Thank you for this. It's very informative. About 12 years ago I was looking for a plastic set and I noticed that most of the sets available had rooks and knights that appeared too small relative to the bishops and queen. In the case of the rook, I especially wanted its size to denote its power relative to the other pieces. I eventually went with one of the HOS sets.
The ratios that you obtained somehow confirms what my eyes were seeing back then, that for a lot of the plastic sets the heights of the rook and knight needed to be increased.
I've done a comparison of 3 plastic chess sets. This is not a review, just a comparison of some measurable metrics, and a few observations. I found it pretty interesting, so I thought i'd share here. The sets I compared were the following:
I understand there are some reasonably well-used sets in the market.
Tip Angle
Finding the angle that each pieces topples is not simple. So to make the comparison reasonably repeatable, I made a jig to tip the piece and help measure the angle. Results are as follows
Not only was the tip angle on the ultimate set the best, it was also very consistent between all the pieces. I'd put it as the winner in this category
Weight
this was a simple metric to get. I just used some scales. Results as follows.
Interestingly, despite the ultimate chess set being more weighty. The best chess set is considered quad weighted, while the ultimate is only triple. I havent seen any standards for single, double, triple and quad weighting in chess pieces. So I'm guessing that is just marketing taking some liberties.
Compliance with Chess Standards
I've looked at the main ones (FIDE and USCF). Despite clams to the contrary, none of the sets fully comply with the standards. The cells in Red highlight the non-compliance.
NOTE: I'm giving the would chess starter set a pass on the height, as it's stated that it's not full height. Though being a scaled from the FIDE world championship set, I still judged it on the ratios.
If you have some insight on how set claim they comply when they dont (maybe I'm interpreting the standard wrong) I'd be interested to hear from you.
For reference the allowable measurements and ratios are as follows.
I hope you enjoyed that. If you think I missed an important plastic set, let me know. I may get it and add it in.