Gyms and Raids Go Hand in Hand?

So everyone knows the new gym system sucks, but has anyone thought what you put in determines what you can Raid?
Wife and I have been playing in our town and are one of the stronger Valor players in our town. We still hold over 10 gyms at anytime and still put in our great defenders. Nothing less than 2500 CP unless it can't even reach that as a level 40 Pokemon. If it can't reach 2500 CP , it's at least a level 35 i.e. Venasaur, Houndooms, Slowking etc.
One thing I've noticed since the launch of the Raid system is that every gym we've held that turned into a Level 4 Raid Boss has only hatched 3 Pokemon: Tyranitar, Snorlax and Lapras. In that order too. More T-Tars then Snorlax which has popped up more than Lapras. Nonetheless, we've never spawned anything else in our Level 4 gyms.
Heard a theory a while back stating Total Combined CP of Pokemon in gym + their Motivation = Level of Raid and possibly the Pokemon.

So this past week, wife and I missed a day of going around the gyms to re-motivate or re-take our gyms. Our town is dominated by Mystic. They took are usual gyms down and placed shit Pokemon. Next day, there were literally almost no Level 4 Raids when our community averages in beating down 6 in a few hours or so.

We took them back after work and guess what happened the next day? The level 4 Gyms were popping up where we had taken back out gyms. Only Tyranitar, Snorlax and Lapras too like it's always been with us so far.

What do y'all think?