Ar-Pharazon’s army, that Sauron surrendered to.
At this point Numenor was very advanced. Don’t quote me on this, but I remember to have read somewhere that they were on the verge of discovering gunpowder. And that they already had steelships?
In any case, we know that they were very advanced, which means that the population that they could support has to be very big.
Numenor was a fertile island, of roughly 435,000 sq kM.
How many people could live there then? I have found a very detailed estimate landing them at around a staggering 12 million on the island. In medieval times, sedimentary nation could at the most mobilize around 4% of their population into their armies. Which leaves us with approximately 480,000 men from the island itself. Now, it could very well be that the island could mobilize even more, since the men living there could live around 3 times the lifespan of a “middle man”. If we are generous and amp it up to even 8% we are left with a little less than a million men already. That is a HUGE army.
But the Numenorean population base wasn’t just the island, but also the colonies. The same guy that composed those numbers said estimated that there was around another 6 million Numenoreans in the northern and southern colonies in middle earth. If they were drafted as well, that gives us another 6,000,000 x 0,08=480,000
So, the Army Ar-Pharazon could muster is anywhere between 1,444,000 to 720,000 men.
Now, the strength in the Numenorean army wasn’t their numbers, but their quality. Don’t get me wrong, they certainly had a bigger army than whatever was in the 3rd age.
But, the Numenorean men were very well equipped. They had hollow steelbows, they had an amazing ranged and velocity, for example. Their equipment was probably the best in middle earth, with the exception of the remaining Noldor.
The real answer isn’t size of the Numenorean army or their equipment or huge fleet. It’s that it is Numenoreans. They are a very powerful people, and far superior to any orc or troll Sauron could muster. Taller, stronger, and more noble than any middle-man, or non-Numenorean human.
Tolkein is a horse breeder. He places a lot of importance on how noble a character is and its descent, its family tree. That’s why Aragorn is so powerful, it’s because he is a pure Numenorean and everyone else isn’t. It means everything in Tolkien’s legendarium.
So the answer to why such a small island could defeat Sauron, is because they were Numenoreans. They were the epitome of humanity in Tolkein’s eyes.
Populations of Middle Earth - The Isle of Numenor (through the 2nd Age)
(1) Who says Númenor was a small island? It was more like an island-continent (or mini-continent). I assume the map below is pretty accurate; it shows that Númenor was even bigger than Gondor and Rohan combined, and definitely bigger than Mordor.
(2) By the time Ar-Pharazôn decided to counter Sauron, Númenor possessed extensive colonies and dependencies in Middle-earth. Harad was under their control, and Umbar was their most important port in the area. This means they had thousands, if not millions of people under their thumb, as well as great quantities of supply. Some Númenóreans had moved—permanently or temporarily—there as lords and colonists.
(3) Númenor was very rich and could sustain a very large population even by itself. It literally had the blessings of the Valar.
(4) Númenóreans were a blessed people. They were taller, smarter, more powerful, more impressive, and far longer-lived (~350 years) than any Orc or Man of Middle-earth. They could also most probably defeat any Elf or Dwarf. The average Númenórean was taller than 6′4″ or 1.93 m. Remember Denethor’s words to Pippin: “And how did you escape, and yet he did not, so mighty a man as he was, and only Orcs to withstand him?” He thought his son could easily defeat any Orc, even a group of them. Given that Boromir was probably no match for a skilled Númenórean warrior, it’s obvious that an army of 10,000 Númenóreans would take more than 200,000–400,000 Orcs to defeat them.
(5) Númenóreans had learned the art of forging various weapons from the Noldor themselves. The arrows of their bows resembled dark clouds falling upon their enemies.
Colonies and tribute.
The truth is, I don’t think Tolkien thought much about military logistics, but he did leave enough information that we can come up with a credible explanation.
It is stated that the Numenoreans were great sailors, and that their ships started returning to Middle-earth during the reign of Tar-Elendil in the year SA 600. They soon began to establish colonies as well as relationships with the Men of Middle-earth. These relationships at first benefited these lesser Men, but later became oppressive. Of their colonies, Umbar is the best known. Pelargir was established as a haven of the Faithful.
So the Numenoreans probably obtained many resources—timber, food, labor—from their colonies. We are told that they demanded tribute from the local rulers. They might also have used locals in their armies either as troops (think Gurkhas) and almost certainly as support personnel. We also know that the Numenoreans in their late moral decline used slaves; Ar-Pharazon’s ships are rowed by “many strong slaves.”
I think there must have been a substantial number of Numenoreans who were not born on Numenor and may never have lived there, rather like Roman or British subjects born in colonies or remote territories. That’s the explanation I use in my head canon for why Elendil, with only seven (albeit large) ships’ worth of people and goods, was able to establish not one but two kingdoms in a very short span of time.