Tournament Previews
Aug 4, 2020
Which tournaments separate players based on skill?
While the main takeaways of this post are still relevant, it does suggest player adjustments relating to the 2020 PGA Championship field. Due to field changes and fluctuating players skills, the adjustments won't apply to future PGA Championships.
An oft-debated topic in the golf (nerd) community is the degree to which different course setups separate the game’s best golfers. A wider spread in scores on the leaderboard could be the result of three distinct causes: 1) larger differences in skill amongst the golfers competing; 2) larger differences in scores between high and low-skilled golfers; and 3) greater variation in scores that is not related to skill (i.e. ‘random’ variation). The first item in this list is not interesting as it has nothing to do with the course setup; all else equal, scores at the TOUR Championship will be more tightly bunched simply because the golfers competing there are closer in skill than at a typical event. The focus in this article will be on the final two points; more specifically, we analyze the degree to which each course on the PGA Tour separates golfers, and why the PGA Championship has historically been an outlier in this regard.

To make headway on this question, let’s think of golf scores as being composed of two parts: skill and luck, where luck is a catch-all term used to describe everything not related to skill. For example, if Justin Thomas played 100 rounds against an average PGA Tour player at a randomly selected course, we would expect Thomas to win, on average, by 2.3 strokes per round. That is, according to our estimates, Thomas’ skill level is 2.3 strokes above that of an average professional. We would also expect Thomas’ 100 scores to have a standard deviation of approximately 2.8 strokes per round. (Recall that standard deviation is a measure of dispersion; given a standard deviation of 2.8, we would expect roughly 68 of JT’s 100 rounds to be within 2.8 shots of his average score — so, if Thomas shot 70 on average, something around 70-75% of rounds would be between 67 and 73.)

At courses where Thomas beats an average PGA Tour player by more than 2.3 strokes per round, we would say that this course creates separation based on skill; at courses where Thomas’ scores have a standard deviation of greater than 2.8 we would say this course creates separation based on luck. It’s worth emphasizing again that ‘luck’ does not only refer to strange bounces off of trees or random gusts of wind, but rather any variation in scores that is not correlated with our estimates of golfer skill.

For this analysis we use data from 2004-onwards; because three of the four major championships are played at different venues each year, we group each of the sets of courses for the U.S. Open, British Open, and PGA Championship together. A golfer’s skill is determined by equally weighting their performances across all courses within the appropriate time frame (i.e. 1-2 years before the event). Due to the nature of our skill estimates, if golfer A has a skill level that is 1 stroke better than golfer B, golfer A will on average beat golfer B by 1 stroke per round. However this average hides interesting, and potentially useful, variation. Continuing with our Justin Thomas example from above, it might be the case that across all courses Thomas is 2.3 shots better than the average player, but at some courses that number is closer to 2.1 while at others it’s closer to 2.5. This is what the value in the first column below indicates: how much a 1 stroke difference in skill is worth at each of the listed tournaments / courses. The second column refers to the random component of scores: at which tournaments do we see the most variation in scores after controlling for differences in skill? (For statheads, we are accounting for the course-specific skill differences of column 1 when analyzing this random variation). We have added a few notable courses in addition to the 4 major championships.

Which courses/events separate players the most?
One obvious way that the first two columns are related is through the par of the course. All else equal, a par-72 course will have higher values for both the multiplier and the standard deviation columns; the more shots that are hit, the greater the separation we will see both in terms of skill and luck. However there is a lot more than just this going on: for example, PGA National is a par-70 course that has above-average random variance. The final column in the table displays the win probability for a top player (think Justin Thomas) at each of the listed courses, holding the quality of field constant. This combines the information contained in the previous two columns. At Augusta National, for example, we expect more skilled players to beat less skilled players by slightly more strokes per round than at the typical course (column 1); however, Augusta National is also a course with higher random variance than average (column 2). The former would tend to increase JT’s win probability, while the latter would tend to decrease it. Overall, we see that the top player’s win probability is slightly higher at Augusta National than at an average course. At courses that have hosted PGA Championships since 2004, we estimate the highest degree of separation based on skill of any course on the PGA Tour; however these courses have also shown above-average random variation, which allowed Firestone CC to take the top spot in terms of where a top player has the largest win probability advantage.

