The Luck of the Draw

Most people would agree that there is some luck involved in golf; a friendly kick off a tree, an untimely gust of wind, or one too many harsh lip outs can all affect a golfer’s score through no fault of their own. Despite the important role luck seems to play, it is, for the most part, hard to quantify.

In this article, we examine one component of luck on the PGA TOUR that is easily quantifiable: the differing course conditions between the morning and afternoon draws of a tournament. This allows us to make statements about who the luckiest, and unluckiest, players were on TOUR last year (with respect to the draws they received).

In most professional events, tee times on the first 2 days are put into a morning wave and an afternoon wave, usually separated by a couple of hours. If you are in the morning wave on the first day you will be in the afternoon wave on the second day, and vice versa. The same golf course can play drastically different at different times of the day; look no further than last year’s British Open for evidence of this (more on this later). This sometimes results in players being on the “wrong side of the draw”, and having to play a substantially harder course than half of the field. We analyzed 32 events on the PGA TOUR in 2016 to determine how much of an impact the draw has on the results of a tournament. (Only 32 events make our sample because some limited field events do not have a clear morning/afternoon distinction).

This first graph shows the biggest differences in (skill-adjusted) scoring averages between the morning and afternoon waves over the first 2 rounds in our sample of tournaments.

To understand the graph, consider the Open Championship in 2016. Over the first two rounds, the Thursday morning wave (i.e. playing round 1 in morning, round 2 in afternoon) played a course that was about 6 strokes harder than the average course in rounds 1&2 in 2016. The Thursday afternoon wave played a course that was only 2 strokes harder, resulting in a 4 stroke advantage over the first 2 days for the latter group. The winner was Henrik Stenson, who played in the Thursday afternoon wave, as denoted by the blue asterisk.

It’s worth noting that Jordan Spieth overcame the largest disadvantage due to the draw over the first two days; he won the DEAN & DELUCA Invitational from the Thursday afternoon wave despite playing a course that was more than 3 strokes harder than that faced by players in the Thursday morning wave.

Next, we determine how much certain players gained or lost over the year due to their series of draws throughout the season. The method is simple; we calculate each player’s strokes-gained relative to the field, and compare that to his strokes-gained relative to his tee-time wave (i.e. morning or afternoon). If a player gains more strokes over the field than he does over his wave throughout the year, than this means he was, on average, on the better side of the draw throughout the year. Clearly, as the number of events gets large, we would expect players’ strokes-gained over the field to be very close to his strokes-gained over their wave (as there should be no players systematically getting good or bad draws). Here are the numbers for 2016:

Let’s do a back-of-the-envelope calculation to evaluate the importance of these differences. In 2016, the relationship between a player’s strokes-gained average for the year, and his end-of-season FedEx Cup rank (before Playoffs start) is as follows: a 0.1 increase in strokes-gained per round is expected to result in approximately a 5-6 position increase in FedEx Cup rank. From the graph above, Louis Oosthuizen had the unluckiest draws throughout 2016; he lost 0.34 strokes per round over the first 2 days of tournaments due to his draw. Because golf tournaments are 4 rounds, the effect on Louis’ strokes-gained average for the year is (roughly) 0.34/2 = 0.17 strokes per round. Conversely, the luckiest player in 2016 was Zach Johnson, whose overall strokes-gained average was increased by 0.24/2=0.12 strokes per round by his series of tee time draws. Taken together, if Louis had been the luckiest player, instead of the unluckiest, he would have had a 0.3 stroke higher strokes-gained average for the year, which should roughly translate to an increase in FedEx Cup rank of about 15-18 positions (given that Louis was of mid-pack rank).

While most differences between players in their luck due to the draw are quite small, it was still the case that some players got dealt a bad hand. If we ever hear Louis complaining about his bad luck, we may be inclined to listen!



What’s wrong with Rory?

Rory McIlroy missed his second cut in a row this week at the Scottish Open. A flurry of news articles and social media posts are likely to follow in the next couple days wondering what’s wrong with Rory. “Where has the lad’s game gone?!” cries a devoted Rory fan — “You can cross him off the list of potential contenders next week.”  tweets a Golf Channel pundit — “It’s simple, really. The deadlifts have finally done him in; this is causing Rory to slump a bit through impact, losing the angle, missing right.” analyzes Brandel.

In my opinion, however, there is nothing wrong with Rory. My argument is simple: golf scores are really random. Below is a density plot of Rory’s scores over the last 2 years.

This is how I like to think of a golfer’s performance; Rory’s score each day (no matter what course he’s on!) is a draw from the above distribution which has mean 2.3, and standard deviation 2.7. Better golfers will have distributions with higher means, and more consistent golfers will have distributions with smaller standard deviations. So, when Rory shoots 2 shots worse than the field, I don’t panic; this isn’t that unlikely (it should happen about 6% of the time).

So, back to Rory’s MC-MC performance over the last 2 weeks. How often should that happen for a player of Rory’s caliber? Well, my sample of data contains the last 2 years, in which Rory played 38 events (I think). I simulate these 38 events 10,000 times (doing exactly what I said above; each round is a draw from the above distribution). I deem Rory to have missed a cut if the sum of his first 2 rounds is less than 0 (so he lost to the field, which should, roughly speaking, result in a missed cut). In 35% of the simulations, Rory had back-to-back MCs at some point in the 38 event sequence.

This is Rory’s first stretch of consecutive missed cuts since May 2015. So, in the 2 year sample I’ve considered, Rory has missed back-to-back cuts on exactly one occasion. This is not unexpected at all, given our simulation exercise above.

Humans love to find patterns in small stretches of data when really there are none. Rory’s poor performance of late is not inconsistent with him still being the same player he’s been for the last few years. That is, he may still be pulling from the same distribution, with mean ~2.3 and sd ~2.7; maybe Rory just had a couple bad draws the last 2 weeks.

Or, maybe he has actually lost it (his putting does look awful). The point is that these last 2 weeks don’t tell us very much about which opinion is the correct one.