Improve Distance or Accuracy?

By: Christopher Conklin, datadrivenplayer@gmail.com

All players have limited time to improve their games, and the reality is that to reach the next level, all areas need improvement (a low handicap player is typically better at everything than a high handicap player). Still, most players want to know where to spend their limited time to make the most improvement the fastest.

This article will focus just on improvements with the driver and specifically ask the question: Is it more important to hit my drives farther or straighter? Anecdotal evidence presented by analysts can be frustratingly contradictory -- those in the "bomb and gouge" camp say losses in accuracy are made up for by the shorter approach shots, while others point out that big numbers typically start with and errant tee shots. Without an evidence-based analysis, the debate rages on.

Fortunately we have data that can help us answer this question, at least at the PGA Tour level. In an article from 2011, Mark Broadie (inventor of the strokes gained statistic) reported the average number of strokes taken on the PGA Tour from various distances and shot conditions. Broadie identifies five shot conditions: tee, fairway, rough, sand, and recovery (where recovery is defined as a place where a player cannot directly attempt to hit the green). The average number of strokes taken from each condition is plotted as a function of distance below:

As might be expected, the average score at a fixed distance is lowest from the tee, followed by the fairway, rough, sand, and recovery. Also worth noting that in all cases the average score begins rapidly decreasing inside 50 yards. There are two surprising patterns in the sand and recovery curves: both show regions around 60-100 yards where the average score is higher than being slightly outside of 100 yards. The sand data may support the conventional wisdom that bunker shots too long for greenside technique and too short for a full swing are some of the hardest shots in golf. The blip in the recovery curve is harder to explain; it could be because the ability to shape a recovery shot around obstacles toward the target becomes more difficult at shorter distances. We should also note that Broadie does not say how many shots were used to produce the averages at each distance -- if there are few sand and recovery shots from these distances, statistical noise may bias the results. Nevertheless, the data suggest that when it comes to sand and recovery shots, intermediate distances are particularly penal.

Apart from these broad insights, we want to to determine a way to use the data to quantify the relative value of distance vs. accuracy. To begin, let's consider just the difference in average scores between the fairway and rough:

One approach to determining the value of distance is to consider how much further back a ball could be in the fairway to have the same average score as a ball in the rough. This case is plotted in the figure below. 

Equivalent positions in fairway and rough

The horizontal axis representation the distance a ball in the rough is from the hole, while the vertical axis represents how much further back in the fairway a ball would have to be to have the same expected score. Close to the green, there is little difference between being in the fairway or the rough, but the difference increases as the distance from the hole increases, to the point where a ball in the 60 yards from the hole in the rough has the same expected score as a ball 140 yards from the hole in the fairway -- 80 yards difference! From this point the difference between rough and fairway decreases, reaching a minimum where a ball in the rough around 250 yards from the hole in the rough is equivalent to a ball 30 yards back in the fairway. From here the difference between the fairway and rough gradually grows, with a small spike when the ball in the rough is about 300 yards from the hole (my suspicion is this is near the edge of a pro's range for hitting a par 5 in two, so being in the rough may force a layup).

The chart above indicates that outside short game shots, a pro needs to be 30 to 80 yards longer off the tee for a shot in the rough to be better than being farther back in the fairway. However, this analysis does not tell the whole story! Even if hitting longer tee shots costs a player accuracy, he probably will not miss every fairway, nor would the shorter tee shot always find the fairway. To properly consider the value of distance relative to accuracy, we must consider the probability that the short shot or long shot hits the fairway.

The contour plot below properly incorporates the probability of hitting the fairway. In this plot, the vertical axis represents the distance from the rough, the horizontal axis represents the probability of hitting the fairway, and the color represents the expected score for the distance/fairway probability combination.

Expected score fairway rough. The black lines represent paths of constant expected score and better answer the distance vs accuracy question. If distance gains correspond to accuracy losses such that a player moves along a black line, the gains and losses perfectly cancel. Changes in distance and accuracy that move a player from above to below a line will lead to lower scores. The largest changes in expected score occur if a player moves perpendicular to the black lines.

To condense this plot into specific numbers, a 10 yard increase in distance off the tee is worth roughly 12 to 33 percentage points in lost fairway accuracy, depending on the length of the approach shot. Greater distance gains or smaller accuracy losses are worthwhile; smaller gains or greater accuracy losses will lead to higher scores. Distance gains are most valuable when the they allow a player to get very close to the green -- next best are those in the 250 yard range. This makes sense: getting to hit a pitch or chip around the green is worth losing some accuracy, while long approaches are not very accurate from the fairway or from the rough, making the fairway less valuable. Conversely, accuracy is most valuable for roughly 50 to 150 yard approaches. This also makes sense: it is the range where a pro is looking to be aggressive, and the ability to control spin from the fairway can lead to short birdie putts. Even where accuracy is most significant, however, the value of added distance is still significant. On a standard par 72 course, a 12 percentage point reduction in fairway accuracy translates to a little less than 2 fairways per round, indicating that in the worst case scenario gaining 10 yards is worth being in the rough off the tee 1-2 more times per round.

