Here's one take anyway.

Caveats: The chart below is just about the postseason. Regular season, schmegular season. The first column (PS) includes this year's postseason appearances, but there's no 2017 additions for the rest since we haven't gotten there yet. Soon, soon. (Maybe tomorrow, Cleveland?) It also includes the year 2000. I'm not one of those sticklers.

Here's the key I used to reach the total on the right:

• Postseason = 1 point
• LCS = 2 points
• Pennant = 3 points
• World Series title = 5 points

You might want to weigh things differently. Originally I thought, “A pennant should mean way more than an LCS, and a title way more than that,” so had something like a 1/3/5/10 point scheme. But under that, you'd have one-time wonders like the Marlins beating perennials like the Dodgers and that didn't seem right to me. So I opted for this. 

But in either point scheme, or almost any you come up with, four teams dominate: Cards, Yanks, Giants, BoSox. Then a big drop.

BTW, as a Mariners fan, it's hard to imagine five teams having worse centuries than the M's, but the numbers don't lie.  

My rooting interests this year, from fave to least, for the eight teams remaining:

1. Cleveland Indians
2. Washington Nationals
3. Houston Astros
4. Los Angeles Dodgers
5. Chicago Cubs
6. Boston Red Sox
7. Arizona Diamondbacks
8. Lima beans
9. The cut I got on my right index finger while washing Jellybean's food can the other day
10. The stain on the sofa that won't come out
11. Steve Inskeep
12. “Transformers 2”
13. That bout with the stomach flu I had after Christmas 2006
14. Steve Bannon
15. The NRA
16. Mitch McConnell
17. Donald Trump
18. New York Yankees

Actually, that's unfair. I'd totally root for the Yankees over those last four.  

Note: If the Indians win it all, which they haven't done since '48, the “longest title drought” title will, for the first time, enter the expansion era (1961-today). And the title holder will be the Texas Rangers, who came into existence as the second Washington Senators in 1961, the same year as the California Angels (who won it all in 2002), then moved to Texas in '72. After that, it's 'Stros, who arrived in '62 with the Mets (who have two titles), then three of the four '69 teams: Padres, Brewers, Expos/Nats. The fourth '69er, the Royals, long considered hapless, are actually, along with the Mets, the second-most successful expansion team in baseball history. 

David Freese forces a Game 7, Oct. 2011