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Oh wait, there is!
This one can be found in a wide variety of soccer and rugby leagues throughout the world, and has become so common that it's amazing that some variation of it hasn't wormed its way into the American sports culture.
You would be hard-pressed to find a soccer league anywhere in the world that doesn't utilize a promotion/relegation system, unless that soccer league happens to be -- you guessed it -- America's own Major League Soccer.
To explain this one, allow me to draw an analogy to a well-known example in the U.S. You know how sometimes on a sunny summer day you and your buddies get together and go out to the ballpark to down a few beers and watch your favorite Major League Baseball team? You do? Good.
Now, you know how sometimes on other days (maybe when the MLB club is in the middle of a ten-game road trip or something) you go to a smaller, crappier ballpark, drink cheaper and less tasty beer, and watch the local triple-A farm team instead? Still with me? Okay.
You know those days when you're really out of luck, and get dragged to the double-A park to watch some nobodies throw a baseball with a total of like 12 people in the bleachers? Okay, you got me on that one. Almost nobody knows what that's like.
Promotion and Relegation systems are like that, except those farm teams are a lot less like farm teams, and a lot more like competitive entities in real leagues fighting for a legitimate prize. That prize? Promotion into the next highest league.
In England, for example, the highest competitive soccer league is the English Premier League, which always has 20 teams. The next league down (or the second tier) is called the Football League Championship. Below that there are still two more tiers consisting of competitive clubs recognized by the governing body in charge of all competitions.
At the end of the season, while the top team in the first tier is crowned champions of English soccer, the bottom three teams face a very bitter reality: they will be relegated to the second tier for the next season.
Meanwhile, the top two teams from the second tier will be promoted to the ultimate honor of eligibility to compete in the Premier League (and I lied, because the third team to be promoted actually is determined by a short playoff-style competition).
While it is an extreme rarity, it is actually possible for a fourth tier club to battle their way (over a minimum of three years) to the top-level of competition.
To put this into perspective, promotion and relegation would be like the Seattle Mariners finishing dead last in Major League Baseball, and being usurped by the Tacoma Rainiers for their spot in the American League West. Which, admittedly, many Seattle fans would not object to seeing.