Interesting to see how this numbering issue works with pinball; I am one of those who assumed #16 would have been the 16th unit off the line.
For those who question the desire for a certain number, I can partially understand. I come from the world of Corvettes. Back in the 60s and early 70s more than a few Vettes got cut up (customized), chopped up (customized), big block engines shoveled into places designed for small block engines, etc. A few of the old Vettes were left untouched. In 1974, along comes the National Corvette Restoration Society and the world started to understand that The Corvette was a classic car. Untouched original Vettes with matching numbers went into the higher dollar value territory.
Two restored Corvettes, side by side, identical in every way, same engine, same tranny, same color, etc. the one with the matching numbers would be worth more money.
1953 Corvette #3 was the first Vette that GM let out the door. That #3 was a lot more than #4 or #5 etc. The Vettes were numbered in their order off of the line (None of this wishy-washy BS of which unit I could attached a number plate to first).
And then later on the matching numbers thing move into the 60's Dodge Charger territory.
As someone mentioned way back in this thread, the later numbers in line are usually better quality wise as the production kinks get worked out and the line workers learn how to assemble the product.
I don't understand the desire for a certain number on a pin, but I do respect it and would be disenchanted to be told that "we will send you a serial number tag. Which number would you like?"