Or was spartan success some sort of misconception? If not, what were the factors that led their army to be so successful?
Consistently successful? The Spartans were nothing of the kind. At best they lost as many battles as they won, although increasingly it seems that they actually lost most of their battles.
The myth of Spartan invincibility is tied in with the concept of the so-called "Spartan Mirage." This refers to the entire mystique surrounding the Lacedaemonians that first appeared in the 5th Century, but which really took off during the 1st and 2nd Centuries, A.D. under the influence of the Second Sophistic. The key elements of the Spartan Mirage are this belief that the Spartiate Similars were somehow morally, physically, and ethically superior to everyone else. As a result of the writers of the Second Sophistic, who glorified the Spartans (and other Greek cities) in an effort to essentially relive and retell the glory days of Greece, by then long-gone, the idea of the Spartiate as this sort of superman who followed orders nobly, cared only for honor and duty, didn't bother with effeminate things or corrupting influences like money, practiced all the time, and obeyed arose. It's not true.
The Spartan Mirage first appears during the early 5th Century, and we find the first instances of it in Herodotus (e.g. when the traitor Demaratus tells Xerxes that the Spartans are far and away the best of the Greeks). At this time the Lacedaemonians were fresh from their final victory in their centuries-long struggle with Argos over domination in the Peloponnese. By any reckoning, Lacedaemon's wars with Argos were the stuff of epic, spanning several hundred years of the most brutal and unceasing warfare, usually for the smallest of gains. What ultimately allowed the Lacedaemonians to prevail was not, as writers like Plutarch liked to suggest, some sort of moral superiority and discipline, but the will to do whatever it took to win. We don't know much about the early Lacedaemonian state, but it's quite clear that in order to win the Spartans essentially cannibalized their way of life, turning whatever their governing bodies were during the Dark Age and early Archaic Period (undoubtedly they followed pretty normal Dorian patterns) and completely turning the state onto its head, transforming it into the autocratic machine that Aristotle condemns and that Plutarch somewhat clumsily whitewashes. The acquisition of Messenian helots fueled that process, and while it's often said that the Messenian Wars were the major motivation for Lacedaemon's radical conservatism and militarization it's not really that simple. The Lacedaemonian state in the Archaic Period essentially burned itself to fuel the wars with Argos, in which the Messenian Wars were essentially a sideshow, although the Athenians liked to harp on them since it was an obvious way to point out how little the Spartans cared for liberty.
Now, during the Archaic Period, when the wars with Argos were going on, the Spartans were by no means prominent in war. In fact, they weren't good at anything, except that their women apparently were considered very pretty. In fact, throughout the Archaic Period it's not the Spartans who are considered good soldiers, but the Argives--so much so that we have several fragments that refer to how fearful the Argives are in war.
In the course of their wars with the Argives the Lacedaemonians forged a completely new state. It was totally autocratic, with the ephors reserving the power to control every aspect of any citizen's, subject's, or ally's life. It was also radically conservative, preserving institutions that had fallen out of practice long before (there are some traditions that may have actually fallen out of practice before the Spartan constitution radicalized itself, and which were actually revived). It was not, however, particularly highly militaristic, at least not in the way that it's usually referred. The Spartiates were not professional soldiers in any way during the Classical Period. They were amateurs, highly skilled ones, but amateurs nonetheless. The Spartiates did not remain at arms for their entire lives, and although they had the leisure to train full-time (and were encouraged to do so by their barracks-style lifestyle and the laws that prevented Spartiates from entering into most social fields or work) that's not all they did. Let's also remember that the vast majority of the Lacedaemonian army was made up of the perioeci, with only a couple thousand Spartiates in the ranks at any one time.
In the immediate wake of their success against the Argives the Lacedaemonians became legends in their own time. All of a sudden they controlled the entire Peloponnese, and in the next decade or so had seized the isthmus as well. They had worn down and eventually crushed the greatest military power on the mainland (so much so that supposedly in their last war the Argives lost so many men that for an entire generation the male population of the city was almost entirely boys--unfortunately for Argos and Greece this was exactly the time when the Persians invaded, so that the Argives declined to fight), although at great cost to themselves. Within only a few decades, by the middle of the 5th Century, however, the Lacedaemonian tide had not only stopped but was rapidly turning inward.
