Preprint · Paper 4 in the series

How much a championship course moves when nothing changes.

Preprint v2.1, 20 October 2026. Not peer reviewed. Data and code are deposited and open, and the paper is citable. A further version is planned once the February 2027 AT&T Pro-Am and the June 2027 U.S. Open add observations on the altered Pebble Beach course.

Three championship courses host a professional field almost every year on the same eighteen holes: Augusta National at the Masters since 1934, Pebble Beach at the Crosby and the AT&T since 1947, and Riviera at the Los Angeles Open since 1929. Treating them as fixed instruments makes it possible to ask a question the rankings cannot: not which course is hardest, but how much one course's difficulty moves, when, and why.

This research was conducted independently and is posted as a preprint, with its data and code deposited. FogBow applies the same methods to member and resort courses.

Finding one: a fixed course moves about a stroke a year — and that figure belongs to the course, not to golf

Three courses, two months, two organizers.

0 0.25 0.5 0.75 1 Riviera L.A. Open · 1973–2023 0.85 Augusta National the Masters · 1983–2026 0.84 Pebble Beach AT&T, per course · 2004–2023 0.79

Two of the three can be tested for stability directly. In every fifteen-year window since 1948 at Augusta and since 1973 at Riviera, the standard deviation stays between 0.6 and 1.1. Pebble's February series is too short for that test.

What the third venue settles, and what it does not. It settles that the figure is not peculiar to Augusta: a course measured under a different organizer, in a different month, on a different coast, lands in the same place. It does not make a stroke a year a constant of golf, and the paper refuses that reading — across fifteen rotating major venues, amplitude runs from 0.06 strokes to 2.88, a forty-fold range. Amplitude is a property of a golf course. These three happen to share one.

A course does not have a difficulty. It has a distribution.

Finding two: the levers, ranked — and the biggest one belongs to the organizer

−2 −1 0 +1 +2 +3 Championship setup USGA U.S. Open · matched players +2.96 Wind per 10 mph of gust · Pebble +1.70 Temperature per 10°F colder · Augusta +0.72 Architecture Spyglass Hill vs Pebble +0.40 Championship setup PGA of America · Riviera 1983 −0.27 Limited, no-cut field five tour events, 2023–24 −0.85 Championship setup PGA of America · Riviera 1995 −1.24 Who is playing, and how signature era · Pebble, total −2.29

Amber is the organizer. The USGA's June setup at Pebble Beach is worth +2.96 strokes on matched players — the same golfers, the same holes, four months apart. Run the same test under a different organizer and the sign flips: the PGA of America's August championships at Riviera played at or below the tour's own February difficulty.

How much weight that carries. Not as much as a single sentence suggests. It rests on five championships, two organizers and three tours. The 1983 figure has a standard error of 0.32 and is not distinguishable from zero. The 1995 championship was played on greens re-sodded to bentgrass that summer, soft and shallow-rooted — a documented cause beyond setup. The direction is clear; the size is not yet.

Two things are deliberately absent from that chart. The 1998 U.S. Senior Open at Riviera played about six strokes over the surrounding Los Angeles Opens, but it is a different tour on different tees with no matched players. And Augusta's lengthening is a sum of hole-relative panel effects: the design is silent on the course total by construction, so it cannot share that axis.

Lengthening is the most expensive lever a club can pull and the one the scoring average sees least. Hole by hole it does work: a tee move adds 0.030 strokes per 10 yards to the hole it touches. But holes get lengthened after they have played easy, so part of that is reversion — the durable rate is nearer 0.01 to 0.02. Augusta National added 660 yards between 1983 and 2026, worth somewhere between +1.3 and +2.0 strokes on that arithmetic, and the course total did not move, because the lengthening held the level against an easing of one to two strokes in everything else.

Which means: a club that lengthens three holes and looks at its scoring average the next season will conclude, wrongly, that it did nothing.

Finding three: Augusta National was getting easier before anyone lengthened it

0 +1 +2 +3 1948–1956 no cut · hardest era +3.11 1957–1980 36-hole cut from 1957 +2.40 1981–2001 bentgrass greens +2.16 2002–2018 +440 yards in this window +2.42 2019–2026 longest course, easiest era +1.52

Seventy-nine Masters on the weather-adjusted instrument. The first 36 holes of the full field are the one instrument the cut cannot affect. The series begins in 1948, when the hourly weather record starts — not all ninety Masters; the earlier tournaments enter the level comparisons only. Results for 1934–1982 transcribed from the 2026 Masters Media Guide.

The course lost most of a stroke across 1957 and another 0.45 across 1981, both before a yard was added. The lengthening era is the only one that rose, by +0.26 — which is not distinguishable from noise (p = 0.30). And it has eased again since the mid-2010s, leaving the most recent decade the easiest in the tournament's history on the longest the course has ever been.

