For all his accolades, Arnold Palmer was under-rated

THE death of Arnold Palmer (pictured, right) late last month at the age of 87 has prompted countless appraisals of his legacy and place in golf’s history. By the most common metric, wins in major tournaments, his seven titles put him in a five-way tie for seventh place, trailing Jack Nicklaus (left), Tiger Woods, Walter Hagen, Ben Hogan, Gary Player and Tom Watson. But such comparisons are fraught with pitfalls: Hagen was already 42 when the first Masters was played, and the PGA Championship employed the volatile match-play format from 1916 to 1957. Similarly, Tom Morris Jr, who won four straight British Opens from 1868-72, only had to beat between seven and 16 rivals to claim the Claret Jug; today, over 150 contestants enter. Moreover, simply counting victories unfairly assesses a player’s performance based on those of his rivals. Was Phil Mickelson’s 17-under-par score of 267 in this year’s British Open any less impressive because Henrik Stenson happened to shoot 264 in the same tournament?

In order to evaluate Mr Palmer’s standing within the sport’s pantheon on a level playing field, we have applied the same methodology we used to size up the Stenson-Mickelson duel in July to every stroke-play men’s major championship in golf history. This approach still has plenty of drawbacks. It ignores all non-major performances, which constitute a large majority of tournaments. And taking a straightforward sum of career totals automatically excludes most 19th-century golfers, who played before most of the majors were founded. Nonetheless, when it comes to modern-era stars competing for the biggest prizes, it should prove fairly reliable. It turns out that the major-title standings are mildly unflattering to The King (as Mr Palmer was known): our range of metrics winds up placing him between third and fifth of all time.

The premise of our historical golf rankings is to evaluate players exclusively on the value of their own performances, disentangling their merit from both their historical context and from the strength of their opponents. Regardless of how often golfers actually won trophies, what should matter is how their scorecards stack up in absolute terms across eras. To accomplish this, we have built a simple model to estimate the spread of scores in major tournaments.

As is the case in most sports, golfers’ performances have been bunching ever closer together over the course of the game’s history. In the 1899 U.S. Open, the best and worst finishers were separated by a whopping 107 strokes; in the 1992 edition of the same event, just 20 distinguished the top of the leaderboard from the bottom. This trend is easily explained by a few factors. The institution of a cut halfway through tournaments has culled weaker competitors. The quality of entrants has also steadily improved, making it harder for one great player to exceed the mean by a large amount. And the extension of events from two days to four has smoothed out players’ round-to-round fluctuations.

Using just a few variables—a tournament’s duration, size, cut rule, average score and year of play—we can build a model to estimate where one would expect a golfer with any given score to finish, regardless of how his opponents actually performed in the event. For example, the 1991 British Open occurred fairly recently in golf history, lasted four days, saw 112 players make the cut and had an average score of 286. In that context, a golfer who shot ten strokes better (a 276) would typically finish either first or second, and have around a 53% chance of victory. However, in a tournament configured like the 1894 edition of the Open—one much further in the past, with an average score of 356, no cut and a smaller field—the same ten strokes above the mean would generally correspond to finishing just tenth out of 52, and yield just an 0.5% probability of a title. This approach shows that Mr Mickelson’s second-place showing in the 2016 Open Championship was in fact the seventh-best scorecard ever submitted at a men’s major: given the tournament’s characteristics, a golfer beating the average by 21 strokes as he did should win 99.7% of the time. Conversely, Sandy Lyle only exceeded the mean by eight strokes when he won the Claret Jug in 1985, a performance with only a 1.7% chance of claiming a title. It just so happened that all of his rivals were off their games that year.

In order to keep bar-room debates lively, we have calculated five different alternative metrics to compare golf’s greats. The most straightforward is career win probability: given a player’s scorecards and the attributes of the tournaments he played in, how many championships should he have expected to win with neutral luck? Of all our indicators, this one is the most flattering to Mr Palmer. Although he actually claimed seven major titles, his performances were more consistent with a total of 7.98 victories. That is the third-best mark ever, behind only the unassailable totals of Mr Nicklaus (who won 18 titles and had an expectation of 17.03) and Mr Woods (who has 14 and an expectation of 12.54).

