Pricing an instruction the vendor has already priced
By the time you knock on the door, the owner has a figure. They got it from a portal estimate, from what the neighbour got in 2022, from what they need in order to buy the next one, or from the agent who came round yesterday and told them what they wanted to hear. You are not walking into an empty room. You are walking into a room with a number already in it.
Most appraisal advice treats this as a problem of persuasion, and it is not. It is a problem of evidence, and specifically of whose evidence is in the room.
The thing that changes the conversation is arriving with the working out rather than with the answer. An agent who says four hundred and twenty is negotiating. An agent who says here are the four houses that sold within a quarter mile in the last nine months, here is what they went for, here is what is different about yours, and here is where that lands us is doing something else entirely: they are handing the owner a method. Once the owner is using your method, the number follows, and it follows without anybody having to lose an argument.
Three things make that work.
The comparables have to be genuinely close and genuinely recent. Two streets away and eighteen months ago is not a comparable, it is a decoration. If there genuinely are not three good comparables, say so, because that is itself a fact about the property and it explains the wider range you are about to give.
The adjustments have to be stated out loud. This one had a converted loft and yours has not, which is worth roughly this. That one backed onto the school. If you do the adjustments silently and present a figure, you are back to negotiating. If you do them out loud, the owner can disagree with a specific adjustment rather than with you, and a disagreement about whether a loft is worth fifteen thousand is a conversation you can win.
The range has to be honest about what it is. A range is not hedging. It is the difference between a price that attracts a viewing in the first fortnight and a price that eventually gets there after two reductions and four months. Say what each end of the range buys them, in weeks.
The hardest version of this is when the owner's number is not an opinion about the market but a requirement. They need four hundred and forty because that is what the next house costs. No amount of comparable evidence touches that, because it is not a valuation argument, and treating it as one is why those appraisals go badly. The honest response is to name it: this is what the evidence says the market will pay, this is what you need, and here is the gap. Then you are both looking at the same problem from the same side of the table, and the options, which are wait, improve, or reconsider the next house, are theirs to pick from.
The agents who win the most instructions are rarely the ones quoting the highest figure. They are the ones the owner believes. Belief is built out of showing your working, and it survives the moment three weeks later when nothing has happened, which is exactly the moment an over-promised number destroys the relationship.
One practical note. Whatever you present, leave it behind in writing. The owner is going to repeat your reasoning to a partner who was not in the room, and they will repeat it badly. Give them something to hand over.