The easing holds for professionals only and for the top 50 in the world, so it is not an artifact of who was invited. It shows on the short holes, in fewer bogeys, and alongside a halving of the advantage to long hitters. That pattern is consistent with presentation, which somebody decides. But the paper tests whether the whole era eased across other venues and cannot reject that either (p = 0.32 and 0.58), so an era-wide component cannot be excluded and the attribution to presentation is an inference by elimination rather than a measurement. Offered as a hypothesis, not a finding.

Finding four: a century at Riviera, and what the third venue separates

The Los Angeles Open has been played at Riviera in 63 editions since 1929, and the PGA Tour's archive holds every player's rounds — 22,089 rounds by 7,021 player-tournaments. Par has been 71 throughout. The course has also hosted a U.S. Open, two PGA Championships, a U.S. Senior Open and, in June 2026, the U.S. Women's Open.

−1 0 +1 +2 +3 +4 1949–1953 Hogan's years +3.50 1973–1982 +1.50 1984–1997 after the 1987–88 step +1.10 1999–2009 +0.30 2010–2018 +0.70 2019–2023 +0.05 2024 and 2026 limited, no-cut field −1.10

0.36 strokes per decade across 1973–2026 (p < .001), against no trend at Augusta over the same years. 1945–48 are omitted as incomplete, 1993 and 2005 were shortened, and the 2025 Genesis moved to Torrey Pines after the January fires. The 1949–53 figure says the course played three and a half strokes over par for the fields of its day, with their equipment — not that those fields would score so against the course today.

The third venue is what separates the golf course from the game. Hold the golfer fixed by birth date — year effects net of player fixed effects, on players aged 27 to 38, where published aging curves are flat — and Augusta eased about half a stroke over four decades while Riviera eased about 0.9, with 370 yards added against Augusta's 660. Whatever the ball and the driver did, they did at both courses. The common part is the game; the 0.4-stroke difference is the courses and their setups, which this design still does not separate from each other.

And an honest negative. Riviera's level fell 0.87 strokes across 1987–88, which looks like an event. A synthetic control built from 51 tour events falls 0.40 of that, and the remainder ranks 41st of 52 against placebo (p ≈ .79). Two cautions travel with it: the synthetic's 0.40 comes from being matched to Riviera's pre-period level — the median tour event moved nothing at all across the same break — and the pre-period fit error is two-thirds the size of the step. The step is a fact about Riviera's level. It is not evidence that something happened at Riviera.

Finding five: a limited field is worth about eight-tenths of a stroke

Five PGA Tour events moved from a full field to a limited, no-cut field in 2023–24. Pooled across them the change is worth −0.85 strokes (p = .02) — though the per-event changes run from −1.9 at Pebble Beach to +0.2 at the St. Jude, so this is an average and not a rule.

At two of the fixed venues it decomposes the same way: part is who plays, part is how a small, no-cut week is prepared and played. At Pebble the split is about 0.66 and somewhere in the range 0.8 to 1.4 — the paper calls that second number the most fragile in it, resting on three seasons with no shoreline weather, and publishes the range rather than a point. At Riviera, on a smaller gap, 0.31 and 0.43. Neither part is the golf course.

Finding six: every course has its own signature

0 +1 +2 +3 Royal St George's 2.88 Pebble Beach 2.76 Shinnecock Hills 1.71 St Andrews 1.52 Royal Liverpool 1.12 Royal Portrush 1.09 Quail Hollow 0.63 Oak Hill 0.55 Royal Birkdale 0.54 Oakmont 0.49 Royal Troon 0.45 Whistling Straits 0.40 Pinehurst No. 2 0.31 Valhalla 0.31 Kiawah Island 0.06

15 championship venues that hosted at least twice between 2010 and 2026. The bar is how far the course's scoring average moved between visits — raw, unadjusted, the same instrument, fields of the same standard. From 0.06 strokes to 2.88: a forty-fold range among the best-run courses in the game, and the most stable and most volatile are not distinguished by governing body, by architect, or by reputation. Augusta National is absent because it hosts every year and so has no gap between visits; read against these same gaps it sits at 0.86.

The same point arrives a second way. The three fixed venues have nearly identical amplitude and entirely different weather drivers: temperature at Augusta, shoreline wind at Pebble Beach, wind at Riviera — and rain at Riviera in the opposite direction, easing the course by 0.56 strokes an inch, because wet February fairways stop the ball running into trouble.

Neither the amplitude nor the drivers can be inferred from anything currently published about a golf course.

A prediction, published in advance

+3.0 strokes over par at the 2027 U.S. Open, with an 80% interval of +1.7 to +4.6. The tour baseline at Pebble Beach is +0.02; the measured difference between tour and championship setup is +2.96.

It was placed on record before Pebble Beach and Gil Hanse announced the alterations made ahead of the championship — about 50 yards on two holes, mostly restoration and narrowing. The paper expects that work to add roughly +0.2 to +0.5 strokes, which is inside the interval, and leaves the forecast unchanged rather than quietly revising it.

