Arnold Palmer, who died Sunday of complications from heart problems, fell just short of being the greatest player in golf history. But for a brief period, he was very nearly as good as anyone who ever played the game — and his greatness came at exactly the right time for a sport seeking viewers at the dawn of the television age.

From 1958 to 1966, Palmer won seven major championships — including four green jackets at The Masters — and finished in the top 10 at 16 other majors. At the heart of that span was a five-season stretch from 1960 to 1964, which, according to our method of “major shares” (which credit players for their expected majors won based on how dominant their scores are relative to the field), still stands as the seventh-best peak performance of golf’s modern era.

Seventh-best doesn’t sound overly impressive, until you consider that slots 1 through 6 are four five-season stretches from Tiger Woods and two from Jack Nicklaus. In fact, that pair so thoroughly dominates any ranking of great golf seasons that merely being in their company is a rare honor. And in terms of peak greatness, Arnie is the only other player in the conversation aside from Tiger and Jack:

YEARS MAJORS PLAYER FROM TO CUTS MADE WINS MAJOR SHARES 1 Tiger Woods 1998 2002 20 7 5.89 2 Tiger Woods 1999 2003 20 7 5.67 3 Jack Nicklaus 1963 1967 18 6 5.45 4 Jack Nicklaus 1971 1975 20 6 5.24 5 Tiger Woods 1997 2001 20 6 5.03 6 Tiger Woods 2000 2004 20 6 4.85 7 Arnold Palmer 1960 1964 19 6 4.78 8 Tiger Woods 2002 2006 19 6 4.66 9 Jack Nicklaus 1972 1976 20 5 4.65 10 Jack Nicklaus 1962 1966 19 6 4.63 11 Jack Nicklaus 1964 1968 18 4 4.59 12 Tiger Woods 1996 2000 18 5 4.54 13 Jack Nicklaus 1970 1974 20 5 4.37 14 Jack Nicklaus 1973 1977 20 3 4.35 15 Tiger Woods 2005 2009 16 6 4.00 16 Arnold Palmer 1962 1966 18 3 3.97 17 Arnold Palmer 1961 1965 18 4 3.94 18 Tiger Woods 2004 2008 17 6 3.87 19 Jack Nicklaus 1965 1969 18 4 3.79 20 Jack Nicklaus 1961 1965 17 4 3.76 21 Tiger Woods 2001 2005 20 5 3.73 22 Jack Nicklaus 1969 1973 20 5 3.69 23 Arnold Palmer 1959 1963 19 5 3.68 24 Tiger Woods 2003 2007 19 5 3.67 25 Arnold Palmer 1958 1962 18 6 3.67 Best 5-year runs in modern golf history Since 1958, when the PGA Championship adopted a stroke-play format. Sources: ESPN, Yahoo

Palmer didn’t remain at that level very long. He made his final top-10 finish at The Masters in 1967, and although he’d have 11 more top-10s at the other majors, he also fell out of golf’s highest tier of players around that time. While still capable of contending at majors, he didn’t do it consistently after the mid- to late 1960s. And by that point, Nicklaus had long since surpassed Palmer as the game’s top player. In Nicklaus’s absence, Palmer could have enjoyed a longer reign atop the sport, but Palmer had the misfortune of winning his first major only four years before golf’s eventual G.O.A.T. would win his.

But in other ways, Palmer’s timing couldn’t have been better. His greatest stretch of seasons coincided with golf’s increased popularity in a booming postwar America, and — even more importantly — the ascendance of televised sporting events in the U.S. With good looks and a swashbuckling style that played well on TV, Palmer became the face of the sport, selling it (and himself) to growing audiences on a national stage.

Ultimately, that will be Arnold Palmer’s most important golf legacy. But in all the talk about his role in popularizing the sport, we shouldn’t forget just how good he was at playing it during his prime. He wasn’t there very long, but when Palmer was at his best, only a couple players in the history of the sport were better.