The Big Four
The Big Four were Dan Brouthers, Jack Rowe, Hardy Richardson, and Deacon White. They played for the Buffalo Bisons from 1881 to 1885, and were then sold as a group to the Detroit Wolverines, playing there from 1886 to 1888.
In 1889, White and Rowe had purchased financial interests in the Buffalo team, but the league prevented White from going there as the Pittsburgh Alleghenys owned rights to him. The dispute was part of the reason the Players League was formed in 1890. White and Rowe ended up playing for Pittsburgh in 1889, while Brouthers and Richardson played for the Boston Red Stockings.
The Big Four were not called that because of their height, as Jack Rowe was 5' 8". Rather, they were strong players. White was already a 33-year-old veteran in 1881, a winner of two previous batting championships, while Brouthers was 23, Rowe 24, and Richardson 26. Of the four, Jack Rowe had the shortest career (12 years), with 298 games at catcher perhaps having an effect in shortening his career.
Rowe's best year was 1881, when he hit .333 and led the league in triples. Richardson's best year was perhaps 1886, when he hit .351 and led the league in home runs. Brouthers, of course, is a Hall of Famer who led the league in OPS+ eight times.
They are sometimes remembered as all infielders, but Richardson played outfield early in his career and later on. They comprised an infield (catcher, first base, second base, and third base) from 1882-1885, along with Davy Force at shortstop.
There are no similarity scores for groups of players, but a somewhat similar group that comes to mind as a comparison is the Los Angeles Dodgers infield from the 1970s of Steve Garvey, Davey Lopes, Bill Russell and Ron Cey which played together for a decade. That infield, however, was never given a nickname that stuck for decades like the Big Four.
"A correspondent calls attention to the fact that the original 'Big Four' were Martin Powell, Winchester, Gillespie and Connor, of the Holyoke Club (in the late 1870's)." - Sporting Life, June 19, 1889