The show in question is complete bullshit. None of the various warriors' tactics or how their weapons were ever used in investigated. Its just straight weapon vs weapon, which is total fail.
When did you ever fight just one pirate, Spartan, ninja, or Apache? You didn't. Pirates always attacked in groups of least sixty...in pirate ships, with over a dozen cannons. Spartan used the shield wall, and always attacked as units. Ninjas are assassins who came up behind you and shoved knives into your back. And Apaches ambushed people, never fighting fair. Skip this show and watch mythbusters instead.
Another thing: they tossed the Indians out of the champs section because of lack of armor or technology, no nevermind that did fight people with armor and superior weapons: the U.S. frikkin military. Just ask Custer. Oh wait...
Edit: Yet anothet thing, they also misused the Crossbow, which was a revolutionary because anyone can use it. It's not meant to be used the same as regular bows and arrows. On top of that, their "assessment" of non-lethal police equipment is bullshit. Yeah, the flashbang didn't kill anyone, but guarantee that if I had the moronic ex-military hold while it exploded in his frikkin face I could walk in and have my merry way with him and he wouldn't be able to do a damn thing about it.
Edit 2: In conclusion, if you're not going to take into consideration just how these historical figures operated while trying to decide who is the best warrior: you're failing. A ninja would never fight a Spartan in the open. If some unlucky ninja encounteder Spartans out in the open, he'd be bumrushed by a whole group. Or, he'd sneak into their camp at night and slit their throats. Ninjas wee assassins, end of discussion.