  NASA's exoplanet Discovery mission Kepler was reconstituted as the K2 mission
a year after the failure of the 2nd of Kepler's 4 reaction wheels in May 2013.
The new spacecraft pointing method now gives typical roll motion of 1.0 pixels
peak-to-peak over 6 hours at the edges of the field, two orders of magnitude
greater than for Kepler. Despite these roll errors, the flight system and its
modified science data processing pipeline restores much of the photometric
precision of the primary mission while viewing a wide variety of targets, thus
turning adversity into diversity. We define metrics for data compression and
pixel budget available in each campaign; the photometric noise on exoplanet
transit and stellar activity time scales; residual correlations in corrected
long cadence light curves; and the protection of test sinusoidal signals from
overfitting in the systematic error removal process. We find that data
compression and noise both increase linearly with radial distance from the
center of the field of view, with the data compression proportional to star
count as well. At the center, where roll motion is nearly negligible, the
limiting 6 hour photometric precision for a quiet 12th magnitude star can be as
low as 30 ppm, only 25% higher than that of Kepler. This noise performance is
achieved without sacrificing signal fidelity; test sinusoids injected into the
data are attenuated by less than 10% for signals with periods up 15 days. At
time scales relevant to asteroseismology, light curves derived from K2 archive
calibrated pixels have high-frequency noise amplitude within 40% of that
achieved by Kepler. The improvements in K2 operations and science data analysis
resulting from 1.5 yr of experience with this new mission concept, and
quantified by the metrics in this paper, will support continuation of K2's
already high level of scientific productivity in an extended K2 mission.
