If you need to explain to someone why your Facebook engagement has been declining, you can use these stats & research to show that you are not alone: Buffer and Buzzsumo analyzed 43 million posts during Q2 2018 and compared their results with Q1 2017. It's a massacre. Total drop in engagement for media/news sites is 64%, for TV shows 61%. This is due to algorithm changes, and subsequently increased activity & competition: The top 20.000 Facebook pages increased their post frequency by 24% over the past year. Another interesting aspect is that in overall engagement/interactions, you're probably better of with approx. 5 posts per day as engagement per post is best when you just post once, but absolute number of engagement will add up to the highest when you post around 5 times - after that, engagement declines rapidly.
A ton of interesting numbers & also good advice on post/page strategies here: