Dr. Kupper is Emeritus Alumni and distinguished Professor of Biostatistics School of Public Health, University of North Carolina at Chapel Hill. His research interests included the development and application of Statistical Methods for public health studies, particularly environmental, occupational, and women's health and quantifying health risks from exposure to environmental and workplace hazards.
Episode Description
Rory McIlroy was leading the 2025 U.S. Masters golf tournament by two strokes after three rounds. So was his ultimate victory a sure thing? How predictive is a lead after three rounds of a golf tournament for victory after the 4th round? In today's episode of stats and stories, we hit the links to explore outcomes in professional golf tournaments, along with addressing whether golf handicaps make for fair comparisons between golfers with guest Dr. Lawrence L. Kupper.
+Full Transcript
John Bailer: Rory McIlroy was leading the 2025 U.S. Masters Golf Tournament by two strokes after three rounds. Was his ultimate victory a sure thing? How predictive is a lead after three rounds of a golf tournament for winning after the fourth round? In today's episode of Stats and Stories, we hit the links to explore outcomes in professional golf tournaments and also address whether golf handicaps make for fair comparisons between golfers. I'm John Bailer. Stats and Stories is a production of the American Statistical Association as well as Miami University's Departments of Statistics and Media, Journalism, and Film. I'm joined in the studio by Rosemary Pennington from the Department of Media, Journalism and Film.
Our guest today is Dr. Lawrence Kupper, Emeritus Alumni Distinguished Professor of Biostatistics at the School of Public Health at the University of North Carolina in Chapel Hill. His research interests include the development and application of statistical methods for public health studies, particularly environmental, occupational, and women's health, and quantifying health risks from exposure to environmental and workplace hazards. He was also an impactful teacher and mentor, as I can personally attest.
I met Larry in the early '80s when I was a student in a master's statistical theory class he was teaching. He encouraged me to pursue a PhD in biostatistics, supported my studies through an NIH training grant, and served on my dissertation committee. It's such a pleasure to have you back here, Larry. It's great to talk with you. In today's program, we’re going to talk to Larry about one of his other passions—golf. He's an avid golfer and has viewed his passion for golf through the lens of statistics. In a recent article in Significance magazine, "Predicting Victory in Golf," and in a 2001 CHANCE article titled, "Is the USGA Golf Handicap System Equitable?"—Larry, it's a delight again to welcome you to the podcast.
Larry Kupper: Thank you so much. It's an honor to be here.
John Bailer: Let’s start with a description—what’s the structure of a four-round golf tournament?
Larry Kupper: Well, typically, the majors consist of four rounds. The first round is Thursday: 18 holes. Friday: 18 holes. Saturday: 18 holes. And the final round is Sunday: 18 holes. You add up the total strokes for 72 holes, including penalty strokes, and you end up with a final score. The player with the lowest total after 72 holes wins. If there’s a tie, there's a playoff. Nowadays, playoffs are either sudden death until someone wins, or a three-hole playoff. That’s how it works now.
Rosemary Pennington: What made you decide to do this study—looking at whether having a lead at the end of the third round could predict winning the tournament?
Larry Kupper: I started playing golf when I was a junior in college, and I got really hooked—thanks to Arnold Palmer, my all-time favorite golfer. I’ve watched the majors every year since 1960, and I’ve always wondered what happens when someone has a lead after three rounds. I’ve played in a lot of tournaments myself—and I’ve choked more than once. Golf is a very frustrating sport because there’s no defense. The ball sits there quietly; it’s just you, a club, and the hole—and it’s all between your ears. I wanted to know what it takes to hold a lead in a major golf tournament, for both men and women. That’s why I was really interested in doing this study—with my wife, Sandy Martin.
John Bailer: Can you tell us a little about the dataset you used?
Larry Kupper: We looked at 25 years of golf data, from 2000 through 2024. We chose that era because we considered it the modern era of golf, with better equipment and many more elite players capable of winning. Players are now driving the ball 50 to 75 yards farther than they were in the ’70s and ’80s. We looked at four men’s majors—Masters, PGA, U.S. Open, and British Open—and four women’s majors—Chevron, PGA, U.S. Open, and British Open. We used Wikipedia and other golf-related websites to gather the data.
Rosemary Pennington: I’m going to admit—I don’t play or really understand golf as a sport. So why focus on a player’s standing after the third round rather than, say, the first?
Larry Kupper: Because most of the pressure comes in the final round. Usually, several people are in or near the lead by then, and I’ve always been curious about how players handle that pressure. That’s when most people tune in—Sunday’s round—so that’s where the drama is.
John Bailer: I looked at some of the top 15 scores from the last Masters. Rory McIlroy had a two-stroke lead after three rounds. But the person two strokes behind him fell to a tie for fifth place. That last round pressure really showed.
Larry Kupper: Oh yeah. If you watched the 2025 Masters, there was incredible pressure on Rory. He had tried 17 years to win the Masters. In 2008, he had a four-stroke lead and shot 80 in the final round. But this time, it was probably one of the most exciting final rounds I’ve ever seen. The lead changed back and forth—Rory was ahead, then behind, then ahead again. He missed a short putt on 18 to force a playoff with Justin Rose, then won in the playoff. Sandy and I were thrilled—Rory’s always been our favorite golfer.
