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If someone from another country plays in a national-level sporting event where all teams are domestic ones, it doesn’t become a “World Series”.

But, having said that, it also feels a bit like misdirection; I highly doubt the World Series is called the World Series because the otherwise US-owned teams involved contain international players. The implication of a 'world event' is that it consists of countries competing with each other, not US teams being open to hiring international players.

It's called the World Series because it considers itself world-class and needs not consider sub-par outliers lying outside of the US; at least I think that's how most people would interpret the phrase. Which is why acknowledging that there are competitive teams outside of the US context makes that particular phrase problematic.

So if the argument in question was "Americans claim to be the best but they suck", you'd be absolutely right and well justified in your rebuttal. But it's not, and I wouldn't make that claim anyway because I have nothing against the US or its baseball tradition.

Unfortunately the argument in question is "Can the World Series be classified as an international event, or does the name reflect nationalistic sentiment instead?"

With this in mind, if anything, this rebuttal seems to provide further evidence against the World Series being aptly named. The message seems to be that the World Series is so called because it considers itself world-class and leagues ahead of other nations (which may or may not be true), and need not attempt to prove this fact by competing in the international stage earnestly or indeed bothering to send competitive teams to world events.

So it indeed seems to be a national event which ascribes itself 'world' status out of nationalistic sentiment. Or at least, I think that's how most people (presumably including Americans) would perceive this name. I highly doubt there's a single American out there who honestly thinks that the World Series is a truly international event where teams from other countries somehow consistently fail to appear in televised finals.