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tokens: We are thankful to the anonymous referee(s) for an insightful report that improved the paper, and in particular for advocating more conservative assumptions about the completeness of the Kepler pipeline. R.I.D. gratefully acknowledges the National Science Foundation Graduate Research Fellowship under grant DGE-1144152 and the Miller Institute for Basic Research in Science, University of California, Berkeley. J.A.J. is grateful for the generous grant support provided by the Alfred P. Sloan and David Lucile Packard foundations. We are grateful to Smadar Naoz for many enlightening discussions and comments, including opening our eyes to other possibilities in Section 4 , for which we also thank Simon Albrecht and Fred Rasio. Many thanks to Adrian Barker, Rick Greenberg, Renu Malhotra, Francesca Valsecchi, and especially Brad Hansen for tidal insights; to Katherine Deck, Will Farr, Vicky Kalogera, Yoram Lithwick, and Matthew Payne for helpful dynamical discussions; to Will Farr and Moritz Günther for helpful statistical discussions; to Courtney Dressing and Francois Fressin for Kepler assistance; and to Joel Hartmann for helpful discussions about the ground-based sample. We are grateful to Subo Dong for constructive comments on a manuscript draft. Thanks to Joshua Carter, Boas Katz, Doug Lin, Geoff Marcy, Darin Ragozzine, Kevin Schlaufman, and Aristotle Socrates for helpful comments, and to Thomas Barclay, Christophe Burke, Jon Jenkins, and Jason Rowe for helpful discussions of Kepler 's completeness for giant planets. We benefitted from helpful conversations with Thomas Barclay about candidate vetting and Howard Isaacson and Rea Kolb about false positives. We are very grateful to Chelsea Huang for helpful discussions and for providing us with a detrended light curve for KIC 6805414. R.I.D. thanks David Charbonneau, Sean Andrews, Debra Fischer, Matt Holman, and Abraham Loeb for helpful comments on the thesis chapter version of this manuscript. Special thanks to J. Zachary Gazak for helpful modifications to the TAP code. We thank Dáithí Stone for making his library of IDL routines available. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. We are grateful to Kepler team for their work in making this revolutionizing mission possible and making the rich Kepler data set available. Some of the data presented in this paper were obtained from the Multimission Archive at the Space Telescope Science Institute (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. This research has made use of the Exoplanet Orbit Database, and the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.