My rudimentaty understanding of this game is that SIMS puts all their recruiting effort into the 1st cycle.  With that said, has anyone done an analysis to figure out approximately how much effort it takes to battle and steal a recruit away from SIMS?

Check the WOTS.  If the message is something like "keeping his options wide open," probably 2-4 HVs, depending on your prestige.  The tighter the kid is with the SIM (again, based on the WOTS message), the more the price goes up.  But once you're ahead, you don't have to worry about the SIM putting in more effort.

The first WOTS message you receive for the kid will tell you something like "X university is really tight with him" or something like "X university gave him some attention, but he may not be a priority for them". The first one requires more effort than the second one in order to unseat the sim.

My general rule is if I get the first message I don't battle the sim unless I expect to have the cash to do it (considering what I will or have spent on other recruits) and I really want the player. If I get the second one and I want the player, I usually go after them unless something changes or I don't have the cash.