Just look across the table even with the two headstring diamonds. See whether the ball is more to the left or right of the diamonds. I think that is easier than seeing whether the edge of the ball is to the left or right of the center of the diamonds, because the situation is symmetrical and humans are good at seeing small asymmetries.
In any case, the official rule has always been the base/center of the ball.
We always played "base of the ball" in every 14.1 tournament I ever refereed in. Same applied in 9-Ball. The real history of Texas Express rules begins with the McDermott 9-Ball Tour during the early 1980's. It was introduced by the three guys who ran that tour, two of them still alive today. Richie Florence then decided to use it for the 1983 Caesars Tahoe Billiard Classic, a tournament that I directed for him. I was completely horrified that he would ask me to make such glaring changes to our beloved game. I knew it would throw a large element of luck into a very skillful game. But Richie was the promoter and he prevailed, saying it would speed up play for television, and he was right about that. The final three matches were televised on ESPN. That was the beginning of the end for "push out" 9-Ball.
To this day I will still say that "push out" 9-Ball is the best way to play the game. More thinking involved and more creativity in shot making. Yes, the matches take longer but there's nothing wrong with that a shot clock won't fix. We used to allow two hours for Races to Eleven, and that worked well for most of the players. There were always a few guys who played too slow and we had ways to speed them up.
The small arenas (usually 3-500 seats) we used for tournaments back then were always packed with people, often with standing room only. There was no TV or streaming (until the 1980's) and I used to say it's performance art. You had to be there to see it! I loved my job and watching pool back then. So many great players and tournaments in the U.S. every year. I was mad if I had to miss one.
Where have all the flowers gone, a long time ago!
