It's actually a figure based on Thoroughbreds, not ponies! Granted, TBs do mature faster than warmbloods, but I wouldn't have thought THAT much faster.
I had a friend whose mother's cleveland bay/holstein/tb/percheron was 16.1 at 4yo and didn't grow a millimetre upwards but DID grow a few miles sideways! Went from a 6'3" rug to a 7'0" rug in a year and STILL going at 6-7yo. There's science to indicate that all horses' growth plates fuse at roughly the same ages but the actual growth rates are very much breed influenced, so a 16hh yearling may slow its growth REALLY fast after that and only end up 16.3, or it might be a slow-growing breed and keep growing at the same rate for longer and end up 18hh+...
for what it's worth though I don't hold much faith in parents' heights as an indicator of the height of an eventual foal. My yearling's parents are 14.2 and 14.3 and it's looking likely Satin will be 15hh, but she won't go much taller. 15.2 if I'm lucky. I know people who've ended up with 16hh horses from 14.2 to 14.2! And I know plenty of people who've ended up with much smaller horses than they intended. All depends on the individual cross, AND the individual genetics the foal has inherited. AND nutrition to a degree. Full siblings can be two and three hands different in height!