The ATP rankings have been a tremendous effort ever since they were invented. Their elegance and simple nature have made it possible to create an objective system to show us the leaders of the tennis world.
Ever since the important data has been lost or forgotten, a quest has begun to check if ATP got the facts right with their own system. They did in most of the part, but there have been a few mistakes which will soon show as turning ugly.
It all starts rather simple and it involves luck. For instance, how lucky Newcombe should be that ATP decided to publish the post-Wimbledon 1974 rankings on July 29th. He managed to score 3 extra weeks as World Number 1. Although ATP's publication of the rankings once in a few weeks is completely justified, because of the difficulty of calculations, this has caused the rankings to be not as objective as they were intended, for you see, many tournaments were played and dropped in-between publications, and each change could show a different World Number 1 just for a few weeks, or one week, without ATP seeing it or telling us about it. The Wimbledon 1974 example is just one of the examples I could find right now, but I have not yet moved beyond 1974. Connors should objectively have scored 3 extra weeks as World Number 1 in July 1974.
Now comes the difficult part. Not knowing of the consequences, ATP decided to create a Bonus Point system completely dependent on the rankings just before a tournament is played. With it, beating Top 24 players would award you points. The bonus point system had two factors: a static one (points for eliminating seeds) and a dynamic one (points for eliminated ranked players). Once we try to calculate the rankings weekly, the dynamic factor plays havoc and inserts a chain error into the official rankings, since we are discovering that if we try to be objective and calculate rankings as per week of tennis played, which was a measure back then, we discover that the much faster modifications of the Top 24 lead to larger and larger differences, creating a Chain Error.
The chain error extends beyond 1974, because points start to drop out having different values than the original, and new ones are added depending on the altered rankings. In a way, the bonus system completely butchered the objectivity of the rankings. It's not ours to judge though, because as I said, ATP was completely justified, but it's ours to correct what once went wrong, and without altering the original system in any way, view the rankings as they should have been.
You can find my 1974 repaired rankings in the rankings database.