The flatter the top/bottom curve is the smaller the overshoot. Bold cuts are wider, thus the top/bottom curve is flatter than the thinner cuts, and the overshoot should thus be smaller. On the pointed ends I usually print out a waterfall and adjust until it looks right.

The flatter the top/bottom curve is the smaller the overshoot

That's why I would think the S would need more overshoot than, say, the O. I wonder if you reach a point where the vertical proportions of a letter like S (or its springy spine?) start to override that rule of thumb.

The flatter the top/bottom curve is the smaller the overshoot.

That's why I recommend to look at the width of the overshoot, not the height/depth.
If you make the overshoot about 1/4 or 1/3 of the glyph width you will usually get a good result, whether the curve is flat or narrow. Typically works for me.

However, you always need to judge visually, there is no way to pass that responsibility on to a mathematical rule.

To answer the initial question: normally two categories, but with exceptions (rather than a third one).

Of the stroke width, you mean?

I just checked Briem and my memory was off. It is greater than 2-3% according to him:

"How much [overshoot] depends on the design. In Times Roman, the letter o is 4% higher than the letter x. ... The letter o in Courier and Helvetica is 7% higher the the letter x,"

In the font I am working on the lower case o is 4% taller than the x. The O is 3% taller than the H. I went by looks rather than a rule; I did compare a number of fonts I like, though.

Mark Jamra has a nice discussion of these issues. He reports that Peter Karnow in testing found that most people put a circle that is 3% greater diameter as the same size as a square.

That’s why I recommend to look at the width of the overshoot, not the height/depth.
Aha! Gotta try that. Thanks.

Tim, I don't understand your principle. Could you do an illustration with flat, round and pointed letters?

For a historical perspective, Harry Carter gives the following in a note to his translation of Fournier.

"To satisfy the eye a 6-pt. o has to be about one-eighth taller than the x, a 12-pt. one-twelfth, a 36-pt. one-fifteenth, and a 72-pt. one-eighteenth. The amount of difference required varies with the degree of the extension of the type and the shape of the shading." [Fournier on Typefounding p. 148 note]

But I've never done an extensive survey to see how these numbers jibe with current practices.

-- K.

Kent, that's interesting, thanks. Those numbers are greater I think than what people would do today.

I just checked the o vs x in the optical sizes of Adobe Jenson: caption-4.1%; regular-4.4%; subhead-4.5%; display-4.4%

So Slimbach didn't follow this guideline of lesser overshoots at bigger sizes.

Tim, I don’t understand your principle. Could you do an illustration with flat, round and pointed letters?

Sorry, I was offline for a few days. Here is an illustration of what I mean with "width of the overshoot":

I find it easier to relate this width to the overall glyph shape than the height.