This is precisely why murder stats are used. Murder is a crime we don't see affected much by expectations for solution. That is, murder gets reported one way or

This is precisely why murder stats are used. Murder is a crime we don't see affected much by expectations for solution. That is, murder gets reported one way or another (far longer than petty crime does anyway.) E.g, someone smashes window and I don't expect cops to do something. So I don't report it. But someone shows up dead on my doorstep, whether or not I expect to them to solve it, id report it because there's a dead person on my doorstep.