Scored leave-one-out against the three Opens already played, the method halves the error of a baseline-only forecast. It also missed 2019, which is why the interval stays as wide as it is rather than being tightened after the fact. If June 2027 lands below +1.7, the USGA has changed how it sets up Pebble Beach. If above +4.6, the shoreline weather will say why.

What this means for a golf course

Everything above was measured on elite fields, and the magnitudes will not transfer directly to an everyday course. The structure transfers to any course whose weather, setup or field varies from season to season, which is every course. A member field is several hundred golfers across a thirty-stroke handicap range, on several sets of tees, in every kind of weather. It is more dispersed than a tour field, not less. What is documented above is a floor, not a ceiling.

Scaled to a typical private club, the raw scoring average would be expected to move 1.5 to 2.5 strokes from season to season, most of it who played and from where. Adjusted for handicap and tee, what remains is weather plus setup: roughly 0.7 to 1.2 strokes. Sampling noise is not the obstacle. With 10,000 rounds a season the random part of a club's average is about ±0.05. These are scaling arguments, and one season of hole-by-hole member scoring would replace them with measurements.

A member field moves more, not less Several hundred players across a thirty-stroke handicap range, on several sets of tees, in every kind of weather. A championship course that changes nothing moves about a stroke a year; that is a floor for an everyday course, not a ceiling.
Green committee: the before cannot be reconstructed afterwards Capital projects are proposed, and later judged, on how members say the course is playing. A measured baseline restates the question as a number: the course played 0.6 strokes harder this season, of which 0.4 is weather and 0.2 is the work. For a restoration the relevant window is the season before construction, and no restored course appears to have been measured on both sides of its own project.
Superintendent: a sensor is only an instrument if it shares the course's exposure The superintendent controls most of the movement that is not weather: firmness, green speed, rough height, hole locations. The program and the weather reach the membership mixed together, and decomposing the scoring series separates them. Distance to the station is not the test. At Augusta National, inland with no sea breeze, a station ten miles away gives the same answer as one three miles away. At Pebble Beach they are not interchangeable: the airport six miles inland explained almost none of the year-to-year variance over the full series, while a shoreline station about a mile from the clubhouse explained half. And at Riviera the nearer airport reads 2.7 mph calmer than the coastal one, so a wind coefficient measured on the far station has to be rescaled before it means anything. Two cautions on the Pebble result: the shoreline instrument is a hobbyist station of unknown height and siting, the series is ten years long, and over those same ten years the airport does correlate. What the comparison establishes is that exposure matters, not that proximity settles it. If the club keeps its own readings, FogBow will use them; if it does not, the public record covers most courses.
Head professional: the index, the allocation, and the setup If a course plays a stroke off its rating on average, members' indexes are off by that much against every other course, and the daily playing-conditions adjustment corrects for the day rather than for a rating that is wrong on average. Hole-by-hole scoring supplies the stroke allocation from evidence: individual holes are stable enough year to year, with standard deviations of 0.06 to 0.15, for the allocation to be reliable.
Resort and public courses: three findings bite harder Composition: a club sees broadly the same golfers every year, a resort a different field every week, and the 2.3-stroke composition effect measured here is the resort case rather than the club case. Exposure: destination courses are disproportionately coastal and open, and the official station some miles inland may not be measuring the wind that governs scoring. Portability: a visiting golfer plays the course once and cannot recalibrate, so a course a stroke off its rating misrates them in a way no scorecard reveals.

Where this sits beside the Course Rating

A Course Rating and Slope are assigned from a physical survey under normal conditions and revised roughly once a decade; they are designed to capture permanent change and to make handicaps portable between clubs. The daily playing-conditions calculation catches part of the weather on abnormal days, but it is capped, applied by day rather than by season, and corrects the player's score rather than the course's rating.

A Course Rating says what a course should yield. A signature says what it does yield, how much that varies from season to season, and what the variation is made of. The two answer different questions, and nothing here replaces the rating or attempts to.

What the paper still needs

Hourly weather records begin in 1948 and hole-level records in 1983, so the earliest tournaments enter the level comparisons only. Field strength is measured by status and rank rather than a continuous skill adjustment. The Pebble shoreline series is ten years from a hobbyist instrument. At Riviera no station closer than 15 km covers the whole series — the nearer gauges closed in 1979 and 2010 — so the wind coefficient carries an errors-in-variables correction. The five Riviera championships are two organizers and three tours, which is too few to settle the organizer question. A further paper will test whether these effects hold at member clubs, using season-long member scoring at a small cohort of pilot courses.

Read the preprint (PDF) →  ·  Data and code →

The four papers →  ·  How the measurement works →

Data sources are public and every figure is computed from the working data set, which is deposited alongside the preprint. No proprietary or club data were used. FogBow LLC is not affiliated with, endorsed by or sponsored by the United States Golf Association, any Allied Golf Association, or any championship organizer, golf club or resort named in this research.