Have there been studies about adding weight on the centerline vs perimeter?

[FourPuttDouble]

Been bored and playing around with some tungsten weights after trying out a buddy's heavy putter. Been looking at some of the putters in the bucket and wondering about weight placement.

 

My basic understanding makes me think that the main difference between putting an equal amount of weight on the perimeter vs right down the centerline is that an off center hit will not twist the face, but other than that, is there any reason not to add weight wherever it'll best fit? 

[MattM97]

Well you kinda just described MOI without describing MOI directly.

 

The more weight you place further away from the COG increases MOI and stability. That's why all those super high MOI putters are larger and have weight further away from center. There's a reason you never really see any successful putters with majority of the  weight directly in the middle or behind the face.

 

Now when you add lead weight most usually put it in the cavity cause there is space and the amount most are placing won't change the MOI much or at all cause total mass plays into MOI as well.