The Delphi case wasn't helped by the sketch that was released first, because, IMO, it looked too much like a photograph, which led to a feeling in the public that every feature was 100% accurate and that it was a "real" person.
Let's say you go grocery shopping and spend about the same amount of time you usually would observing other shoppers (that is to say, not that much time because you didn't realize that anything untoward was going on). Later that same week, police come to your door and tell you that you may have observed a murderer in the baking goods aisle and they are hoping you can describe him well enough to make a composite sketch of his face.
So you sit with a forensic sketch artist and they help you make a composite - by definition, creating a face, from your memory, by piecemeal. Setting aside the biological question of if piecemeal fashion is even how our brain remembers faces (there's good evidence that it's not), the sketch artist might start at the top and ask you to describe the hairline of a man you saw in the store that day. Or, they might show you a book of several different hairlines to choose from. Then they'd work their way down - looking at several different versions of eyebrows, nose shape, cheekbones, choosing a face width, lip sizes, chin. You probably are not going to be accurate on every feature. You're going off your memory and it's not that strong because you didn't realize you'd be quizzed on this later. Probably the face had one or two elements that you're pretty sure about because they were more noticeable, for whatever reason. Let's say its the nose and a widow's peak in the hair. But the eyes and chin you end up picking for the composite are more generic because you're just not sure.
So now that the sketch is done, is that a real person you're looking at? I'd say no, it's not a real person. It's your memory, and at best it's a resemblance, as Doug Carter called it. Some features may be pretty close to accurate and others are definitely off or, at least, don't contribute to what the person actually looks like. Furthermore, it is a common technique for sketch artists to slightly exaggerate those features in the image that you were confident about (think about how a cariacature artist might draw Jay Leno's chin). The hope is that by drawing them in a slightly exaggerated fashion, it would help that feature stand out to a person who knows this man well enough to recognize him from a not-totally-accurate rendering.
Let's say that both you and one other shopper were able to complete composite sketches of a man seen in the baking aisle. How similar might they be? You noticed his nose and hair. The other shopper didn't notice those things, but noticed eyes and lips. Neither of you really noticed how old the person was. The images created from the memories of each of you actually could look like different people to the brain of someone who wasn't in the store and never saw the man at all. But are they different people? Maybe you are describing one man, and the other person someone else. Maybe it's the same man, but you each noticed different things, or one of you had a better memory. We will never really know, because people notice and remember different things and
these sketches are memories, not photographs. What's likely is that when the man from the grocery store is found, he won't look exactly like either sketch but there will be small things you can pull out of each one that were somewhat correct.
So what good to the public is a composite sketch then, if it's not going to look exactly like a real person? The hope is that it looks similar enough that 1. another witness in the area is triggered to come forward to describe what they observed, or 2. someone who knows that subject personally is able to recognize some of the features well enough to talk to police about their suspicions. Usually this does not occur in a vacuum. The recognition occurs because someone sees a resemblance AND puts together information about that person's actions that fit what is known about the crime.
See this in action in this case:
EU graduate, former Afton cop charged with Missouri murders
A woman's 75 year old mother was raped and murdered. A witness saw a man driving a jeep in the vicinity of the crime. The composite sketch of that witness's memory was placed on a billboard that the victim's daughter drove by every day. Every day she stared at it and thought, "I don't know who that is." But one day a lightbulb went on and she realized she recognized the chin - just the chin - though the rest of the face was wrong. She realized the chin looked like that of a man she used to date years before. She went to police with that information and that man, Jeffrey Moreland, was later linked to her mother's murder by DNA as well as other murders and rapes.
