Possible Clues:

• Big baseball events ... and a hint to 20-, 37- and 43-Across
• Ballpark events, or what 17-, 31- and 48-Across all have
• Baseball rarities nowadays ... or a phonetic hint to the starts of 17-, 26-, 48- and 57-Across
• Once-common baseball events ... and a hint to 16-, 24-, 46- and 57-Across
• Baseball events