By Andrew Mooney

Cue Jim Nantz and the tinkling piano: the Masters is officially under way. The field of 93 will attempt to duplicate the legendary green jacket-winning performances of years past, including a “who’s who” of golfing royalty: Tiger Woods, Jack Nickalus, Arnold Palmer, Phil Mickelson, Seve Ballesteros.

Though the competitors always play the same course, Augusta National has undergone many significant changes since it hosted the first Masters tournament in 1934. As a result, it’s difficult to compare performances at the Masters across the years. Simply tabulating raw scores is not the most accurate way to do it; in different years, the field faces different temperatures, winds, and moisture, not to mention the alterations to the course itself and the equipment in players’ bags.

In a piece written in 2011, Grantland’s Bill Barnwell proposed another method for evaluating golf scores using a statistical measure called a Z-score. Barnwell’s argument was that a golfer’s actual raw score was less important than how that score compared to the rest of the field.

Take two victories by Golfer A and Golfer B, each of whom shoot 11-under-par, while the runners-up each shoot 6-under-par. They look equal, but the rest of the field’s performance matters. Let’s say the third-place finisher in Golfer A’s tournament shoots 5-under-par, but the third-placed duffer in Golfer B’s tourney shoots 1-over-par. Player B has clearly outperformed the rest of the field to a greater level than Player A, but raw margin of victory fails to capture that detail.

A Z-score measures the number of standard deviations a particular observation is from the mean of those observations. When applied to golf scores, a Z-score can tell us how different a player’s score was from the average, in addition to incorporating the range of those scores. Barnwell applied this method to the four major tournaments and recorded the top-20 performances since 1960, three of which came at the Masters, which you can read here.

As the first round kicks off today, I decided to examine the greatest performances in the history of the Masters more in-depth. I gathered the 72-hole scores for every Masters tournament, pulling the data from golfobserver.com all the way back to 1934. I then converted each year’s raw scores into Z-scores so I would have a uniform standard for comparison across years. Since a low score in golf is good, a more negative Z-score reflects a better performance. The 20 best scores are in the table below.

Many people point to Tiger Woods’ 1997 Masters as the most impressive 72 holes Augusta has ever seen, significant not only for his otherworldly display of golf, but for the fact that it came at age 21, it was his first major win, and it was the first time a non-white player had won the tournament.

Though Woods’ score of 270 remains a tournament record, his performance was slightly less superior relative to the rest of the field than Jack Nicklaus’ 271 in 1965. Woods defeated second-place Tom Kite by 12 strokes in 1997, three more than Nicklaus bested Arnold Palmer by. But only eight other players were under par in the 1965 tournament, compared to 15 in 1997. Nicklaus’ lower Z-score suggests that his total of 17-under came in a more difficult overall course environment and thus exhibited more dominance than Tiger’s 18-under.

A couple of other takeaways from this list:

- Woods, Nicklaus, Raymond Floyd, and Nick Faldo are the only golfers to appear on this list more than once.
- In 2005, Chris DiMarco submitted one of the best-ever Masters performances and finished second, falling to Woods in a playoff, much to the relief of the Nike marketing department.
- Doug Ford tied with Tommy Aaron for the worst to-par score on this list at five-under, but in Ford’s case, only two other players in the tournament finished under par.
- In gathering this data, I was also able to uncover the worst performances in Masters history (for players that made the 36-hole cut). The most shameful 72-hole score at Augusta came in 1940, when Chick Evans posted a 43-over, shooting 82-84-86-79 for a total of 331 (Z-score: 3.627). In second-to-last place is the aforementioned Tommy Aaron’s 2000 Masters, which came 27 years after he donned the green jacket. A score of 25-over can be forgiven for a man of 63, but it still yielded a ghastly Z-score of 3.346.

One thing to note about this, however, is that the Z-scores don’t account for the changing level of talent in the playing field over time. Yes, Nicklaus was slightly better compared to his field than Tiger was in 1997. However, if we assume that the field is even slightly better in the modern era – and given the proliferation of golf on a global scale, this seems a fair assumption to make – then Tiger’s 1997 score, and all the modern scores deserve extra consideration.

By using a z-score, or student-t test, I’m assuming the scores are normally distributed. How do you account for the kurtosis?