Mark Broadie is a professor of Economics at the Graduate School of Business at Columbia University. On top of that, he's an avid golfer and has spent a lot of time analyzing the causes of golfers' success.
In 2008, he published the article "Assessing Golfer Performance Using Golfmetrics", which would start the Strokes Gained revolution in golf metrics (although he doesn't use the "strokes gained" term, he uses the term "shot value").
The article is very academical, but is also written in a way that makes it very easy to understand. Its main points are the following:
The paper starts by pointing the limitations of standard statistics (as number of putts or greens hit in regulation) in golf, which are:
Mark Broadie and his team created a software called Golfmetrics to "capture and store golfer shot data and to quantify differences in shot patterns between players of different skill levels". With Golfmetrics, Broadie and his team entered in their database 40,000 shots of more than 500 rounds played by more than 130 golfers of different levels and started the number crunching to analyze what drives performance on the golf course.
Shot value (what we now know as "strokes gained") is a "measure of the quality of a shot relative to a scratch golfer’s average shot from a given situation".
To calculate shot value, Mark Broadie first defines fractional par, which is an "estimate of the average number of strokes that a scratch golfer needs to complete a hole", depending on the distance to the hole and the lie (tee, fairway, rough, sand, etc). The fractional par is estimated using all the data gathered using Golfmetrics.
The shot value is the difference between the fractional par at the start of a shot and the fractional par at the end of a shot (minus 1 to take into account the actual shot taken):
Shot value = Fractional par at start - Fractional par at end - 1
If shot value is positive, it means it was a good shot that reduced the fractional par by more than one shot. If the shot value is negative, it was a bad shot and the fractional par at the end of shot is larger than the fractional par a the start minus one.
As Broadie says, "there are many ways to shoot the same score on a hole, but the shot value calculation shows which shots contributed more (or less) to the overall score".
"An overlooked golf performance measure is consistency and consistent golfers have few very poor shots and few 'blowup' holes". Using shot value, Broadie defines an awful shot as a shot with a shot value with of less than -0.8 and a great shot as one with a shot value of more than +0.8.
A simple measure of consistenncy would be the number of awful shots in a round. An inconsistent golfer may find reducing the number of awful shots an easy path to lower scores.
The last paragraph of the article summarizes what shot value means for analyzing golfers' performance: