  Broad absorption line quasars (BALQs) present a large diversity in their
broad absorption line (BAL) profiles. To investigate what physical parameters
underlie this diversity, we construct a sample of BALQs which covers
lambda_rest ~ 800-3000 {\AA}, based on the Sloan Digital Sky Survey DR7 quasar
catalogue. The average BAL properties are evaluated by taking the ratios of
average BALQ spectra to the average spectra of matched samples of non-BALQs,
where the matching is based on various emission properties. We find the
following properties. (i) There is no detectable Lyman edge associated with the
BAL absorbing gas (tau<0.1). (ii) The known increase of average absorption
depth with the ionization potential extends to the higher ionization N V and O
VI BALs. We also find that the C IV BAL profile is controlled by two
parameters. (i) The He II emission EW, which controls the typical velocity of
the C IV BAL, but does not affect the absorption depth. (ii) The spectral slope
in the 1700-3000 {\AA} range (alpha_UVl), which controls the C IV peak
absorption depth, but does not affect the typical velocity. The He II EW and
alpha_UVl also control the observed fraction of quasars that are BALQs. We
suggest that a lower He II EW may indicate a weaker ionizing continuum, which
allows the outflow to reach higher velocities before being overionized,
possibly without a need to invoke a shielding gas. A redder continuum may
indicate a more inclined system, and a larger covering factor and larger column
of the outflow along the line of sight.
