  While the Advanced LIGO and Virgo gravitational-wave experiments now
regularly observe binary black hole mergers, the evolutionary origin of these
events remains a mystery. Analysis of the binary black hole spin distribution
may shed light on this mystery, offering a means of discriminating between
different binary formation channels. Using the data from Advanced LIGO and
Virgo's first and second observing runs, here we seek to carefully characterize
the distribution of effective spin among binary black holes, hierarchically
measuring the distribution's mean $\mu$ and variance $\sigma^2$ while
accounting for selection effects and degeneracies between spin and other black
hole parameters. We demonstrate that the known population of binary black holes
have spins that are both small, with $\mu \sim 0$, and very narrowly
distributed, with $\sigma^2 \leq 0.07$ at 95% credibility. We then explore what
these ensemble properties imply about the spins of individual binary black hole
mergers, re-analyzing existing gravitational-wave events with a
population-informed prior on their effective spin. The binary black hole
GW170729, which previously excluded effective spin equal to zero, is now
consistent with zero effective spin at ~10% credibility. More broadly, we find
that uninformative spin priors generally yield overestimates for the effective
spin magnitudes of compact binary mergers.
