Continuous sac+gungnir vs sac+gungnir+hex

Assuming you have 50% buff duration but only 90% crit rate without hex
is it more beneficial to wait for hex before using sac?
Similarly, if you had 100% (or even 97) without hex, is it still worth waiting for hex?

i'd like to say it's dependent on your attack and critical multiplier, but i can't say for sure. probably it's better to wait for hex to activate (even though the darn thing takes like 10 seconds) since you get 40 attack for almost two minutes or two cycles of gungnir, but i'd like to have a mathematically proven answer (which i, unfortunately, am too lazy and tired to calculate ._.)