  The behavior of merging black holes (including the emitted gravitational
waves and the properties of the remnant) can currently be computed only by
numerical simulations. This paper introduces ten numerical relativity
simulations of binary black holes with equal masses and equal spins aligned or
anti-aligned with the orbital angular momentum. The initial spin magnitudes
have $|\chi_i| \lesssim 0.95$ and are more concentrated in the aligned
direction because of the greater astrophysical interest of this case. We
combine this data with five previously reported simulations of the same
configuration, but with different spin magnitudes, including the highest spin
simulated to date, $\chi_i \approx 0.97$. This data set is sufficiently
accurate to enable us to offer improved analytic fitting formulae for the final
spin and for the energy radiated by gravitational waves as a function of
initial spin. The improved fitting formulae can help to improve our
understanding of the properties of binary black hole merger remnants and can be
used to enhance future approximate waveforms for gravitational wave searches,
such as Effective-One-Body waveforms.
