In Little Big league, the Minnesota Twins end the season in a dead heat with the Settle Mariners for the AL Wild Card spot. I haven’t watched this movie in a while, so I don’t remember the #s, but I’m pretty sure they say them in the movie. (on faux-Sportscenter).
Of course, in the book Hobbs strikes out and the Knights lose the pennant on the last day of the regular season. And, if that wasn’t bad enough, there’s a mention that the Commissioner is going to make the Knights forfeit all the games they won with Hobbs playing because he threw the last game.
Didn’t they appear in the Championship game one season?
Meh.
If you want a real team that never existed, I present
The St. Louis Purple Stallions of the National Football League.
After the Cardinals left for Arizona in the late 1980s, the civic leaders in St. Louis began an effort to bring in another football team.
They pursued this effort energetically, but not wisely. At various teams there were three separate groups pursuing rights to a team, a stadium, broadcast rights and everything else.
Eventually things shook out, and when the NFL was ready to grant an expansion franchise, the St. Louis group was right at the front of the pack, along with Charlotte. We had the ownership, the name, the logo, the souvenir hats and t-shirts, even a fight song.
The only thing that was missing was the stadium lease. One of the rival groups had secured that, and they weren’t willing to give it up without a substantial piece of the action. The NFL wound up awarding the other expansion franchise to Jacksonville, the hats and t-shirts were shredded and the owners were the laughingstock of the sports world. Eventually St. Louis would get the Rams.
Sometimes, just to be nasty, a deejay will play the fight song, though.
Final record: 0-0-0.
Post #8. 
The California Bulls (1st & Ten)
Not a whole team, but Fidel Castro was a pitcher for a MLB team in the Wild Cards novels.