Here is my team's schedule
https://365.strat-o-matic.com/team/schedule/1638702 . Some of the games where I saw were close and where the pitcher's hitting was a factor in the win:
Game 20 Byrd W 4 to 2, 3 hits, 1 run, 1 rbi
Game 22 Rowe W 2 to 1, home run
Game 30 Byrd W 5 to 4, 14 innings, 1 for 2, 1 rbi
Game 67 Rowe W 2 to 1, 1 for 3, 1 run
Game 120 Rowe W 11 to 6, 12 innings, 2 for 2, 1 run, 2 rbis
Team Pitcher's hitting Runs, RBIs, ABs, Hits, AVG
Homestead Grays 186, 38, 31, 411, 80, 0.194647202
Opponents team average 22.3, 17, 368, 49.6, 0.1348881
Difference 15.7, 14, , , 0.060
My pitcher's hit 60 points higher than my league opponents did in average during the regular season. If the entire lineup hit 60 points higher at each place in the batting order, think what a difference that would make.