After mental reboot, Harry Higgs starts strong in Bermuda

You hear the traditional wisdom all the time – it’s difficult to follow a great round of golf with another great round. While this notion is intuitively appealing, it could also be a product of confirmation bias: whenever a golfer plays poorly following a low round, golf analysts and observers are quick to use that wisdom as an explanation, thus confirming the theory. However, when a player goes low on consecutive rounds, it’s not used as evidence to discount the theory. As usual, the truth reveals itself in the data.  Using round-level data on the PGA TOUR from 2000-2016, we first calculate each player’s baseline relative-to-field scoring average on a 3-year rolling basis (this will be the measure of each player’s typical performance at any given point in time). Then, for each round played, we calculate the difference between a player’s relative-to-field score that day, and their baseline relative-to-field score; let’s refer to this as “personal strokes-gained.â€� Example: If Phil Mickelson typically beats the field by 1 shot, and then plays a round where he beats the field score by 4 shots, his personal strokes-gained would be 3. We want to look at the relationship between a player’s performance in a given round to his performance in the round that follows. For our purposes, we classify rounds into different “bins”; for instance, one bin is defined as the set of rounds where a player had a personal strokes gained of 8 or more. The other bins are defined similarly — rounds with personal strokes gained of 6-8 shots, 4-6 shots and so on down to -8 or worse shots. We’ll then assess the distribution of personal strokes gained depending on which bin a player’s previous round belonged to. Sticking with the Mickelson example, where we have assumed Phil typically beats the field by 1 shot, suppose he beats the field by 5 shots following a round when he beat the field by 4 shots? In the first of these two rounds, Phil’s personal strokes gained was 3 shots, so he enters the “2-4 shots” bin, and the object of interest to us is then how Phil plays in the next round (in this case above, he had a personal strokes gained of 4). We do this for all players and rounds and are able to obtain “conditional distributions” of personal strokes gained, where we are conditioning on how a player played in his previous round (as defined by the bins). In lay terms, we are simply looking at the personal strokes-gained of the set of players who all fell into the same bin in their previous round, and looking for any differences between these sets of players (ex: do those who had 2-4 personal strokes gained in their previous round play better than those who had 0-2 personal strokes-gained in their previous round?). To start, the average personal strokes-gained for each bin is shown below: A very clean relationship emerges; if you’ve played well in the previous round, it is more likely, on average, you will play well in the following round. The analogous statement holds for poor play. This is not all that surprising; it simply means that form, good or bad, tends to last more than a single round. Although, there clearly is a tendency to regress to the mean at work here as well. The next figure gives a better sense of the entire distribution of personal strokes-gained conditional on playing at a certain level in the previous round: The horizontal bar in each box is the median of the data, the upper and lower bounds of each box is the 75th percentile and 25th percentile respectively, and the ends of the lines are the maximum and minimum values excluding outliers (where an outlier is defined as 1.5* the 75th percentile, and 1.5* the 25th percentile). Note that the most extreme rounds are contained in the middle bins; this is expected as these bins contain by far the largest number of rounds, and consequently there is the greatest potential for an outlier to emerge. In this final figure we report a transition matrix, reporting the probability of moving from one bin to the next in consecutive rounds. There is a lot of interesting information here, so take a long look: To ensure you are interpreting this correctly, the top left box states the following: given a player’s personal strokes gained was 8 or better in their previous round, there is a 1.35 percent chance that their personal strokes-gained is negative 8 or worse in the next round. It is surprising to us how well-defined the relationship is between a player’s performance in one round to the next. For example, consider the column for bin (2-4); as you move from the bottom row to the top row we are looking at the set of players who played increasingly better in their previous round, and the probability of entering the (2-4) bin is increasing monotonically, just as expected. Finally, the answer to the initial question: there is no evidence supporting the claim that it is more difficult to follow up a great round with a good round. A big reason this claim makes sense intuitively is that it is simply very unlikely to shoot a really good round (say, 6 or more strokes better than usual). Therefore, it’s unlikely that an exceptional round will be followed by another exceptional round — but this is always the case irrespective of a player’s performance in the previous round. Brothers Matt and Will Courchene grew up in a Canadian household full of golf fanatics. In 2016, they launched a DataGolf blog in hopes of contributing fresh and unbiased insights to the sport. Matt, a PhD student at the Vancouver School of Economics, focuses on applied econometrics and causal inference, while Will, who has a Masters of Economics from the University of Toronto, focuses on statistical modeling and data visualization.

