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On May 4, 1871, on a ball ground laid out on the Camp Allen Civil War camp site west of downtown, the Fort Wayne Kekiongas defeated the Cleveland Forest Citys 2–0 in the first game played in the National Association of Professional Base Ball Players — the first professional league, and the game from which the major-league record is conventionally traced. The site today is Camp Allen Park, a neighborhood city park, and the game is commemorated there: a historical marker at Huron Street and Center Street reads, in part, "The 1st major league baseball game… was played here May 4, 1871. Kekionga whitewashed Cleveland 2-0," and a monument placed on the site in 2017 added a permanent memorial. The game, the clubs and the league are the Sports chapter's; the TinCaps' own game notes still carry the site line — professional baseball's first league game "played at present-day Camp Allen Park just outside of Downtown Fort Wayne."
The record needs one caution, and the Sports chapter documents it in full: Fort Wayne's other old ball ground, League Park, carries a marker crediting it with Kekionga games, but the Kekiongas never played there — League Park's major-league history is two games in 1902, a generation later. Camp Allen is the 1871 ground. It takes its name from the Civil War camp that occupied the site before it, where Indiana regiments mustered in the 1860s; the park preserves both layers of the ground's history, and its fame in the wider world rests on a single afternoon — nine innings, two runs, and the start of professional baseball as a league enterprise.
Sources: Historical Marker Database, Camp Allen marker (Huron Street at Center Street); Fort Wayne TinCaps game notes (milb.com); the Sports chapter of this history for the 1871 game, the 2017 monument and the League Park marker's error.