Well, generally, if you find a perfect or near perfect point away from a village site (i.e. in an area with lots of pottery shards and other artifacts), it was a lost arrow. Not always, but many times.
There's a canyon here outside of town. Near Winona. Yes, the "Flagstaff, Arizona...don't forget Winona..." of the "Get Your Kicks On Route 66" song. (I'll settle everyone's curiosity who haven't been here---there's NOTHING in Winona!!!! A frickin' gas station---whoo-hoo! Take pics, tell the family, stop for souvineers!
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Anyway, I could see my backdrop well beyond the other side of the canyon, so decided to see how far the arrows could go. Got some stumper arrows out of the quiver and let go. It cleared the canyon and landed on the other side. Well, now, when we crossed over to retrieve our arrows, I couldn't find one. About four months later, a co-worker who knows I'm into traditional archery comes to tell me he wants to show me this great artifact he found. He shows me that lost arrow!!! I said, yeah, seen it before. It's mine, but you can have it if it means something to you. Oh, and you might want to check with the museum, but I'm pretty sure the Sinagua tribe didn't have plastic nocks, steel field points, or Port Orford Cedar. To be fair, the nock was black, so he might have thought it was horn or something.
Oh, well, whaddya gonna do with people???
I generally look for an arrow for about 5 or 10 minutes. After that, it becomes an offering.