# Who Benefits from Wide Fairways?

As we approach the Masters, I am reminded again of the ways in which Augusta National has been transformed over the last few decades in an effort to reduce the advantages of long bombers -- most notably with the introduction of a "second cut" in 1999. We see similar narrowing of the fairways at other majors; most notably the US Open. Such changes are typically justified as placing a premium on accuracy, but is that correct?

While the conventional wisdom has advocated narrow fairways to reward short, accurate players, there is a new chorus of advocates for the opposite viewpoint (see for instance, Andy Johnson's post arguing the narrow fairways at the 2019 PGA championship benefited long hitters). Their argument is that narrow fairways decrease fairway accuracy for *all* players, but the long hitter with a short iron out of the rough has an easier approach than the short hitter with long approach from the rough. The best, most recent anecdotal evidence is Bryson DeChambeau's dominance at Winged Foot in the 2020 US Open. On the other hand, advocates of the conventional view point to courses like Harbor Town as examples of narrow venues that historically benefit short, accurate players. In 2019 the blog Data Golf attempted to answer this question with their statistical performance model, but found no correlation between fairway with and driving distance advantage across PGA Tour courses.

Part of what makes this question difficult to answer (and probably why Data Golf did not find significant trends) is that the severity of a missed fairway will vary not just from course to course, but often from hole to hole. A missed fairway in Augusta rough is not as penalizing as US Open rough, which is not as penalizing as trees, water, or out of bounds. Understanding these effects are not only important for tournament directors looking to create a balanced test, but also can affect the strategy choices for individual players as they seek to understand when to be aggressive and when to be conservative off the tee.

In a previous post I explored the relative value of distance vs accuracy off the tee, concluding that in most cases distance gains are worth more than comparable accuracy gains on the PGA Tour, depending on how often a player hits the fairway. In this post I will extend this analysis to consider fairway width explicitly and consider which fairway widths and which missed-fairway obstacles give long players the biggest advantages.

## Assumptions

In order to explore this question, we need to consider how fairway accuracy changes with fairway width and driver distance. Ideally we would gather data for each drive on tour, measure the distance, accuracy, and fairway width. However, this data is not publicly available, so we will instead make some assumptions.

First, we will assume that tee shot dispersion is *normally distributed* (follows a bell curve). Next, we will assume that the *angular distribution* (the number of degrees off line, rather than the distance off line) is fixed for all driver distances. In other words, we will assume that a short hitter is just as likely to be 5 degrees off line as a long hitter, but because the long hitter hits it further on the 5 degree path, his shot will finish further from his intended target.

There are a few reasons to be suspicious of this second assumption. It is likely that the angular distribution grows with distance for several reasons: a fast, aggressive motion may be more difficult to control, and extended time in the air allows for spin and wind to have a larger effect. Nevertheless, this assumption is a good starting point to explore the relationship between distance and accuracy, and avoids adding additional assumptions that would be required to generate a more complicated model.

To get realistic numbers from these assumptions, we used 2019 PGA tour data to estimate the average angular dispersion. With an average driving distance of 295 yards, an average hole distance (par 4s and par 5s) of 470 yards, and using 30 yards as a typical fairway width, we estimate an angular standard deviation of about 3.3 degrees for tee shots. In other words, we estimate that 68% of pros' tee shots are within 3.3 degrees of their target (roughly the same as two finger widths at arm's length).

Finally, we will consider the simplest golf hole possible in order to keep the analysis straightforward. We assume the fairway width is fixed across the entire length of the hole, and that there is only one type of hazard if the fairway is missed -- either rough, sand, or a situation requiring a recovery shot. We will not consider more complicated holes with multiple hazards, nor will we consider the effects of fairway contours, hole shape, etc.

While these assumptions are a simplified version of reality, they allow us to investigate how fairway width affects score, and how the answer changes based on the type of lie faced when the fairway is missed.

## Results

A broad overview of the effect is shown in the surface plots below. The plots show how the expected score on a 470 yard hole changes with fairway with and driving distance, with each plot representing the case when a missed fairway is either rough, sand, or requiring a recovery shot. The horizontal axis represents the fairway width, the vertical axis represents tee shot distance, and the color represents the expected score. Black lines represent combinations of distance and fairway width that produce the same expected score. We consider driver distances from 270-320 yards, representing the range of average driving distance on the PGA Tour in 2019.

Expected Score Surface Plots

Let's first analyze the Fairway vs. Recovery plot on the far right, as it is the most dramatic. First, notice that when the fairway is very narrow (on the left side of the figure), the black lines are nearly vertical, indicating that there is very little difference in scoring between short and long hitters in this range. On the other hand, when the fairway is very wide the black lines are almost horizontal, indicating long hitters have an advantage over short hitters, and that adjusting the fairway width does little to affect this advantage. These results make sense: nearly all players will hit a 100 yard wide fairway, so there is little advantage to being accurate. On the other hand, having to hit a recovery shot is a significant penalty for missing the fairway with little distance advantage for this length hole. These two factors mean that accuracy becomes particularly valuable when the fairway is narrow and the miss requires a recovery shot.

The remaining two plots, Fairway vs. Rough and Fairway vs. Sand, are harder to analyze visually. On the one hand, they show the same behavior at the largest fairway widths, indicating that extremely wide fairways benefit long, inaccurate players, as expected. However, the penalty for missing the fairway is not as severe from the rough or the sand, so long hitters still have an advantage over short hitters. It is not clear, though, whether that advantage is growing or shrinking as the fairway width changes. Furthermore, these results are for a 470 yard hole only; the results could be different at other hole lengths.

To better identify the effect of fairway width, we considered each fairway width individually and computed the average strokes gained by adding 10 yards of distance to the tee shots (keeping angular accuracy constant). These results are plotted as a function of fairway width in the figures below. A positive value for strokes gained indicates that, on average, the long hitter has the advantage. Unlike the plots above that show results for a single hole length, each curve in the figure below represents a different hole length.

Average Strokes Gained

These plots are somewhat hard to read because the curves don't show a uniform trend. However this chaos does indicate that the effect of fairway width depends strongly on the hole length. Let's first consider the Fairway vs. Rough plot on the left. Note that the strokes gained value is always positive, indicating that long hitters always have an advantage over short hitters. However, the fairway width where the advantage is minimized/maximized depends on the hole length. For 350, 400, and 450 yard holes, the long hitter actually has the largest advantage on the *narrowest* holes, while the distance advantage is minimized around 40 yards. For 500, 550, and 600 yard holes, the trend reverses; long hitters have the advantage on the widest holes, with the advantage minimized on the narrowest holes (perhaps because missing the fairway on a reachable par 5 may require laying up).

The Fairway vs. Sand and Fairway vs. Recovery plots show more complicated variations with hole length. Both actually show an advantage to *short hitters* on 400 yard holes when the fairway is very narrow. This is likely because for holes of this length the long hitter is left with intermediate sand or recovery shots, which are especially penal. Both plots also have the same curve shape for 550 yard holes, with distance advantages always growing with fairway width. The remaining hole lengths show a variety of dependencies on distance -- some times long hitters benefit from narrow fairways, sometimes from wide fairways.

One last method to visualize the data is to consider the fairway width where distance is the least valuable. This fairway width is plotted as a function of hole distance for each hazard type below:

Optimal Width For Short Hitters