I wasn't able to post yesterday . . and I really missed a lot I guess. I don't have any clue what this 1/16th business is about, and BrunsNick had the best advice here. Hit your lines, if you do that, perfect fit. And I really don't get what you're talking about with the thumb going side to side . . because unless you're missing by 1/8th on the fingers or something, it doesn't affect it. We're talking adjusting thumb left or right by a millimeter or two for missing by 1/32 or something. Anybody who misses a span by 3/8 shouldn't be allowed to touch a ball period. I don't know what pro shop people do in your area, but up here, we hit lines. I measure 3 or 4 times before every cut, I start the hole with the tip of the bit, turn the machine off, then lower it down until the bit is almost resting on the ball to make absolutely certain the edge of the bit is going to be right on the line, and THEN I drill the hole.
I've had to plug and drill fingers only before measuring from the thumb several times, and it's a certifiable pain every time. Again, Nick is right, hit your lines and it doesn't matter, but I don't like wasting a bunch of extra time measuring. The real issue here is do you drill cut to cut or full span? If you drill cut to cut, it makes ZERO difference if you measure right and hit your lines. Drilling full span is different. We do that primarily because 95% of our customers use grips, and most of them don't have stuff drilled very often, so the likelyhood of their grip size changing is pretty high. If we go cut to cut, we would have to change it all the time based on grip thickness. If we just go full span, we never have to measure the grips. If you start with the thumb, you get that in, then you have to measure the thickness of the front wall of each grip, then subtract that from the span to get where you actually have to put the lines. If you go fingers first, you layout the ball, drill the fingers, install the grips, then just measure each side, draw your line, and drill.
So I suppose my deal is a speed and simplicity thing, fingers first equals fewer steps and less time spent, point and case. If you can hit lines and prefer to go thumb first, go with it. But I go fingers first, hit lines, and will have the ball done and out the door before you get the ball off the press. Seriously though, I'll video myself punching a ball, but I'll go 4x4 3/8 to make it easier to get into the picture. 3/8 is still 3/8. My daughter starts youth leagues an hour before I get on the clock tomorrow, so I've got time to mess around with this. The ONLY reason I could see doing thumb first is if you do the centerline transfer method, then of course you'd have to drill the thumb first, but nobody here said anything about that.
So really the major point here is what Nick said, hit your lines, but don't act like fingers first or thumb first has any effect on accuracy, because it doesn't. I find fingers first to be more efficient, and I'm merely defending that point.