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Rickie Fowler, who lives minutes from PGA National Resort, returns to defend his title against a strong lineup with plenty of local firepower fronted by FedExCup champions Justin Thomas, Rory McIlroy and Tiger Woods. Masters champion Sergio Garcia arrives to make his first U.S. start of 2018, as will a trio of other top Europe-based professionals. Woods was a late entry, committing to his first back-to-back starts since undergoing spinal fusion surgery last April. FIELD NOTES: Thailand’s Kiradech Aphibarnrat, winner of the World Super 6 Perth earlier this month, makes PGA National his first U.S. start since the 2016 Web.com Tour Finals. Also coming across for their first U.S. appearance of the year are England’s Tyrrell Hatton and Austria’s Bernd Wiesberger. … In all, PGA National is slated to welcome 10 of the top 25 in the current world rankings. … FedExCup leader Patton Kizzire is one of four commitments among the top 10 in the PGA TOUR’s season points race. … Fowler, Thomas and Woods are among at least 14 Honda entrants who keep a home within 45 minutes of PGA National. FEDEXCUP: Winner receives 500 points. STORYLINES: Fowler, who owns six top-4 finishes on TOUR since his four-shot romp a year ago, hopes getting back to home base will break the hex. He also led after 54 holes in Phoenix, but a closing 73 dropped him out of the top 10. … A Fowler victory would make him just the second back-to-back winner in Honda annals, alongside Jack Nicklaus (1977-78). … Garcia arrives with a victory already on his ledger this year, winning in Singapore to start his schedule. He was second behind Adam Scott at the 2016 Honda. … Woods tees it up near his Jupiter Island home for the first time since 2014, when back spasms forced his withdrawal 13 holes into the final round. He was the 2012 runner-up behind McIlroy. … It’s the final chance for pros to get into next week’s WGC-Mexico Championship, with spots for anyone not previously qualified among the FedExCup top 10 or who moves into the world’s top 50. … Since PGA National became host in 2007, the “Bear Trap� trio of Nos. 15-17 has accounted for 18 percent of all bogeys in the event, 33 percent of all double bogeys and 38 percent of all triples or worse. COURSE: PGA National (Champion), 7,110 yards, par 70. Designed with major events in mind, the original George & Tom Fazio layout was site of the 1983 Ryder Cup where Lanny Wadkins’ birdie at No.18 vs. Jose Maria Canizares dashed European upset hopes. The original also was the backdrop for the 1987 PGA Championship, captured by Larry Nelson, before Jack Nicklaus was brought in for a 1990 redesign that introduced golfers to the perilous “Bear Trap� closing stretch. The course also staged 19 Senior PGA Championships through 2000, going on tournament hiatus until the Honda arrived in 2007. 72-HOLE RECORD: 264, Justin Leonard (2003 at Mirasol). PGA National record: 267, Camilo Villegas (2010). 18-HOLE RECORD: 61, Brian Harman (2nd round, 2012). LAST YEAR: Fowler ended a nearly 14-month victory drought with a four-shot win, pulling away with a Saturday 65 before enduring a roller-coaster final day. Fowler began a windblown Sunday with a four-shot advantage, which proved useful when he putted into a sprinkler hole on the way to bogey at No. 4 and found the water two holes later for double bogey. Gary Woodland’s birdie at No. 13 cut the margin to one before Fowler’s putter found the range. Fowler drained a 40-foot birdie at No. 12, then connected from 25 feet at the 13th. Another birdie at the par-3 16th gave him a five-shot cushion before a bogey/bogey finish left him with a 71. Woodland (69) also finished bogey/bogey to share runner-up honors with Morgan Hoffmann (68). HOW TO FOLLOW TELEVISION: Thursday-Friday, 3-6 p.m. ET (Golf Channel). Saturday-Sunday, 1-2:45 p.m. (GC); 3-6 p.m. (CBS). PGA TOUR LIVE: Thursday-Friday, 7 a.m.-3 p.m. ET (featured groups), 3-6 p.m. (featured holes). Saturday-Sunday, 9 a.m.-6 p.m. (featured holes). RADIO: Thursday-Friday, noon-6 p.m. Saturday-Sunday, 1-6 p.m. (PGA TOUR Radio on SiriusXM and PGATOUR.com).

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