Baeyer-Villiger oxidation of a ketone to an ester by a peroxy acid involves initial formation of a sort of "hemiketal" between the reagents which then undergoes acid-catalyzed rearrangement by the mechanism shown by curved arrows in the following scheme:

The key element of this rearrangment is migration of substituent group (A or B) of the ketone with its electrons to attack the nearer peroxy oxygen atom and displace the carboxylic acid. We formulate the rearrangement as, for example, a methide or a hydride shift. [Note that protonation helped make the carboxylic acid a better leaving group.]

An obvious question is "Which ester is formed?" that is "Which group migrates more easily?"

A series of investigations in which one determines the ratio in which esters are formed from a variety of different ketones allows one to establish a scale of "migratory aptitudes." As the textbook states on page 412, the approximate order of decreasing ease of migration is hydrogen > tertiary alkyl > secondary alkyl > phenyl > primary alkyl > methyl.

At first glance this order seems crazy. One might think that if an anion is migrating, the more stable anion should migrate more easily. What see instead that the more stable cation migrates more easily.

The lesson we learn is that, although we may draw the curved arrow showing an anion migration, the anion never breaks free of the rest of the molecule. What is really important is the availability of the bonding electrons the the C-A (or C-B) bond to mix with the sigma* orbital of the O-O bond and displace the carboxylic acid from the nearer oxygen. The group that would form a more stable cation holds the bonding electrons less tightly and makes them more available (higher HOMO) for attacking the O-O bond.

Thus, paradoxically, the better cation is the better "anionic" migrating group. (Of course a free anion is never truly involved and in the transition state for the migration the migrating group looks more like a cation, surrendering electron density to the O-O group, than like an anion.)