I'm glad you asked, because this is in fact a very formidable question and one that I've been pondering for quite some time. Several times a day this question pops up in my head. I usually try and tell myself that it's an opinionated question because there's almost no way that a single human being is able to ask each person on the planet which team they think is baseball's most proponent.
Wherever you are, whether it be Houston, Denver, Seattle, Toronto or Detroit there will always be people claiming their home team is all that matters. Similarly, There's a good amount of baseball fans -- even with the slightest knowledge -- who are only aware of one team in baseball, their favorite.
How can you distinguish team popularity? Are there more substantial methods or studies that can prove one team is more frequently spoken or written about than others? I mentioned that polling each of the many-billions of people on this planet would be pointless, and very time-costly, which is why I decided to use another method to measure team popularity. I was inspired by an intriguing method used formerly by Nate Silver, now of the New York Times and also by former Beyond the Box Score columnist, Steve Slowinski. Silver's phenomenal idea included using social media and online resources to peg the winner of the presidential election back in 2008.
By using "Google hits returned" from searching a certain phrase, name, or topic Silver was able to determine strength in voters during the election. In other words, which candidate would be elected President. Slowinski used the same proxy to break down the most popular or biggest rivalries in baseball, which he contemplated to be not only imperfect, but simply a tool of his that he personally thought was reliable to utilize in order to establish and find out information.
I guess my ambitious outlook on Steve's work led me, or leads me to always trust such great think-pieces of his, which is why I used the same exact method to peg the most popular teams in order. In doing so, something I found quite intriguing was how similar my off-the-top-of-my-head predictions were actually similar to the results. And again, while this method is by no means a sure fire conclusion to data, it looked right, which is why I followed through. Here's what I came up with...
By going with this data, there were several things that came to mind from the time I started as well as after all of the data was compiled. First and foremost, I typed in *(team name)* in to Google. If I typed in "Yankees" or "Orioles" rather than the entirety of it's name, I most likely would have came back with many more results, but results that had absolutely nothing to do with the respective team. Or for that matter, baseball. But on the other side of the coin, problems arose with a team like "Los Angeles Angels of Anaheim,' as it's obviously the longest team name in baseball. On a side note, and a totally irrelevant one, I wondered if the Angels realize, and if so, care about their team name for SEO (Search Engine Optimization) purposes. It's probably the hardest name to type, and it takes the longest to do so as well. In any case, search results are search results, and this is the data that I put in my back pocket and left Google with.
Additionally, I was going to use team Twitter followers and Facebook "likes" to compile popularity data, but chose not to. Why? Glad you asked. Each team operates their Twitter account differently. The Blue Jays boast around 47,000 followers, while the Marlins are hovering around 8,000. Does that mean the Jays are significantly more popular than the Marlins? Quite possibly, but I found out that more importantly, it was a result of the way their Twitter accounts were dealt with. The Jays tweet over twenty times per day on average, while the Marlins only tweet the links to articles posted on the team site, or lineups. So basically, follower counts are dependent on tweet frequency, because the more you tweet -- especially being the official team Twitter account -- the more followers you will get. This is not to say it's only dependent on Tweet frequency, because it's not, but I felt using Twitter followers was irresponsible.
Something worth keeping in mind is that this list, or at least the results I conveyed don't at all have anything to do with the amount of fans for which each team possess'. The Google search returned the results of the exact team name I searched, and nothing else. The Pirates are close to the top, which could very well be a result of a random Pirates fan Googling "Pittsburgh Pirates game score" because he wants his Buccos to win, but it could be a Reds fan Googling "twenty reasons why the Pittsburgh Pirates are the worst team on the planet. And I hate them"
The system I used has many flaws, and there's a strong chance that it's very out of line with reality. Of course, it doesn't display magnitude of popularity, just quantitative results. But it's the way that I compiled the data and I'm confident in the results and reasoning that happened to come out of it.