Figures like Alexander the Great, Mehmet II, and Ranjit Singh were known for accomplishing great conquests while they were still very young. How much of these accomplishments were a result of their own talents, and how much was due to other factors like luck/advisors/veteran generals?

I can't speak much for their first conquests, but a factor that comes into play for the later conquests is the respect and belief the soldiers had in these men's leadership. In his book on the great game, Peter Hopkirk briefly describes Alexander Burnes' journey to Lahore, where he meets Ranjit Singh. By that point Ranjit Singh was an old man, and Burnes was incredibly impressed by the amount of respect such a small man (in stature) got from everyone around him.

Later in his journey Burnes arrived in Kabul, where he met Dost Mohammed (who at that point ruled over parts of Afghanistan). Dost Mohammed was a young man, but in a short amount of time had managed to gain quite a bit of respect. Again this really impressed Burnes, so much so that he tried his best to form an alliance between Dost Mohammed and the British Empire.

As far as Alexander the great goes, the only source I can cite is a documentary (which is probably not good enough for this subreddit), but I'm sure other people will have better sources. Alexander the Great at the apex of his career was considered basically on par with a god.

While it is true that respect and fame are gained over time, I think that (aside from other contributing factors like those you mentioned in the title) it is because these men were young when they started their conquests that they managed to be so successful. Dost Mohammed's rise to power was partly due to his confidence and his arrogance (both of which are traits I'd attribute at least in part to age), which combined with other factors gained him the respect not only of his soldiers, but also of Alexander Burnes.

So I'd argue that these men's military talents and other factors were not enough to make them as successful as they became, because they had to be combined with a good deal of charisma and with the trust their soldiers placed in them.

Source: Peter Hopkirk "The Great Game"

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