old-coon's answer is right on spot. He says: "unless something happened in that field that made it a good place to search".
Like if you researched and found that that was the spot of an old camp-stop grounds, or a stage stop had been there, or any other such human activity in yester-year. But to simply go out to any old furroughed field, will not be productive. Oh sure, a field-worker might loose a coin now and then, but that's utterly random and doesn't make much sense. It's much more productive to go where something used to be (old homesteads, saloon, etc...)
Now in Europe this advice may not hold true. Over there, a lot of their cultivated fields have been continuously plowed and worked for 1k to 2k or more years. So do the math, and you'll see, that a random passerby or fieldworker loss adds up over time. So yes, over there, they can just walk into any random field, even if nothing except agriculture had ever gone on there, and yes, find things. But over here in the USA, especially on the west coast, our history is just too short. Where I'm at, for instance, we've had barely 100-ish yrs. of agriculture (before that was cattle). So if I walked into any random field, and worked for long enough, sure, I'd eventually find a wheatie or something. But it would be utterly pointless as the time spent would be better spent going to a park. However, if I researched and learned that there used to be a 1-room school house, or stage stop or something there, then the period targets would turn up perhaps.