It's a saying as old as the tournament itself: "The Masters doesn't begin until the back nine on Sunday".

While not literally true, it is a widely held belief that the critical holes of the tournament are for the most part contained on the inward half of the course. Indeed, Amen Corner, the famous trio of holes at Augusta National (holes 11-13), seems to play a big role in the outcome of each year's version of the event.

In this article, using hole-level data from each playing of The Masters since 1983 (excluding the 1985 and 1988 versions due to lack of data), we estimate the percent contribution of each hole to the total variation in scores each year. Intuitively, the method we use allows us to separate differences in 72-hole scores into hole-specific differences. While the findings for the most part line up with previous intuition about which holes are especially critical at Augusta National, there are also a couple surprises.

First, some definitions are in order. How should we think about the "importance" of a single hole to the outcome of a golf tournament? Here, we use the variance (i.e. the spread or dispersion) in scores on a given hole to assess its importance. To understand the intuition behind the relationship between the variance in a hole's scores and a its so-called importance, consider the following simple example:

Suppose 100 golfers play 2 holes, and suppose their aggregate scores (the sum of their hole 1 and hole 2 scores) exhibits some variance (i.e. every golfer did not shoot the same score). Further suppose that every golfer made the same score on hole 1. Then, in this example, we would say that hole 1 contributed nothing (0%) to total scores, while hole 2 contributed everything (100%). In hindsight, the golfers could have just skipped hole 1 and it would have made no difference to the total outcomes.

Loosely speaking, the greater the variation in scores on a given hole, the greater is that hole's contribution to the total variation in scores. This method tells us which holes contributed most to separation between all players over 72-holes (as opposed to which holes allowed the eventual winner to separate himself, for example). Statistically, we are doing a simple exercise known as a variance decomposition (see endnote for details).

Below we plot the percent contribution of each hole at Augusta National to the total variance in scores for every year in our sample. We've included a smoothed curve to show the general trend for each hole as the annual numbers are quite noisy. Also included are the grand averages over all the years in the right panel:

On average, the thirteenth hole has consistently been the most important hole at Augusta National in the last thirty five years. It typically contributes about 8.4% to the variance in total scores (if all holes contributed equally, they would each contribute 100/18 ~ 5.6%). Other important holes have been fifteen, twelve, and sixteen. Note that, all else equal, par fives will tend to contribute more than par threes, as there are more shots taken on longer holes and therefore more possibilities for different scores. In general, the narrative about the importance of the back nine at Augusta National is borne out by this analysis.

However, an exception to the back nine narrative is the seventh hole. Other than the two par fives, it is the only front nine hole ahead of any back nine holes in terms of their average contribution over this time period. We will revisit the importance of the seventh hole later in this article. It is also interesting to look at trends in holes' percentage contributions over time: the fifteenth and the second are both holes that exhibit downward trends. Especially in the case of the fifteenth, the decline seems to coincide with the time at which changes were made to each hole (~ year 2000). Of course, this is noisy data, and we don't want to rationalize every pattern we see; but it is food for thought, nonetheless.

Another interesting dimension to be explored in our data relates to how each hole's percentage contribution differs by round. In looking at these numbers, recall some of the traditional pins used on specific days at The Masters (especially on Saturday and Sunday). Here are the averages for each hole by round number from 1983-2017:

The thirteenth hole is the highest contributing hole in every round. This is reassuring to us, as this consistency across rounds makes it more likely that the method is picking up something meaningful (as opposed to just statistical noise). An interesting data point is the sixteenth hole in round four; despite the traditional Sunday pin, which results in many shots funnelling within a few feet of the cup, the hole still produces a lot of variation in scores. Also, again take note of the seventh hole: it's highest contribution is made by far in the fourth round, in which the traditional pin has been in a bowl in the front section of the green.

Recall that the variance decomposition tells us which holes contributed most to the separation between all players in the field. In this final table, we shed some light on which holes allowed the top finishers in the tournament to separate themselves. Here are the scoring averages of the top 10 finishers relative to the field average on each hole from 1983-2017. We also include the averages before and after the year 2000; this is the midpoint of our data, and also a time at which changes were made to several holes at Augusta National.

In general, the findings are similar to those from the variance exercise above, with the back nine, and specifically holes twelve, thirteen, and fifteen, being the section of the course where the top finishers separate themselves. Also, we see the seventh make another appearance as a critical hole. There are also some discrepancies between the hole rankings here and in the earlier exercise (the sixteenth, for example); this is not surprising as the variance decomposition does not capture the exact same information as this exercise.

Looking at the "Pre 2000" and "Post 2000" columns we notice two particularly interesting changes: 1) the seventh hole went from the 7th ranked hole pre-2000 to the 1st ranked hole post-2000! and 2) the fifteenth hole fell from the 2nd rank before the year 2000 to just the 9th rank after. Further, both of these changes align with the hole-specific percentage contribution trends we highlighted above, which leads us to believe there may be something worth looking into here.

Below are two pictures of the seventh hole (courtesy of Golf Digest), before and after changes that were made in 2002 by Tom Fazio. The hole was lengthened by forty-five yards and new trees were planted along both sides of the fairway. Prior to the change, the hole measured just 365 yards and most players could fly it past the trees, leaving a short wedge into the green. After the redesign, the hole measured 410 yards (and has since been lengthened) and had a significantly narrower landing zone off-the-tee. Given the data and analysis above, it appears these changes have transformed the seventh hole into one of the more influential holes at Augusta National.

The fifteenth hole underwent changes in 1999. The tall pines that block out most attempts by players to go for the green in two were transplanted to their current position on the left-hand side of the fairway. It may be that these changes resulted in fewer players attacking the green in two, effectively turning the hole into a short par three for players who hit poor drives. The trend is particularly stark for the fifteenth hole in our first graph: there is a clear break before and after 1999 in its percentage contribution to the variance in total scores. We don't know what was meant to be achieved with the 1999 changes, but their effect may have been to reduce the role of the fifteenth hole in the outcome of The Masters.

On the whole, the analysis here aligns with the traditional Masters narrative which highlights the importance of Amen Corner and the inward nine at Augusta National. However, an under-appreciated hole seems to have emerged from the data presented here as well: the seventh. Perhaps the famed Masters adage should make room for another hole in its company.