Where the mark goes, and why the math is the fiddly part
A watermark is one line of text drawn on the page, so the only real decision is where its starting point sits. For a horizontal mark in the center, that is half the page width to the left of the middle and a little below the middle. For a diagonal mark the text is rotated about its own start point, so the start point has to be placed before the visual center rather than on it - otherwise a 45-degree watermark drifts off toward a corner.
The mark is sized in points and measured with the font that will actually draw it, so a long word is centered on the page rather than hanging off one side. If the text turns out wider than the page - a long company name at a large size - the result says so instead of pretending the mark fits, and you can shorten the words or lower the size.
Top and bottom placements sit a fixed distance from the edge, which makes them behave like a header or a footer. The center placement is the one to use for the classic diagonal stamp, because it cannot collide with a page number or a running head.