Here's a nice little graph of the changing championship odds through the playoffs. I started to color the lines by team, but there was way too much orange and red to make it worthwhile.
Worst position for San Francisco: 2.2%, when they were down 0-2 in the NLDS
Best position for Detroit: 47.89%, when the World Series was tied 0-0
Best position for an LCS Loser: 52.55%, when St. Louis was up 3-1 on San Francisco
Best position for an LDS Loser: 24.09%, when Washington was up 1-0 on St. Louis
Best position for a Wildcard Loser: 6.24% for Atlanta, narrowly above the 6.22% for Texas
Seeing that St. Louis line so high reminds me how a lot of St. Louisans felt, that the Cardinals were destined to make and even win the World Series when they were up 3-1 in the NLCS, and when they had the comeback against the Nationals. But, we ran out of magic, and San Francisco won an impressive 7 games in a row to finish the NLCS and sweep the World Series.
By the way, the Sweep-and-get-swept the Tigers pulled off has actually happened twice before. First, in 1990 when Oakland swept Boston, then got swept by Cincinnati. Then, just 5 years ago in 2007, Colorado swept the Diamondbacks (with aid of Matt Holliday), then got rolled over by the Yankees in 4 straight.