Restrictor rings are placed inside a bats barrel (normally at the sweet spot) to restrict the bat from flexing past the point of allowable certification. These rings can also be called inner discs, restriction rings or Bbcor rings. There are more prevalent in Bbcor baseball bats than any other although men’s slow pitch ASA bats have them also. The rings can be found in Demarini, Louisville Slugger, Marucci, Easton alloy bats, and Combat Bbcor bats. Not everyone of the above models of bats have the rings but most do. Some alloy and composite bats do not have such rings. The Rawlings 5150 alloy is one that does not. It incorporates the thickness within the manufacturing of the bat as you can see below.

The Marucci Cat 7 is another alloy that does not have a ring. They claim it creates dead spots in the barrel. 

What are some bats that have these rings?

Worth and Miken ASA men’s slow pitch bats. Most of the newer ASA bats have this “ring” (2016 and above). But it is not really a ring but more of a 2^nd barrel inside the barrel. This is designed to restrict the walls from flexing farther than the inner insert tube. The tube is connected to the end cap by a metal rod and glued into place.

Monsta men’s ASA bats also have an inner tube inside the barrel. They actual coined the term FIB (floating inner barrel).  The Monsta bat inner tube is held in place by foam which is similar to how Easton secures their end loads on Bbcor bats.

Louisville Slugger men’s ASA bats also have inner tubes except they place discs onto the tubes and secure the tube by the end cap. The fastpitch bats also have these inner restrictor discs (pictured below right).

Some Combat men’s slow pitch bats have a restriction ring also. They are not put on every type model bat although. There ring is a little different, it has a metal disc secured to plastic frame that is glued into the barrels sweet spot with flexible epoxy(pictured below left).  Bbcor composite Combats all have an aluminum restrictor ring glued to the barrels inner sweet spot.

Bbcor Louisville sluggers also have the inner rings but theirs is made of thick composite and is a part of the composite make of the bat. As in the ring is in the middle of the bat but there is a layer of composite running down the barrel securing the ring; so technically it is a part of the barrel.

Demarini Bbcor composite and alloy bats have a metal restrictor ring inside the barrel also (pictured below).

Some alloy Marucci bats also have a metal ring although the new Cat 7s do not have such a ring.

Easton Bbcor alloy bats also have a metal restrictor ring inside the barrel although the composite Bbcor Eastons do not have such a ring (pictured below).

Rawlings composite fast pitch bats have a tube just like the Worth and Mikens listed above.

 This is by no means an all-encompassing list but I just wanted to maybe explain the different types of rings and their purpose.

UPDATE:

The Demarini Senior baseball bats have a retool for 2017. They are also putting a composite sleeve (ring) inside the barrel to restrict flex of the bat (pictured below).