How was Sparta able to defeat Athens at he end of the Peloponnesian War?

The Peloponnesian War (431-404 BC) was an ancient Greek war fought by Athens and its empire against the Peloponnesian League led by Sparta. Historians have traditionally divided the war into three phases. In the first phase, the Archidamian War, Sparta launched repeated invasions of Attica, while Athens took advantage of its naval supremacy to raid the coast of the Peloponnese and attempt to suppress signs of unrest in its empire. This period of the war was concluded in 421 BC, with the signing of the Peace of Nicias. That treaty, however, was soon undermined by renewed fighting in the Peloponnese. In 415 BC, Athens dispatched a massive expeditionary force to attack Syracuse in Sicily; the attack failed disastrously, with the destruction of the entire force, in 413 BC. This ushered in the final phase of the war, generally referred to either as the Decelean War, or the Ionian War. In this phase, Sparta, now receiving support from Persia, supported rebellions in Athens' subject states in the Aegean Sea and Ionia, undermining Athens' empire, and, eventually, depriving the city of naval supremacy. The destruction of Athens' fleet at Aegospotami effectively ended the war, and Athens surrendered in the following year. Corinth and Thebes demanded that Athens should be destroyed and all its citizens should be enslaved, but Sparta refused.

The Peloponnesian War reshaped the ancient Greek world. On the level of international relations, Athens, the strongest city-state in Greece prior to the war's beginning, was reduced to a state of near-complete subjection, while Sparta became established as the leading power of Greece. The economic costs of the war were felt all across Greece; poverty became widespread in the Peloponnese, while Athens found itself completely devastated, and never regained its pre-war prosperity.[1][2] The war also wrought subtler changes to Greek society; the conflict between democratic Athens and oligarchic Sparta, each of which supported friendly political factions within other states, made civil war a common occurrence in the Greek world.

Greek warfare, meanwhile, originally a limited and formalized form of conflict, was transformed into an all-out struggle between city-states, complete with atrocities on a large scale. Shattering religious and cultural taboos, devastating vast swathes of countryside, and destroying whole cities, the Peloponnesian War marked the dramatic end to the fifth century BC and the golden age of Greece. [3]