The sample baseball report describes their methodology and shows the type of data they gather.I would be interested to hear how the data was collected that supports the conclusion that not only was there a decline but within a specific age group. Not sure how you would even go about such a task without relying on some very convoluted data. Until then I would view any of this with a high degree of skepticism.
The first paragraph in the article indicates the participation rates came from a survey by the Sports & Fitness Industry Association (SFIA). Their reports are not hard to find, but most will cost you if you're not a member - https://www.sfia.org/reports/all. These reports are done by a professional research group and are higher quality than most done for a publication. Here are links to a couple of free ones:
- SAMPLE_SFIA_2012_Single Sport.pdf (Baseball)
- The Journey of Sports Participation in America