  We derive empirical constraints on the volume averaged `effective' escape
fraction of Lyman Alpha (Lya) photons from star forming galaxies as a function
of redshift, by comparing star formation functions inferred directly from
observations, to observed Lya luminosity functions. Our analysis shows that the
effective escape fraction increases from f_esc^eff ~ 1-5 % at z=0, to f_esc^eff
~ 10 % at z=3-4, and to f_esc^eff=30-50 % at z=6. Our constraint at z=6 lies
above predictions by models that do not include winds, and therefore hints at
the importance of winds in the Lya transfer process (even) at this redshift. We
can reproduce Lya luminosity functions with an f_esc^eff that does not depend
on the galaxies star formation rates (SFR) over up to ~2 orders of magnitude in
Lya luminosity. It is possible to reproduce the luminosity functions with an
f_esc^eff that decreases with SFR - which appears favored by observations of
drop-out galaxies - in models which include a large scatter (~ 1.0 dex) in
f_esc^eff, and/or in which star forming galaxies only have a non-zero f_esc^eff
for a fraction of their life-time or a fraction of sightlines. We provide a
fitting formula that summarizes our findings.
