Specifically, part VI and VII of that series.
> In short: Sparta’s overall military performance is profoundly average over the Classical period. They don’t even manage a winning record!
> It is hard to avoid the conclusion that while Spartan tactics may have been modestly better than most other Greek states, Spartan operations were dismal, placing severe limits on how effectively the Spartan army could be utilized.
The problem with Sparta was their inability to incorporate other people into their culture. An example of a warrior tribe very similar to Sparta but did properly incorporate new cultures is Rome, and they conquered the entire Mediterranean that way. We would probably have called it "The great Spartan Empire" if Sparta was a bit different.
Edit: I think the "myth" part was that Spartan warriors were any better than others elite soldiers. They weren't. But they fielded a disproportionally large amount of elite warriors for their size. Rome did the same, and made their new territories also adopt that culture, which allowed them to just expand and expand.
No, it wasn't. It had a broadly similar population; it's just that most of that population were slaves. And they did have slave auxiliaries, so it wasn't necessarily a manpower issue.
They had conquered other territories which they used as auxiliaries, yes, but those were just normal Greek troops and wasn't anything special or unique to Sparta. And the reason small Sparta could conquer them in the first place was the strong army they had. Not strong as in super human, but strong as in numerous well trained soldiers. Anyone who made their kids practice warfare got soldiers to that level.
Better equiped? check
Better trained? check
Winning record? nope
What axe are you wanting to grind?