While the contour plot and analysis above does a much better job of evaluating the trade-offs between distance and accuracy off the tee, they are still incomplete because they assume that a missed fairway only leads to shots from the rough, as if no bunkers, trees, or other obstacles exist. Ideally we would incorporate not just the probability of hitting the fairway, but also the probability of hitting the sand off the tee and the probability of needing to hit a recovery shot. While we could add these variables, deriving insight would be much more complicated, conclusions will be course-dependent, and visualizing the results would be much more difficult. Instead, we will consider two extreme cases below to help understand how sand and recovery shots change the analysis.

First, suppose the hole being played is one where all tee shots that miss the fairway end up in sand (perhaps a penal desert course). We can generate a contour plot similar to the fairway-rough comparison above:

Expected score fairway sand

For distances greater than 180 yards, the plot looks very similar, except that fairway accuracy is more valuable. Above 180 yards, 10 yards of distance is worth only 10-20 percentage points in lost accuracy. Additionally, we see distance gains that allow a player to get close to the greens are quite valuable almost regardless of loss of accuracy.

The situation looks quite different from 50-150 yards. In this range, accuracy is much more important than when the penalty was simply rough. Distance gains become even less important as fairway accuracy decreases, to the point where we see no scoring gains in distance if the fairway accuracy is very low. This point makes sense when considering the scoring average from sand curve in the first figure: in this range, being closer to the hole does not improve scoring average much, and may even make things worse. While it is unlikely to find a scenario where all misses find the sand, it is worth noting that when the landing area is 100 yards from the hole and surrounded by bunkers, laying back may be especially worthwhile.

Finally, let's consider a scenario where the hole being played is one where all tee shots that miss the fairway require a recovery shot (perhaps a very tree-lined course, or old-school U.S. Open rough, or Augusta National before the second cut was added). The contour plot for this scenario is shown below:

Expected score fairway recovery

This plot looks like an extreme version of the Fairway vs. Sand plot. Above 200 yards, the contours are linear but with a steeper slope, indicating 10 yards of distance are worth only 7-8 percentage points in lost accuracy. At closer distances, though, accuracy becomes extremely important. This should be expected -- from less than 200 yards in the fairway, a pro will hit a lot of greens in regulation, so a recovery shot is a costly penalty. As with the sand comparison, if the fairway accuracy is low, we see few gains from distance. Even in the best scenarios in this range (when the fairway accuracy is high), 10 yards of distance is only worth about 2 percentage points of accuracy (about 1 fairway every 3-4 rounds). It is also worth noting that unlike the rough and sand cases, there is no instance where being able to get close to the hole off the tee becomes more valuable than accuracy. This makes sense too -- being close to the green isn't helpful if it requires a sideways shot.

Summary

The results above provide some insight into whether distance or accuracy is more important. While the likelihood of being in the fairway, rough, sand, or deeper trouble will vary from hole to hole, we can see some general trends from the analysis above:

• For long approaches and beyond, distance gains are particularly valuable. Even in the Fairway vs. Recovery analysis, 10 yards of distance were worth hitting 1 fewer fairway per round.
• Distance gains that get a player around the green are worth almost any accuracy loss that does not need a recovery shot. The opportunity to hit a short game shot is only not worth it if that shot cannot hit the green.
• Accuracy off the tee is most important for short iron and wedge approaches, but even there distance gains can be valuable. If the penalty for missing the fairway is sand or worse and the chance of hitting the fairway is low, laying back may be worthwhile. If the penalty is only rough, however, an extra 10 yards is worth missing an extra fairway or two per round.

This analysis does not just apply to tee shots; it can also be used to determine what to do on a second shot on a par 5. In general, getting around the green is always worth it so long as a recovery shot is not needed, whereas laying back with a more accurate club may be worth it when the closest you can get is still more than 50 yards from the green -- especially when the landing area is surrounded by sand or worse. 

It is important to highlight a few caveats for this analysis. First, as noted at the top, the data used here is from the PGA Tour; it may not apply to average or even highly skilled amateur players. In particular, the difference between fairway and rough performance for amateurs may be less than on tour, given how well tour players utilize spin from the fairway (and use new, clean wedges). However, the insights drawn from the analysis provide a logical starting point for amateur analysis (for example: distance gains are more significant when the approach shots are too long to be very precise even from the fairway). An amateur interested in performing a similar analysis should begin tracking scores from various distances and lies.

Second, these results are for the average PGA tour player, and the data do not indicate how much variation exists at each distance. A very good bunker player may have a significantly different curve than a great wedge player. Similarly, the number of shots considered from each position is not reported, leading to random biases in the reported data.

Additionally, the data used here are from 2003-2010, and technology and rule changes in the last decade could change the calculus. On the one hand, drivers have become more forgiving, suggesting distance has become more valuable. On the other hand, the majority of this data set came before the USGA banned square grooves, suggesting there may be bigger difference between fairway and rough performance today.

Finally, this analysis does not incorporate how much effort is required to achieve distance or accuracy gains. A player who has nearly maxed out his distance or accuracy ability may make faster gains elsewhere, regardless of what the charts say is the best improvement route.

Nevertheless, we see that in most cases distance gains are more valuable than accuracy gains. Swing away!