Baseball glove manufacturers worked with MLB players, maybe none more so than Draper Maynard. Below is an ad from 1935 touting D&M's relationship to major league baseball.

In 1930, Lew Fonseca approached D&M about designing a mitt to his specifications. After experimentation, a mitt was developed with its most visible feature being elimination of the perimeter lacing and grommets in favor of a leather binding at the crotch. This was done to improve flexibility and the "Flexo Model" was born. Below is and ad from 1931. The mitt also features a fixed leather strap web.

In 1932 the design of the Fonseca model was tweaked with the addition of a buckle web and laced wrist strap.

In 1934, the buckle web was replaced with a generic laced web.

In my mind, the buckle web version is the one to have. Below is an example that shows the crotch design elements pretty clearly.

