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This is not Recreation Ballpark; it's Athletic Park, and it was Visalia's first enclosed baseball diamond.
This picture is not precisely dated, but it appears to be from the early 1920s. If you click the image and look at the enlarged version, you'll see a rich example of early 20th Century small-town America in detail. Notice the cars parked on either side of the grandstands (any classic car enthusiasts out there? Can you give us an exact year on these models?), and the absolutely jam-packed crowd overflowing out of the stands and spilling down either foul line.
While we don't have a firm date on the picture, we do know that the diamond was built in a two-week span in June of 1899, and it is believed to have stood near the modern intersection of Willis Street and Mineral King Avenue (an area that was, at the time, referred to as "the northern end of the city"). Volunteer baseball enthusiasts helped build the fences (look closely at the backstop), while the grandstands were subcontracted out to local construction firms.
Three more random observations: first, you really did have to keep your head up as a spectator in those days. There didn't appear to be any netting or chickenwire to shield fans from foul balls, and those stands are almost as close to home plate as modern Rec Park's grandstand. Second, this lefthanded hitter must have been known to hit the other way, because that's certainly how the middle infielders were playing him. And third, the right fielder proves that outfielder's demeanors haven't really changed in a century.
My thanks to Visalia historian extaordinaire Terry Ommen for unearthing this picture and the newspaper clippings that explain it.