led from the great ships which were supposed to bring pirates for Mordor. Dante gives the estimate of 14,000, which was composed of Aragorn and his rangers leading men rallied from the southern fiefs (remember how only a tenth of the expected forces came?).

 

The Black Ships: To give an idea of how much men Aragorn mustered at Pelargir, we should identify the fleet they captured. Gimli described the fleet as ‘fifty great ships and smaller vessels beyond count.’ An ocean capable ship that relied on both wind and man power would make the ‘great ships’ comparable to the Galley. Galleys had multiple decks for oarsmen and sported several masts. One particular type of ship that Tolkien mentioned is the dromund, which seems to be derived from the real world dromon, a galley-type warship. The smaller vessels could have then consisted of ram-ships, troop transports and non-ocean faring longships. A ship similar to the Viking Skei could have fulfilled the role of troop transports as they were smaller than Galleys, had a single deck of rowers, and sported a single mast that made them ocean capable and independent in operation. Longships like the Snekkja, although incapable of traveling in open sea, could have been towed by the larger ships until they were in traversable rivers. Since they were upon the Anduin River, it was possible that many of the smaller ships were Snekkja-types as they were best used in rivers and coastal landings.

There were fifty great ships at Pelargir, so the guesswork lies in how many ships ‘beyond count’ is. Since longships couldn’t travel from Umbar to Pelargir conveniently, they could have been towed by the fifty great ships (deducing that there were 50 or less Snekkja-types). As for the troop transports and ram-ships, a random but conservative guess numbers them between forty to fifty. 

A typical Galley had an operating crew of 70 sailors and 120-plus oarsmen. Transports like the Skei-types could house a rowing crew of 70 to 80. Snekkja-type longships were smaller and only had a crew of 40 rowers. Since the oarsmen of Skeis and Snekkjas were considered the soldiers themselves (there was no room for anyone but oarsmen), it was unlikely that a transport/longship crew were slaves since they would have been armed. This would make the crew from the smaller ships exclusively from Umbar and Harad while the slaves of Gondor were shackled on the larger ships.

With an estimate on how large the fleet is and their crew capacity, Aragorn and Angbor must have rallied around 14000 men to completely fill the ships and have a surplus of 4000 men to travel on foot, totaling 18000 in all.

How many of these were rangers and how many were peasants is hard to guess, but it seems like the entire force of rangers from the north came. They were able to protect the borders of the shire very well for an indefinite amount of time, as well as Bree and similar settlements. They were refereed to as their own group of people and I imagine there would be around 500 of them, but if anyone has any more definite numbers please say so. The Dúnedain were "dour-handed" and indeed truly wonderful warriors, I'd say they were better fighters than even the elite guards since they a) had more pure blood meaning they were taller, stronger and tougher and b) their entire existence revolved around fighting orcs.

Under the numbers of 14,000 and 500, we end up with 13,500 more soldiers from the fiefs. I'd imagine they were mostly peasants who had taken up arms and were therefore untrained, but that's just what makes sense to me and may not necessarily be true. So, adding all these numbers together, we end up with

~5,150 Rohan cavalry

~850 Permanent Rohan cavalry

~13,850 Untrained Gondor peasants

~8,050 Professional Gondor soldiers

~1,350 Elite Gondor soldiers

300 Elite Gondor cavalry

~500 Dúnedain Bad@$$es

Going up against an absolutely enormous force from Mordor. How many? Dante estimates 70,000-100,000 orcs, 26,000 evil men, and 5,000 mounted evil men (most of the evil men were elsewhere).

 

Morgul Host & the Vanguard of Osgiliath: This mass of Orcs was gathered and sent to overrun Osgiliath, and eventually formed the bulk of the force laying siege to Minas Tirith. The vanguard sent upon Osgiliath fought with Faramir’s men, and was described to outnumber Gondor’s defenders by ten. This leads to the conclusion that the vanguard numbered around 20000. Of course, the vanguard did not consist of the entire host, as was only sent as an attachment. From this, I estimate that entire Orc host itself would number around the 70000-100000 range.
Haradrim at Pelennor Fields: The first mention of the Haradrim was a force heard skirmishing against Faramir’s men in the background while Frodo slept. It is assumed that this force was defeated and scattered, but was just a fraction of what Sauron was building up. At Pelennor Fields, the combined arms of horsemen, footmen, and soldiers mounted on Mumakil was three times larger than the 6000 Rohirrim, or 18000.

Gothmog’s Reserves at Osgiliath: 
After the arrival of the Rohirrim, Gothmog signaled his reserves to enter the fray. This force consisted of Axemen from Rhun, Variags of Khand, “Southrons in scarlet, and out of Far Harad, black men like half-trolls.†The reserves would not have been that significantly big, but would have been enough to wedge between the Rohirrim and Imrahil’s party, as they were described as “Some now hastened up behind the Rohirrim, others held westward to hold off the forces of Gondor and preventing their joining with Rohan.†This entire force should be greater than 10000, but it did not consist entirely of Haradrim. I would say that around 5000 were the described Southrons and Men of Far Harad.
Since a large amount of Easterlings {the ones from Rhun} were deployed elsewhere, I would think that a smaller portion of the reserves were Easterlings, summing around 3000.
 The only time the Variags of Khand were mentioned was when they were sent in after the Rohirrim had arrived. The Variags were compared to the Rohirrim, so they could have been a major cavalry arm of Mordor, besides Harad. The remaining men from the reserves that I have previously would give them a small force of 5000.

