Back in the days when I went to spring training (after the Sox moved to Fort Myers), I spent quite a bit of time at the minor league camp and one could wander around the area. I recall standing right next to a player who was listed as the same height that I am and I could see the button on the top of his cap. They were very lax about recording height and my guess is that they went by what a player listed. This led me to make up my own method of interpreting heights: someone who was 5'6" became 5'9"; 5'9" became 5'10", 5'11" became 6", etc. Maybe they actually measure players today.