  We produce and analyze eclipse time variation (ETV) curves for some 2600
Kepler binaries. We find good to excellent evidence for a third body in 222
systems via either the light-travel-time (LTTE) or dynamical effect delays.
Approximately half of these systems have been discussed in previous work, while
the rest are newly reported here. Via detailed analysis of the ETV curves using
high-level analytic approximations, we are able to extract system masses and
information about the three-dimensional characteristics of the triple for 62
systems which exhibit both LTTE and dynamical delays; for the remaining 160
systems we give improved LTTE solutions. New techniques of preprocessing the
flux time series are applied to eliminate false positive triples and to enhance
the ETV curves. The set of triples with outer orbital periods shorter than
~2000 days is now sufficiently numerous for meaningful statistical analysis. We
find that (i) as predicted, there is a peak near i_m~40 deg in the distribution
of the triple vs. inner binary mutual inclination angles that provides strong
confirmation of the operation of Kozai-Lidov cycles with tidal friction; (ii)
the median eccentricity of the third-body orbits is e_2=0.35; (iii) there is a
deficit of triple systems with binary periods <1 day and outer periods between
~50 and 200 days which might help guide the refinement of theories of the
formation and evolution of close binaries; and (iv) the substantial fraction of
Kepler binaries which have third-body companions is consistent with a very
large fraction of all binaries being part of triples.