Mr Palmer’s mildly bad luck—or tendency to choke when a trophy was on the line, depending on one’s interpretation—stems primarily from the 1966 U.S. Open. His score of 278 beat the field average by a massive 19 strokes, making it the second-best performance of his career. Sure enough, he led Billy Casper by seven strokes heading into the final nine holes. But Casper then mounted one of the greatest comebacks in golf history to tie Mr Palmer and force a playoff, which he went on to win comfortably. Although Mr Palmer’s showing was good enough to win 94.6% of the time, he just happened to run into a stronger opponent. Mr Palmer also lost a U.S. Open playoff to Mr Nicklaus in 1962, with a score of 14 strokes above average that corresponded to victory about half the time. Whether Mr Palmer deserves demerits for falling to such formidable opposition is in the eye of the beholder.

The primary reason the career-win-probability metric is so favourable to Mr Palmer is not his slight underperformance, but rather the remarkable good fortune that some of golf’s other greats have enjoyed. Although Mr Player secured nine major titles, compared with Mr Palmer’s seven, his scorecards only support a career total of 5.87 victories. No one seemed to bring their “A” game to the 1959 British Open, which Mr Player won despite beating the average by a mere ten strokes, which should have yielded a championship just 6.6% of the time. His victory in the 1974 Masters was similarly unimpressive, at nine strokes above average and a 13% chance of victory. Moreover, when Mr Player happened to be on a good run, he rarely ran into a rival having a better one: he won all three times that he turned in a scorecard with over a 50% probability of victory. Bobby Jones, whose seven major wins tie Mr Palmer’s, similarly won 2.23 more majors than his scorecards would indicate. However, in Jones’s defence, he had only half as many opportunities as subsequent players did: the Masters was founded after his peak, and as an amateur golfer he was ineligible to play in the PGA Championship.

Historical win-probability totals also reveal some underappreciated greats. Unsurprisingly, following his heart-wrenching loss to Mr Stenson, Mr Mickelson ranks as the unluckiest player ever, with just five major titles despite scorecards that suggest he deserved 7.35. But close on his heels is Tom Weiskopf, whose only major victory came in the 1973 British Open. He beat the field by 15 strokes at the 1976 U.S. Open, by 13 at the 1973 U.S. Open and by 12 at the 1975 Masters, but came up empty, losing to Jerry Pate, Mr Nicklaus and Johnny Miller. With average luck, Mr Weiskopf would have been a three-time winner.

One drawback of using win probability is that it fails to distinguish between merely outstanding performances and historically dominant ones. Improving from ten strokes above average to 20 might increase win probability from 5% to 99%, but going from 20 to 30 only raises it from 99% to 99.9%. In order to give the most impressive showings of all time their due, an alternative is to count the standard deviations above average expected by our model. This measure assigns the same weight each additional stroke of improvement in a given tournament.

If we ignore all below-average performances, then Mr Palmer’s total of 79.24 comes in fifth, ahead of all the other seven-major winners but just behind those with eight or more. Because this statistic gives more credit to good-not-great showings than win probability does—placing tenth out of 75, say, is well above average even if it comes with zero chance of victory—it is largely a measure of longevity. As a result, it ranks Mr Watson, who remained a contender in majors into his late 50s, ahead of Mr Woods, who has looked washed-up since age 38. Similarly, it penalises Mr Palmer, who won all of his majors in a seven-year span, and by the late 1970s was no longer a serious threat.

There are a few ways to tweak this approach to emphasise peak excellence at the expense of career bulk. One is setting the cutoff at two standard deviations above average—roughly placing in the top 2-3% of finishers. Another is limiting the sample to a player’s handful of best performances—we’ve chosen seven, in honour of Mr Palmer’s major-title haul—using either win probability or standard deviations above average. The latter methods are also arguably fairer to earlier generations of players, who had fewer stroke-play majors to compete in and thus accumulated lower career totals. All three of these peak-centric approaches push Mr Woods into first place, just ahead of Mr Nicklaus: no one, not even the Golden Bear, was better than Tiger at his best. Mr Palmer places fourth in all of them, trailing Mr Mickelson in both standard-deviation metrics, and Hogan on win probability.

No matter how you slice it, the numbers tell a fairly consistent story about Mr Palmer’s place in golf history. While Mr Nicklaus and Mr Woods appear light-years ahead of the competition on almost every metric, mostly in that order, Mr Palmer sits squarely atop the second tier, at least when it comes to stroke-play majors. There’s a strong case that Hogan, who won a pair of match-play PGA Championships, may have been better, and it’s hard to know what to do with Hagen, Jones or John Henry Taylor, giants of the game’s early years. And among modern greats, it wouldn’t take much for the resurgent Mr Mickelson to overtake him. But Mr Palmer’s record more than justifies his reputation. If anything, pundits have probably sold him a bit short.


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