This makes no sense.
First off "Big" and "Small" market are not only defined by TV ratings, but also by the amount of money the team can spend and how many people walk through the gate, as welll as the revenue they move.
Second, the bigger and more populated the place you play at, the more likely you are to have a big fan base. The entire upper echelon of high-rating, high-spending teams is comprised of teams that play in cities with dense populations. You couldn't be more wrong if you tried.
Third, what you spend does matter, and it matters a lot. You can't be a big-market team if you don't spend.
You are confusing popularity with market size.
Btw, i know the definition. Which is why i'm making this point.