John Bailer: You looked at the likelihood of winning based on lead size, and I was surprised how often a four-stroke lead didn’t hold up. I think in the British Open, it was just two out of five.
Larry Kupper: Yes, some results made sense. The bigger the lead, the better your chance of winning—it’s a statistically monotonic relationship. One-, two-, three-, four-, five or more-stroke leads—the more strokes, the better your odds. But bigger leads are also rarer. So while the pattern held, the data showed how often even strong leads evaporate.
Rosemary Pennington: So what did you find that was unexpected?
Larry Kupper: Sandy and I were curious which majors were hardest to hold a lead in. For men, if you had at least a one-stroke lead after three rounds, it was hardest to hold that lead in the U.S. Open and British Open—harder than in the Masters or PGA. I think it’s because winning a title representing your country adds pressure. For women, it was hardest to hold the lead in the Chevron and U.S. Open. But the U.S. Open stood out for both—only about 34% of leaders held on to win. That consistency surprised me.
John Bailer: I was also thinking about how the psychology of a one-shot lead might feel like a tie. If you’re only ahead by one, it doesn’t feel secure. Are there patterns in player performance related to this?
Larry Kupper: Absolutely. Even with a two-shot lead, there are no guarantees. Another interesting finding: across all majors, men and women with at least a one-shot lead won only about 43% of the time. That was surprisingly consistent. The U.S. Open remained the toughest to win from the lead.
John Bailer: Did you come across examples of players leading from start to finish—after round one, two, three, and four?
Larry Kupper: Not in our dataset. But I can tell you—I’ve seen some painful final-round collapses.
John Bailer: We’re talking with Larry Kupper about golf. Larry, to change gears a bit—I was surprised by the complexity behind defining a golf handicap? Can you explain how it’s constructed and used?
Larry Kupper: Yes, I can. The paper we wrote in 2001 got quite a bit of attention, even featured in Newsweek. A short article titled "Why You Lose" explained that high-handicap golfers don’t get enough strokes when playing against better players. The U.S. Golf Association didn’t acknowledge any issue.
Here’s how the handicap system works: Typically, golfers post about 20 scores. Let’s say I shoot an 84 at the UNC golf course—I write that down. After 20 scores, the club submits them monthly to the USGA, which calculates a Handicap Index.
Each score is adjusted for course rating and slope rating. The course rating reflects what a scratch golfer would shoot—say, 72.2. The slope rating indicates difficulty for an average golfer—113 is standard. Easier courses have lower slope ratings, harder ones higher.
You use those values to calculate a handicap differential for each score. Then you take the lowest 10 of your last 20 differentials—or the lowest 8 now—and average them. That’s your Handicap Index. For example, if mine is 15.5, and I’m playing someone in a tournament, the club converts that to a number of strokes—let’s say I get 12. My net score is my gross score minus 12. That’s how it works.
Rosemary Pennington: What are handicaps used for?
Larry Kupper: To make matches more equitable. In our paper, we used fictional players: Steady Eddie (low handicap) and Wild Willie (high handicap). Let’s say Eddie shoots 80 with a 6-stroke handicap—his net is 74. Willie shoots 90 with a 17-stroke handicap—net is 73. Willie wins. In theory, they should have an equal chance. But they don’t—because the system uses your best scores.
John Bailer: And that favors more consistent players?
Larry Kupper: Exactly. We found that Wild Willies are much more variable than Steady Eddies. Because the system uses your lowest scores, Wild Willies are penalized—their best scores are much lower than their typical ones. So Eddie can end up with a two-thirds chance of winning. The system favors consistency.
John Bailer: How did the USGA respond?
Larry Kupper: They still use the system. Their justification was: “There should a focus on potential.” But it’s not fair in medal (i.e., stroke) play.
One interesting twist: in large tournaments with many Wild Willies, one of them often has an exceptional round—and wins. So even if the system isn’t fair one-on-one, it can work out in large fields. That is why stratifying into flights is recommended.
John Bailer: When I looked at the 2025 Masters, I noticed the top two finishers had the highest round-to-round variability. That ability to recover after a bad round seems important.
Larry Kupper: Absolutely. That’s classic regression to the mean. If you shoot a 62, you’re likely to shoot worse next time. We all live with regression to the mean.
Rosemary Pennington: So now when you watch someone like Rory McIlroy go into the final round with a lead, how confident are you?
Larry Kupper: Depends on the lead. With a four- or five-shot lead, I feel pretty good. But with just one stroke? Not so much. Today’s fields are so deep—30 to 40 players could win any tournament. Back in the ’60s and ’70s, it was maybe five to eight real contenders. Now you have great golfers from all over the world—Britain, Scotland, Norway, Sweden, Spain, Japan—everywhere.
John Bailer: That’s all the time we have for this episode of Stats and Stories. Larry, thank you so much for joining us.
Larry Kupper: This has meant so much to me. It’s one of the highlights of my career.
John Bailer: Stats and Stories is a partnership between the American Statistical Association and Miami University's Departments of Statistics and Media, Journalism, and Film. You can listen to us on Spotify, Apple Podcasts, or wherever you get your podcasts. Share your thoughts by emailing statsstories@amstat.org, or visit statsandstories.net. Be sure to join us next time, when we explore the statistics behind the stories—and the stories behind the statistics.