All of these would be real soldiers with training and good equipment. So how the heck did Gondor and Rohan win the battle so decisively when they were outnumbered at least 3.8 to 1 (my estimates for the Gondorian troops are probably a little bit high)? This is where my question comes in.

How many soldiers from one army would it take to beat one soldier from another army? How many peasants to orcs? How many Dúnedain to Rohanian cavalry? How many average Gondorians to an orc? Ex-cetera... I'd like to keep this in the third age since the numbers Tolkien gives us for forces in the first and second ages is just "A frickin' lot" whereas there can be fairly decent estimates made of the forces in the third age, particularly Pelennor. However, I do remember one thing to keep in mind while replying, the disaster of the gladden fields as written in UT was 200 of Isildur's finest knights against 2,000 orcs, a 10 to 1 ratio. More importantly, the orcs didn't have an assurance of victory throughout the whole fight, particularly at the beginning when they have a big charge and the Dúnedain slaughter all their great orcs while losing hardly any men. So, anybody have any ideas on the rate of exchange between soldiers of the third age? I think it's important to keep in mind the enormous distinction between cavalry and infantry. One example of how much more effective it was is the Mongols of the middle ages under Genghis Khan (and his sucessors), who conquered nearly all of Asia and parts of Europe (forming the largest contiguous empire in history) with an army that was mostly cavalry.

As the answer from me to you CUR: The MEN of Gondor would be very doughty indeed, for it would be silly for Sauron not to attack before the siege of Gondor, because he did not want to waste his army on a attack.

Yes, they would be very good warriors, but were they better than Rohan's cavalry? I think not, since being on a horse is a very big advantage. I'd rank them like this:

Gondor Heavy cavalry

Rohan Permanent cavalry

Dúnedain Bada$$es

Rohan Regular cavalry

Evil Cavalry/Gondor Elite guards

Gondor Professional guards

Uruk-Hai/Evil Men

Orcs

Gondor Peasants

I'm somewhat unsure about Gondor peasants being below orcs, but in my opinion, training wins out over size and strength. Further, the Gondor elite cavalry are at least ten times better than the orcs, meaning, in my opinion, that if it were Imrahil's 300 against 3,000 orcs, the end result would be a field of 3,300 dead. Any opinion on the numbers I estimated?

I just read the Beorn section of the hobbit. In it, Gandalf says something along the lines of, "there was the goblin king and thirty or forty of his goblins, even if it was a fair fight, what could 13 dwarves do against those numbers?" Which is interesting. Supposing there were thirty nine goblins and one goblin king, the dwarves are only outnumbered three to one, which makes me wonder if the dwarves in the hobbit were trained warriors or not. It makes sense to me that the nobility would know how to fight well, and Thorin and co. certainly chopped up goblins at five armies. Furthermore, Gimli killed 42, the majority of whom were probably uruks, so it would make sense for the thirteen, even if they were all lesser warriors, be able to kill 39 goblins.

The dwarves were mostly men who had most likely been learned in arms and so forth. I think the only ones who were warriors were the ones like Balin and Dwalin, Thorin, and Gloin. The others had probably never met a goblin in their life. But the goblins for the most part were not veterans of wars, making the dwarves mightier due to their strenght and quality of their weapons. The Gondorians who protected Southern Gondor weren't peasants, but trained soldiers. The peasants, merchants, fisherman, or 21st century salesman would of been moved to the strongholds or fastness in the mountains. The people south of Minas Tirith cared about themselves too.

I think the only ones who were warriors were the ones like Balin and Dwalin, Thorin, and Gloin. The others had probably never met a goblin in their life. But the goblins for the most part were not veterans of wars, making the dwarves mightier due to their strenght and quality of their weapons.

Except that the goblins and dwarves were constantly warring in the north, hence the constant references to the war in the hobbit. I think the thirteen were probably at least decent warriors since most of them survived the battle of five armies. Do you think the thirteen could kill thirty or forty goblins? I think they could, especially with Orcrist scaring them greatly.

 The Gondorians who protected Southern Gondor weren't peasants, but trained soldiers. The peasants, merchants, fisherman, or 21st century salesman would of been moved to the strongholds or fastness in the mountains

I am not so sure about this. In times of war, kingdoms often recruit all able bodied men to fight, we see this happen at Helms Deep, and I don't think Gondor had that many professional soldiers. Aragorn raised his soldiers from the fiefs; Wikipedia says on fiefs, 

 

In 13th-century Germany, Italy, England, France, and Spain the term "feodum" was used to describe a dependent tenure held from a lord by a vassal in return for a specified amount of knight service and occasional financial payments (feudal incidents).

However, knight service in war was far less common than:

castle-guard (called Burghut in the Holy Roman Empire) the obligation of a vassal to serve in a castle garrison of the lord),

suit in court (the vassal's obligation to attend the lord's court, to give him counsel, and to help him judge disputes)

attendance in the lord's entourage (accompanying the lord when he travelled or attended the court of his lord so as to increase the social status of the lord),

hospitality to the lord or to his servants (accommodation).

Only the uncommon knighthood requires training, and then it is only a few knights while the majority of the fief would still be more concerned with getting food than learning to fight. However, I think the majority of the guards of Minas Tirith were well trained soldiers who had perhaps even had real field experience. So in my opinion, Gondor had a lot of real soldiers and some peasants.