We’re getting there, Mr_John. As you’ve since noticed, I didn’t ask you to measure twice. But neither did I doubt the 24-tooth count.
However, if the 3/8"-drive ratchets are 24-tooth instead of 20-tooth, that changes my swing-arc calculation a little in their favour. Still, it’s 2 inches per click at the end of the handle for the regular length 3753N, plus play. More, about 3 inches, for the longer flex-head models. Sounds like a lot to me.
Not only is that the minimum space you need to get any ratcheting action at all, but even when you have more space, you’ll need to do more swings per fastener revolution.
For example, if you need 2 inches and you’ve got 3.9 inches, you’re still only going to get 1 click per swing, which is 15 degrees (360/24) of fastener rotation. With 3× the tooth-count (72 teeth, like Snap-on), you’d get not 3 clicks but 5 clicks in this case, which is 25 degrees of fastener movement. So the Snap-on gets the bolt out with 40% fewer swings in this contrived but explanatory case.
With more teeth, there is less wasted work in tight confines.
I guess I’ll have to get my hands on one of these peculiar Kokens to see how the swing versus back-drag trade-off works out in practice.