How Much Deeper Has Golf Become In The Last 25 Years?

This question is one that is very relevant for a variety of reasons. However, the reason I wish to explore this question is to help aid golf fans (and analysts) who wish to compare achievements across generations of professional golf. It is not uncommon to see people carelessly compare golfers between generations by simply looking
at number of wins.

A typical analysis is the following:
Jack has 18 majors, Tiger has 14, therefore Jack is the best golfer of all time.
Needless to say…this kind of talk needs to end.

In order to investigate if/how much golf is getting deeper, we need to come up with a few different ways of measuring “depth” in golf. Note that these measures cannot be related to changes in actual skill level over time, just the relative dispersion of skill level over time.

MEASURE 1:
Difference between CUT LINE and LEADERS after 36 Holes

If golf is getting deeper, one would think that the number of shots between 36 hole leader and the cut line would be smaller than it used to be (since competition should be stronger). Below is a plot of the averaged number of shots separating the leader and the cutline for each year since 1983.

Screen Shot 2016-08-13 at 2.16.59 PM

Of course, we do see the separation decreasing over time, but not by much.In 2015-16, the cut is on average 1 shot closer to the lead after 36 holes than it was back in 1983. So there is some bunching, but not as much as we would expect to see.

Perhaps it makes more sense to look at the distance between 5th place and the cut line. This way, we don’t have individuals who are leading the field by 4-5 shots through 36 holes skewing the data upwards. Below is the same plot, but showing the difference between 5th and the cut line.

Screen Shot 2016-08-13 at 2.16.31 PM

Again we see the downward trend indicating more bunched leaderboards heading into the weekend. Not a very large difference between the early data and the more recent years (only a  bit less than a shot).

So, while we do see that leaderboards are more bunched since 1983, the trend is much weaker than we expected.

MEASURE 2:
Number of Players with AT LEAST One Top 10 Finish Per Year:

If golf has been getting deeper, we would expect to see more and more players contending over the course of the year. If more players register a top 10 each year, it just simply means that the pie of pro golf is being split into thinner and thinner slices. It would also suggest that the “anyone can win” rhetoric we hear from players has truth to it. Below is the plot that tracks unique top 10 finishers per year since 1983:

Screen Shot 2016-08-13 at 3.00.58 PM

We can see that there has been a steady upward trend in the data. More and more players each year are entering the conversation by registering at least one top 10. In 1984, there were 138, the number of players with a top 10 in 2010 was 195, an increase of 41%.

To put it simply, there are just more cooks in the kitchen now than there used to be, and that is going to make it harder to do anything, whether it be making the cut or trying to win.

MEASURE 3:
Variance of Scoring Averages

This last measure is pretty simple, I am simply looking at how variable the scoring averages are by year. The more variance there is, the wider the range of talent on tour that year. So as variance goes to zero, we approach all players having the same scoring average. If the PGA Tour is getting deeper, we should see scoring average variances falling over time. The plot is shown below, and only players who played at least 20 rounds that year are included in the calculation.

Screen Shot 2016-08-13 at 4.06.47 PM

Here is proof that the talent level on Tour is really bunching up. In the 80’s, the variance of scoring averages was much higher than it is now, and it is decreasing very steadily. Variance is pretty much half of what it used to be. What this means is that the relatively good players aren’t as good anymore, and the relatively bad players aren’t as bad.


So what have we learned here?

Basically, there are 3 measures of PGA Tour depth analyzed above. All 3 show that the Tour is becoming deeper, and it does not appear that this trend is stopping.

To me, this means that given you are on the PGA Tour in 2016, you are going to have a much harder time making cuts and contending than if you played on tour in the early 80’s, due to the bunching of talent.

So next time you want to compare Jack to Tiger (or even Tiger to Rory/Jordan/Jason), remember that as time moves forward, it is getting harder and harder to win. Jack had to worry about a lot fewer legitimate players than Tiger, who had to worry about fewer legitimate players than Rory.

To hammer this point home, if this trend continues, the 2060 Player Of The Year might only have a win or two, instead of 4 – 5 that we see today, because everyone will be so good.

Please keep this all in mind when you are having GOAT conversations, in any sport.

Distance-Adjusted Driving Accuracy

Generally speaking, the further you hit the ball, the further off line you can hit it. A 300 yard shot that starts off 1 degree to the right will end up more distance from the target line than a 200 yard shot that starts off 1 degree right, all else equal. It is this basic notion that I am going to apply today to create a distance-adjusted measure of accuracy off the tee. Consider the following diagram:

diagram

This diagram is drawn for a player with an average driving distance of more than 300 yards. The hypotenuse is the average driving distance of the player, and the horizontal line is his average distance from the center. Using basic trigonometry, I can obtain the angle “a”; the angle between a player’s average driving distance and their average distance from the center. Using that angle I can then calculate the distance of the line labelled “Adjusted Accuracy” – this will be the predicted number of yards from the center if the player’s average driving distance was 300 yards. So for players who hit it further than 300 yards, their Adjusted Accuracy will be less than their actual average distance from the center, while the converse is true for players who hit it shorter than 300 yards.

Clearly, I have made a big assumption here; I have assumed that average distance from the center is a linear function of the average driving distance. This is likely not true. However, for shots hit over 260 yards it may be a reasonable approximation. Also, notice that the slope is different for each player; it is determined by their average distance from the center and their average driving distance.

Note that choosing the normalized distance to be a 300 yard drive is irrelevant; what is going to determine the ranking of the players is the angle “a”. Once you have this, you can make the normalized distance any distance you would like. The absolute value of the Adjusted Accuracy measures will change, but the ranking of the players will be preserved.

I use 2015 Shot Link data to calculate player’s average distance from the center, and average driving distance, only using par 5 tee shots. I only want par 5 tee shots because I would like the players to be hitting drivers. To calculate the Adjusted Accuracy at 300 yards, I use the following formula:

Adjusted\_Accuracy = 300 \cdot [sin(90-(cos^{-1}(ADC/ADD))]

where ADC=Average Distance From Center, and ADD=Average Driving Distance. The unit used is yards.

The Adjusted Accuracy rankings for 2015 are shown below:

Screen Shot 2016-08-07 at 8.24.07 AM

Here, “Distance” is the average distance from the center, “Adj_Distance” is the Adjusted Accuracy using 300 yards as the normalization, and “Diff” is the difference between a player’s ranking in the unadjusted versus the adjusted accuracy measures. It can be seen that there is not much movement at the top, which surprised me a bit.

Next, these tables give the biggest movers up the adjusted rankings and the biggest movers down the adjusted rankings, respectively:

Screen Shot 2016-08-07 at 8.25.59 AM

Screen Shot 2016-08-07 at 8.24.52 AM

I honestly thought we might see Bubba move up even further, as I’ve always thought he drives it remarkably straight given his length. It can be seen that while the unadjusted and adjusted rankings are not drastically different, there is still a fair bit of movement between the two.

There are certainly other ways I could have tried to adjust for distance in measuring driving accuracy. However, this method is intuitive and computationally simple, which made it appealing. Leave a comment if you have thoughts on the usefulness of this statistic or ways through which it could be improved!