On Opening Day of last season, Baseball Prospectus’ playoff odds gave the Arizona Diamondbacks a 1.2 percent chance of making the playoffs. Until May 25th, their record remained under .500, and their playoff odds stayed stuck under 2 percent. That was when they made their move, morphing into the season’s most surprising success. From May 26th through the end of the season, they went 69-44, winning the National League West with eight games to spare.

There’s no way anyone could have known that the Diamondbacks would be that good, for the simple reason that they weren’t that good. The D-backs had a run-of-the-mill rotation and relief corps, a defense that was no better than decent, and a league-average lineup that hit much worse away from Chase Field. However, they also stayed healthy, losing the fewest days to injury of any NL team. Perhaps more importantly, they recorded a league-best 28-16 record in one-run games, which often hinge as much on luck as they do on skill. As a result, they outplayed their third-order winning percentage—an expected record based on underlying statistics and adjusted for quality of opponents—by 10 1/2 games, the biggest margin in baseball.

The Diamondbacks were better than we thought they’d be, but they were also a lot luckier. We can’t predict which teams will enjoy good fortune in 2012, but we can try to pinpoint a few clubs that could be unlikely contenders if the balls bounce their way. This year, five teams have playoff odds under 2 percent as of Opening Day. There probably won’t be another 2011 D-backs in the bunch, but the following three teams are the best candidates to take a surprising step forward.

Kansas City Royals (68-94, 0.3%)
Kansas City’s position players are projected to be the youngest in the AL by almost a year and a half, with a collective age of 26.2. Most likely, that means the Royals are still too raw to contend. However, their youth allows us to dream: if their mix of former high draft picks and top prospects matures more quickly than expected, they could make great strides as soon as this season.

The Royals had the seventh-best offense in baseball last season and could climb even higher on the leaderboard in 2012, if Eric Hosmer and Mike Moustakas improve upon their rookie seasons and spring sensation Lorenzo Cain adds some speed to what was the AL’s fourth-worst baserunning team (-4.0 BRR). Cain will also aid Kansas City in center fielder, where he’ll replace Melky Cabrera, whose -18.0 FRAA was the third-worst of any player last season. Thanks in part to Cabrera, the Royals were one of the majors’ worst fielding teams last season, converting balls in play into outs at the seventh-lowest rate of any team. This season, we project them to be about a win better than average on defense.

The Royals will need their fielders to be among the best in the league if they’re to have any hope of contending, since their rotation leaves a lot to be desired. Bruce Chen has never pitched more than 51 innings for a team that made the playoffs, and he’s Kansas City’s Opening Day starter. Unless something finally clicks for Luke Hochevar and Jonathan Sanchez, any success the Royals have will come in spite of their starters. Fortunately, Jonathan Broxton, Greg Holland, Aaron Crow, and Tim Collins give the team the makings of a strong bullpen even with Joakim Soria out for the season.

Seattle Mariners (69-93, 0.5%)
If Jesus Montero meets his .295 TAv projection over a full season, he’ll be the best hitter Seattle has had since 2009. Even so, the Mariners’ offense won’t be a strength, but with Montero, improvements by Ichiro and Justin Smoak, full seasons from Dustin Ackley and Mike Carp, and either a bounceback by Chone Figgins or a coup by Kyle Seager, they could avoid offensive ineptitude that led to last-place finishes in each of the past two seasons.

If Franklin Gutierrez can come back healthy, he and shortstop Brendan Ryan would give Seattle two of baseball’s best up-the-middle defenders. The big-league rotation isn’t deep behind Felix Hernandez, but respectable ERAs aren’t out of reach for anyone in Safeco Field, and reinforcements are on the way. Top pitching prospects Danny Hultzen, James Paxton, and Taijuan Walker could conceivably start the season on the same Double-A staff, and Erasmo Ramirez, another talented starter, ended last season one level away from the majors. The Mariners won’t rush any of those arms, but one or more of them could crack the roster in the second half of the season.

Pittsburgh Pirates (73-89, 1.7%)
PECOTA projects the Pirates to finish with a better record than either the Royals or Mariners but still fall eight wins short of avoiding their 20th consecutive sub-.500 season. No one has won money by betting on the Pirates to succeed since 1992, and this probably won’t be the season that stops being true. However, there are a few reasons to think the Pirates might be on the verge of breaking even, and breaking even means being a few wins away from a Cinderella season.

Erik Bedard and A.J. Burnett give Pittsburgh at least two starters who miss bats, which they sorely lacked last season. The team can hope for full seasons from Alex Presley, Jose Tabata, and Pedro Alvarez, who would give his team a big boost at the plate by regaining his 2010 form. Veteran imports like Rod Barajas and Clint Barmes aren’t exciting, but they’re better than the players they replaced. Andrew McCutchen remains the only Pirate with star power, but there are fewer empty positions on this Pirates team than there were during the worst of their lean years.

A version of this story originally appeared on ESPN Insider Insider.

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Other not impossibles that could contribute ...

Luis Mendoza becomes this year's Ryan Vogelsong, or better.

A rejuvenated Michael Saunders actually replaces Gutierrez with a better bat.

McGehee and a Jones/Hague platoon give the Pirates league-average-ish production at the corners. And Jeff Karstens, it turns out, actually did turn a corner.