Originally Posted by JMich

Why? The half hp means you and your friends get less EP, the flee means you all get fewer SEGs. Why use them? I can see a case where you use the flee one when you will be one shotting the EGs, but then you don't need the other one.
Reminder, once you kill an (S)EG (whether your own or a shared one), you can encounter a new one. So the one EG you cause to flee could give one SEG and 3 more EGs to continue the encounters. So I do find both potions and elixirs to be of no use once your friend list starts getting properly populated.

During phase two, I make all EGs that I can't oneshot with a single weak attack flee, and search further for an SEG instead. My main limitation is Focus, not Stamina, so I preserve my Focus for SEGs and generally have plenty stamina to find myself a new one.

The half HP is because the past few events I was generally the "big hitter" within my friendslist. Big enough that I could often one-shot the spawns on my friendslist, but held off on that till the last 15 minutes to give other people a chance at getting a hit in.. There are players who deal way more damage than me, but sadly not in my friendslist.
So, when an SEG is too big for me and those on my friendslist to take down without elaborate pudding consumption, I halve it into a more managable size, and save the pudding for other SEGs of managable size. I rather use 12 focus (my own focus + 1 pudding) to kill 2 SEGs with 55 million health each, than 1 SEG worth 110 million health.