I've been back and forth on this, and found not only conflicting data and answers, but strange geometric reasoning.
1. "the pad radius is the long (valve-side) lever arm length", but (if true) why are there so many shorter exceptions?
2. "the radius is the valve lift" (no reason given)
3. "as long as it doesn't present an angle to the stem it's not important"
Clearly, the radius must present at whatever arc position of the lever during the full range of lift. If the radius is too small, the stem edge strikes the rocker lever at zero &/or full lift, rather than the pad. If the radius is too large, rolling motion is reduced and scrub increases.
AFAIK, since there is both rolling and scrubbing motion involved, is the radius an attempt to reduce scrub to the absolute minimum?
I've tried to plot changes in ratio, but it's all over the place...
Almost all of the better on-line tech stuff is aircraft, locomotive, diesel, etc. with roller tips and useless.

Kit - Rather than a circular curvature I think the ideal shape would be of spiral form - either an involute or a logarithmic spiral. Both probably would have the valve-side lever length as the base circle diameter of the spiral.
Involutes have the property of always being (and pushing)  at right angles to the line-of-action (the valve stem). Logarithmic spirals can be made to have a true rolling motion.
 On the rare occasions that I have had to make a rocker I have made up a ball-and-socket arrangement between the end of the rocker and valve stem which has worked quite well. Ball-and-sockets are used on a few production engines - notably the Oz Ford SOHC 4-litre sixes. Stan Sainty (in Oz) also uses the same arrangement on his Top Fuel engines.

All sliding contacts in a valetrain are usually designed to produce rotation in the axisymmetric parts, in order to equalize wear.  Surfaces like tappet faces usually have some degree of crowning and the mating cam profiles have a slight axial taper. This combination ensures a slightly off center, but consistent, contact condition which continuously rotates the tappet.  

Achieving valve rotation is not so important in modern engines that use hardened valve seat.  In some older engines, like old small block Chevy's with the exhaust valve seats machined directly into an induction hardened area of the cylinder head, valve seat recession was a serious problem.  So these Chevy engines would use a "rotator" built into the exhaust valve(balll valve) spring retainer.  The rotator was a type of ratcheting device that would index the valve slightly during each spring compression.  It was the torsional motion of the spring wire as the helical valve spring was compressed and relaxed that drove the rotator around its axis.

As for your question regarding the definition of the ideal rocker arm tip profile, as I noted it's some form of conjugate action.  I can describe what the curve should look like, but unfortunately I'm not smart enough to tell you how to mathematically derive such a shape.

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