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Sight marks and sight tapes
A sight mark is the setting a sight is moved to for a given distance, and building a reliable set of them is how a sighted archer hits the middle at any range.
Why a bow needs a mark per distance
An arrow flies in an arc, dropping as it goes, so a bow aimed dead level only hits the centre at one distance. To hit the centre at another range the archer moves the sight so that, when the pin is on the gold, the bow is angled to send the arrow the right height.
The setting for each distance is the sight mark. A recurve archer slides the sight block up the bar and reads a scale; a compound archer turns the scope up or down. The set of marks is unique to that bow, arrow and archer.
Building and recording marks
Marks are built by shooting at a known distance and adjusting the sight until the group centres, then recording the setting. Because the arc is smooth, an archer who has marks at a few distances can interpolate the ones in between, and a sight tape prints the whole scale from a couple of known points.
Sight-mark calculators and printed tapes take the arrow speed and a known mark and generate a tape for every distance. They are a starting point; real marks are confirmed by shooting, because wind, form and arrow condition all shift them.
Why the mount has to be solid first
Sight marks only stay true if the sight is mounted solidly and returns to the same place. A sight that shifts in its mounting, or a mount that is not square to the riser, makes every recorded mark unreliable.
That is why the first job is a correct, secure sight mount on the riser. Once the sight is fitted properly and holds zero, the marks an archer builds can be trusted.
Fit a sight that holds zero
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Sources: Archery GB · Wikipedia: Sight_(device) · Wikipedia: Recurve_bow