An important point to note here is that our definition of skill is only meaningful as it relates to the types of courses played on the PGA Tour. For example, if most courses on tour disproportionately reward distance, then the 'high-skilled' golfers will tend to be those that hit it far. Consequently, if there is a course that disproportionately favours driving accuracy, this might show up in our analysis as one that does not reward skill (because the better golfers are those that hit it far but not accurately, so they will perform worse at this course). However, we don’t need to just speculate on that thought, we can gain some insight into it from our course fit plots. For example, from the table above we see that Waialae is a course that narrows skill gaps; from its course fit plot, we see that this is because Waialae gives a below-average reward to nearly every skill you could care about. Below we have produced our course fit plots for the 4 major championships:

"Event Fit" at Major Championships
PGA ChampionshipPGA
U.S. Open
The Masters
Open ChampionshipThe Open
Radar Plot: PGA Championship
Plot Info
Average PGA TOUR Course
PGA Championship

Toggling through each event offers several interesting takeaways regarding the types of players who benefit from each major championship setup, but let’s stick with this week’s event, the PGA Championship. Every skill except for 'around-the-green' is favoured relative to the average PGA Tour course. (This is consistent with the 1.08 skill multiplier we saw in the first table.) Intuitively this makes sense, as PGA Championships are traditionally set up similar to regular tour stops, but the courses are typically longer and have thicker rough. It seems reasonable that these heightened, but still familiar, conditions would amplify the skill gaps we observe week-to-week on tour.

Looking a bit closer at the plot we see that driving distance, which is already the most important skill at the average course, is a disproportionately favoured one at PGA Championship setups. This has been a criticism from the architecture community about past PGAs; they believe that driving distance has become an overemphasized skill in professional golf. While we tend to believe that the reward for driving distance relative to other skills is reasonable, the argument that it has become too important does seem to hold more weight in weeks like this. Moving away from the data for a moment, we can recall watching the PGA Championship at Bethpage Black last year, and it was apparent that a player like Kevin Kisner would have to putt the lights out to compete with the likes of Koepka, DJ, or McIlroy, simply due to his lack of distance and power.

The conclusions from the above discussions make the direction of our event/course fit adjustments pretty straightforward for this week: good players will get positive bumps, bad players will get negative bumps, and average players won’t receive much adjustment either way. Longer players will receive additional positive bumps, but long players are typically 'good' players, so this shouldn’t alter things too much.

The next issue is one that is rarely addressed — how do these intuitive judgements actually translate into strokes per round adjustments to each player's expected performance? Lucky for you we provide a detailed breakdown of our predictions each week on our skill decomposition page; here are the five largest positive and negative course fit adjustments this week (excluding Club Professionals):

Top 5 Positive Adjustments:
1: Justin Thomas (+0.25)
2: Rory McIlroy (+0.23)
3: Brooks Koepka (+0.22)
4: Cameron Champ (+0.22)
5: Tony Finau (+0.20)
Top 5 Negative Adjustments:
1: Shaun Micheel (-0.26)
2: Brian Stuard (-0.18)
3: Brendon Todd (-0.18)
4: Steve Stricker (-0.18)
5: Jim Herman (-0.16)

A final interesting thing to consider is whether players who are only slightly above average benefit from playing a course that amplifies skill differences. On the one hand, their skill at this course will be further above average; on the other hand, the skill of the top players will move further above theirs. By looking at our finish probabilities for this week’s PGA Championship from both our baseline model (which assumes an average course setup) and our full model (which includes course-specific adjustments), it can be seen that it is only the top 10 or so golfers who see an increase in their win probability. However, as intuition would suggest, while golfers who are a bit further down in the skill distribution don’t see their win probabilities increase, they do see their Top 20 and cut probabilities increase under the model that takes account of this week's course.

To wrap up, we’ll point out two names where these adjustments have made a difference this week: using the full model we are finding a bit of value on Rory McIlroy, and a large edge on Hideki Matsuyama, in this week’s outright markets. That’s all for this preview, enjoy the first major of 2020!