The link below is to a figure with the distributions of "facial competence" among candidates for the the United States House of Representative in 2004 and Senate from 1992-2006, as measured by Matthew Atkinson, Seth Hill, and Ryan Enos using the method described in "Candidate Faces and Election Outcomes: Is the Face-Vote Correlation Caused by Candidate Selection?" (Quarterly Journal of Political Science 4 (3), pp 229-249). Note that the shaded regions of the distributions represent challengers.
For an example of the instrument we used to generate these scores. You can visit Seth's page. This is a mockup of the survey, with which we presented participants with randomly drawn pairings of candidates.