It's popular to think of "eras" in HBD as the lively-ball "Steroid Era" with its torrid offense, and the "Post-Steroid Period" with its ascendant pitching.
In most worlds, and certainly in Major Leagues, there have been more distinct periods than just 2 each with its own scoring characteristics.
In summary, there has been a long, steady downward trend in scoring, bringing HBD pretty close to actual MLB levels.
Here are the 5 pretty easily-distinguished "eras" in Major Leagues history (runs per team per season):
Seasons 1 and 2 - The Wild West: teams averaged 847.5 runs per season. Home runs galore. Quite a few individual hitting records and the foundations of many career hitting records.
Seasons 3-8 - The Mini-Steroid: offense was still dominant, but there was clearly an adjustment, as scoring fell 4% to 814 runs per team per season. There wasn't much season-to-season variance either - a high of 823 and a low of 806.
Seasons 9-13 - The Transition: biggest percentage drop between eras - scoring fell 6.5% to 761 per team per season.
Seasons 14-28 - The Long Normal: the longest period with a relatively static scoring environment, but still a big drop of 4.8% from the previous era, to 724.5.
Seasons 29-31 - The Little Ice Age (???): Seasons 29 and 30 were the 2 lowest-scoring seasons in league history at 686 and 695, so it was looking like we had entered another new era. Season 31 recovered to 711 (the low end of Long Normal levels), so it's not totally clear that we've had another algo adjustment. But the 3-year average of 697.3 is down another 3.75% from the Long Normal.