Putting Science
Dave Pelz published Putt Like the Pros in 1989. Pelz had been studying putting since the early 70's. His work clearly demonstrates that putting improves on higher quality greens and that pros could improve their putting performance with proper practice. This is important because the USGA Greens Section has been working actively to improve greens all over the country. Over the last decade, the PGA has carefully monitored greens on courses where PGA Tour sponsored events are held. These courses risk losing their tournaments if course conditions don't meet PGA standards. In addition, Pelz's training programs for putting and the short game are well known to dedicated and committed competitive professionals. This chart summarizes the relationship between distance and the percentage of putts made.
Note the parabolic nature of the curve beginning at approximately ten feet. Please note that reducing the distance from a thirty foot birdie putt to a fifteen foot birdie putt doubles the number of birdies made, but this would only increase the number of total birdies by 5 percent. I have no data but have read that the average birdie putt is 20-25 feet in length. Cutting this distance in half would again double the number of putts made, but it still only increases the total number of birdies by 10 percent. Looking at data for birdie conversion (This is the percent of time a player makes birdie after hitting the green in regulation):
The actual number of birdies has increased by almost 20% [(30%-25%)/25%], or almost twice as much as would be expected if putting remained constant and pros were able to hit the ball twice as close to the hole on their approach shots. If pros were hitting the ball twice as close to the hole, the number of greens hit in regulation should increase dramatically.