I don't think there is any fixed value for minimum height. As far as I see when using SHIFT+UP and SHIFT+DOWN to resize the scrollbar appears exacly when the two arrow buttons/icons are fitting the hight.
And their height is not varying with font size, but with scaling factor set in Windows properties. And may also depend on Windows itself, what arrow icons it draws for scrollbars. They have a uniform look not defined by VFP. So that minimum likely varies with OS version and scale setting.
For me, the scrollbar icons appear at 39 pixels height on Win10 with 100% scaling. I need to test how scaling changes that, but it's clearly the visibility of the two up and down scrollbar buttons, that turns the scrollbar on and off and I would need to err, if the font scaling of Windows does not also affect certain system metrics like scrollbar width and so also button sizes. SYSMETRIC(6), which says it's for the height speaks for 2*17=34, but that it's 39 - odd - speaks for adding in more things to draw, there is the line surrounding the Editbox itself in Windows 10 flat control look that is only 1 pixel, in Win95-xp it was a 3d look that took 2 pixels. The middle line between the buttons is perhaps shared, there you have a reason the value can be odd.
Just by the way, the VFP Sysmetric() function only provides some system measurements, the Windows API call GetSystemMetrics offers more. This function could not only give varying results in different windows version because of 3d and flat look and scaling, the formula for minimum vertical scrollbar height could differ depending on how controls are defined with their frame or not. You can, for example, turn themes off and decide for flat or 3d look of controls. And yes, then it changes from 39 to 37 in flat look. So it has to do with more than one system metric and it even depends whether VFP uses the system flat look (with themes turned off) or it's own flat look. They all differ. What stays constant is the condition the scrollbar buttons can appear both, fully. So there will be no simple final formula and you better use a rough thing like 3*sysmetric(6), enough height to draw two buttons and whatever additional pix3els to fiddle with surrounding lines of the scrollbar buttons, the scrollbar itself and the control. Also, because the control height is including the control frame, it's not an inner canvas height.
Bye, Olaf.
Olaf Doschke Software Engineering