For Ranged Builds, the Sentinel's Hat is overpowered compared to the Scholar's Hat

I play a fully ranged build by using only firearms and adding ranged and critical infusions to all my gear. I really like the Scholar's Dress and Hat so I crafted those pieces with the remainder from the Sentinel's Set.
When I multiply my ranged damage with the critical stats of my character and compare it to my friend's build which is made from a full Sentinel's set that is infused to be a hycrid melee and ranged damage, his ranged damage with his rifle is astronomically higher than mine!
Because of the incredibly high ranged damage stat on the Sentinel's Hat, any player who cares only about stats and playing a ranged builid would be pigeon holed into wearing a Sentinel's Hat.

Because I am a ranged player, I would ask to have an equally powerful ranged stat added to the Scholar's Hat. Yes, this is a biased request; however, the current case is that the Sentinel's Hat is mandatory for any competitive ranged build.

On the Nightingale's store apge and in video trailers---the female protagonist wearing the reddish orange Scholar's set is wielding a pistol--perhaps consider adding ranged damage to her Scholar's Hat to give some power to that pistol!