That's pretty normal for a first time out.
Think about where you headed to (near the concession stand), and how it's probably the first place any metal Detectorist checks.
I usually give a spot about 15 minutes and if it doesn't turn up anything that you'd expect, I'll work beyond the typical "gotta check there" locations.
For example, on that baseball diamond, do you know if people sit along the OUTER fence line and watch? I've found some great stuff out there, knowing that there's a handful of folks who typically prefer that location. It's not many, but after 10-20 years, it adds up.
Also check any large grassy areas around the field. Just grid them. You'd be surprised how many people sit out there and practice, or wrestle, or picnic. There's stuff everywhere... except where some other Metal Detectorist already cleaned it up!
A good strategy, too, at elementary schools is to do a line or two against the pavement (or playground area), and if you don't find anything, walk a full 40 feet away and do another line. More often than not, you'll start finding stuff. Many Detectorists will hit what they think are "hot spots" but they are hit by EVERY metal detectorist who comes by... the result is they think the field is hunted out, based on a sample only. I've found some KILLER finds by simply gridding fields It takes a long time to do it, but stuff is out there! Found 5 gold rings in one elementary school that regularly had detectorists hit the tot-lots and the first 15 feet near the asphalt playgound. Blew my mind that there were so many. With those 5 rings came between 25-30 others (about a half-dozen silver). What this told me is that there can be a GREAT field... but folks don't bother with it, because it can appear "hunted out" because they hit the same "obvious" spots every one else does.
Cheers!