Today Dan Formeman-Mackey, Tim Morton (Princeton), and I measured the rate at which Sun-like stars host Earth-like planets! Foreman-Mackey did all the heavy lifting—it was a frantic hack day of sorts—but the work was based on the incredible data sent to us by Erik Petigura (Berkeley). Our measurement of "eta-Earth" involved building a period and radius distribution model which, when multiplied by survey completeness and transit probability, does a good job of modeling Petigura's scatter plot of data points.
IMHO, the correct definition of eta-Earth is the number of planets per star per natural-logarithmic interval in some pair of quantities, which could be radius and period, or which could be mass and insolation, evaluated at Earth's properties. That is, it involves an extrapolation or interpolation of any distribution function (measured from the observational data) to the location of Earth. From Petigura's data, and given assumptions (some listed yesterday), we get a number like five percent, plus-or-minus a percent or two. Importantly, this is five percent per natural-logarithmic interval of radius and per natural-logarithmic interval of period, so it should be compared to other papers and press releases with that clear definition in mind. Also, of course, it is conditioned on some pretty severe assumptions.
This blog post does not properly convey my Stoked-ness.
[Note added later: We found a bug in the code; the rate is probably a factor of two larger even!]