All of us have had to learn one thing or more the hard way, but It will help you remember to check for Yourself and not take anything for granted in the future. It's all part of the process. I know the let down you must be feeling, Looks like that was a nice cue you had in the works there.
I understand that this was purchased, but When making your own basic design billet You can do the math as already mentioned, It's easy enough, or an even easier way is to simply measure your tenon size, set your calipers to half of that number, put one end of them to your center, and get a mark, then use something held to that mark to draw or etch a circle that is the same size as your tenon on the face of the rod that you are using for your billet. if you want you can then make another circle to represent the OD of the finish size, and then you know that somewhere between those should get your depth in the range of where you need to be, and can use the mark on the face as a visual reference. looking at things from a similar prospective When purchasing billet though, You can use the calipers to make sure they won't wipe out before installing them in the cue.
Another thing to be concerned about is using a billet that is too wide for the amount of indexed points, because given the wrong set of circumstances, the borders can be wiped out as well.
Greg