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Brian H (misunderestimated)These are two of the best players from the short-lived predecessor to the National League, the National Association 1871-75. After that these two among others continued (albeit breifly) to star in the NL.
Unfortunately the NA is general not recognized as a major league so the feats of these players are largely ignored. Additionally these two had very short careers (at least in organized baseball) so that they fall short of the 10 year rule for the HOF.
As I recall, Barnes, the great fair-foul hitter before the rule was changed, was injured around 1877 and never returned to greatness. McVey meanwhile went west in the late 1870's where he played in the nascent western leagues. Both of these men starred on the great National Association Boston club and then briefly on the WHite Stockings with Spalding and Anson.
THe only players whose careers peaked in the 1870s that are in the HOF are basically recognized for their role as pioneers -- George Wright, Spalding and Candy Cummings, who supposedly invented the curve.
Along with these two Deacon White and Joe Start and maybe Tommy Bond really warrant HOF consideration if you accept the premise that the 1870's (and the National Association) should be fairly represented in the HOF. To me the most deserving is Deacon White, who continued to excel well into the 1880s but was in his prime in the 1870s.
http://www.baseball-reference.com/w/whitede01.shtml
http://www.baseball-reference.com/m/mcveyca01.shtml
http://www.baseball-reference.com/m/mcveyca01.shtml
http://www.baseball-reference.com/s/startjo01.shtml