This morning, friend of the VORG and ESPN stats nerd Mark Simon forwarded this tweet to my attention:
— Mark Simon (@msimonespn) April 25, 2016
I rooted through the Retrosheet gamelogs for all games with more than 22 runs scored, and then aggregated them based on date of game and final score. I determined that the record is 27 runs, scored in two games that each ended 14-13, way back on August 9, 1899.
In one of the games, the Cincinnati Reds used a seven-run eighth inning to defeat the Brooklyn Superbas 14-13. In the other instance, after the Pittsburgh Pirates scored seven in the top of the ninth to take a 13-8 lead, the Philadelphia Phillies rallied for six runs of their own, walking off by that same 14-13 score.