What the hell happened? Well the Spartans had a series of very impressive campaigns during the very beginning of the 5th Century, eating up the isthmus and coming to the gates of Attica. It was the Spartans who got the ball rolling in Athens by supporting the expulsion of the tyrants with military force, but then they slipped up when they occupied the Acropolis and attempted to set up the same sort of puppet-tyranny that they had established elsewhere. The Athenians weren't about to allow that, and stormed the Acropolis in force, routing the Spartans and securing the city. Early democratic Athens was a powerhouse far out of proportion with her size and importance. In about ten to fifteen years of nearly constant wars with her neighbors, all of whom were attempting to take the city while it was still disorganized, she not only defeated but crushed everyone around her, and even was able to bite off significant chunks of territory in Boeotia and Euboea. It's quite accurate to say that the Athenians single-handedly stopped the Spartan advance.
From here begins the long Spartan decline. It can really be dated to the Athenian blunting of the Spartan advance, because the Lacedaemonians at this point suddenly turned inward, ceasing their attempts to push northward out of the Peloponnese and attempting to completely consolidate their position. Because the Lacedaemonians turned so completely inward there wasn't very much new coming out of them, and most of what was was second-hand and word-of-mouth (the idea of Laconic speech, being brief, to-the-point, and not especially informative begins in this period, when the Spartans were not very willing to speak with foreigners and provide information about themselves and their state). Not particularly accurate stuff. The ephors and the officials seem to have been adept at manipulating foreign perceptions of their state, and the idea that the Spartans trained constantly and were taught warfare but no art first appears around this time. Now, much of these stories had a decent amount of truth in them, but they didn't tell the realities of the situation, and built up a false idea of Lacedaemon in the minds of foreigners--so much so that at Sphacteria the generals laughed at Cleon for thinking that the handful of Spartans were no threat (except for Demosthenes, who of course went on to successfully assault the Spartiate force and capture them alive), despite the fact that the Spartiate force was tiny, demoralized, and dying of hunger.
During the Second Sophistic this perception of the Spartans increased even more. The Spartans didn't really exist anymore by that time, and from the time of Sparta's defeat at the hands of the Thebans the only knowledge of Sparta that remained was this mysterious, almost mythical idea that didn't really correspond to any reality. Particularly strong were myths of the Spartan training system as fostering extreme discipline, or the morality of the Spartans. The writers of the Second Sophistic often liked to categorize people and cities as embodying particular attributes or virtues that they saw as being characteristic of the Classical Greeks, and Sparta was molded into the exemplary moralistic and disciplined old-style conservative state, mostly on the basis of the stories and legends that used to bounce around.
So it's not really the case. However, the Spartans were dominant for a short period at the end of the Archaic Period and the beginning of the Classical Period, mainly from their defeat of Argos which left them in an extremely powerful position in Greece as a whole. It must also be noted that although the Spartans weren't really that effective a military player throughout most of the 5th Century (the Athenians ran circles around them both in the Peloponnesian War and the First Peloponnesian War, although the foolishness of their leaders often prevented them from appreciating the situation they were in) they didn't have many chances to prove themselves. The image of the disciplined, invincible Spartiate soldier already existed after their defeat of Argos, and was held in the minds of anyone who dared cross them. If you look at the 5th Century the Lacedaemonians fought almost no engagements before the Peloponnesian War, and most of these were easy victories against poorly-prepared enemies. During the Peloponnesian War we see the extreme vulnerability of the Lacedaemonians, as they actually end up losing more battles than they win. In the end, their army basically disappears.
And a follow up question if anyone has the data: is there a list of how may battles the spartans fought, and of those, how many they won (a form of battles fought to battles won ratio)?