Finding a bunch of players on the verge of a “breakout” season isn’t necessarily all that hard. Finding a bunch of almost universally-undrafted players who are on the verge of a “breakout” season? That’s a little tougher.

Anyone can make a case for the Rays’ Matt Moore, the Cubs’ Anthony Rizzo or the Mets’ Matt Harvey, all young promising players ready to take the step from good to great as breakout candidates in 2013. But each of them were selected in every draft out there, often in the middle rounds.

The seven players to follow, however, also may be primed for their own breakouts this season—and still may be available in the free-agent pool. So if you need some help rounding out your roster, or if you’re looking for the next who-knew pick-up, dive in. Or at least update your watch list.

Only players with an average draft position (ADP) of 260-plus on ESPN Fantasy Baseball’s Live Draft Results were considered.

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