Just did Boston's data for 2013 because they scored the most runs in MLB with 853. They outscored the Reds by 155 runs.
Even with the Red Sox potent offense and the use of DH-- they were shutout................
11 times. Yup, the same number as the Reds. They scored 3 runs or less 61 times compared to the Reds 72. Remember, they have a DH while the Reds have to bat a pitcher. The Cards scored 3 runs or less 65 times.
Boston of course padded their run total by scoring 9 or more runs 26 times for 285 runs. (The Reds had 178) So a difference of 114 runs.
If your looking for an offense that always scores 2-3 runs a game, it won't happen. Even the Red Sox offense who scored 155 more runs than the Reds (or 22% more runs) still got shutout the same amount of times as Cincinnati did, and they had a DH in DAvod Ortiz who batted .309 with 30 HR's, 38 doubles and 78 walks for an .OBP of 395. Suffice to say, he did significantly better than what the Reds got hitting wise from all of their pitchers.