Buffering by percentage instead of distance?

[dlj19220301]

Pretty simple question. I have a shapefile of different-sized polygons, but I don't want to buffer them by a uniform distance. I want to reverse buffer them by a percentage. An example would be buffering each polygon by -50%. 

I don't know if this is already a built-in option. Or do I need to calculate a field in my attribute table with this value, and then set the buffer option to "field" instead of by "distance"? 

Thoughts? 

[KateDoughty1]

Not sure if this is still relevant or open but in ArcGIS Pro 3.2, you can buffer by a field. Divide the area percentage by perimeter length and us that field to calculate your desired linear buffers.