ORLANDO, Fla. — In a fashion befitting someone born in 1929, Arnold Palmer valued a certain comportment, like men removing their hats when they went indoors. Rory McIlroy, born in 1989, played in the famed Arnold Palmer Invitational for the first time in 2015 and watched with a bit of wonder as the hat protocol was politely enforced in the players’ dining room, sometimes by a smiling Palmer.

“I came to really like it,” McIlroy said of the etiquette still practiced at the event in honor of Palmer, who died in 2016. “It’s one of the ways you still feel Arnie’s legacy and presence.”

A week ago, after Tiger Woods sustained serious injuries in a car crash, talk of Woods’s legacy and presence was pervasive on the PGA Tour. This week at Arnold Palmer’s tournament, which Woods has won eight times, the link between the two golf legends seems stronger than ever, perhaps in ways that may shape Woods’s standing in the game going forward.

After the first round on Thursday, Mcllroy and Corey Conners were tied for the lead at six under par.

With Woods still on their minds, numerous players have made the connection, keenly aware that the impact Palmer made on golf and international culture was replicated by Woods 40 years later. “Certainly, Arnie was and should be the role model for all professional golfers,” Jordan Spieth said Wednesday.

Sam Saunders, Palmer’s grandson who has played on the PGA Tour, said he believed that his grandfather had laid the groundwork for what Woods later accomplished, and that the annual appearances by today’s top golfers at the Palmer Invitational had become a way “for them to remember that Arnold Palmer kind of started it.”

Saunders added: “We wouldn’t be doing what we’re doing right now were it not for his bringing the game to television and making it popular, making it a game for everyone. He started it, Tiger has continued it, and so many great players along the way have added to that.”

A younger generation of pro golfers seems to revel in the Palmer lore at Bay Hill, the tournament site. Near the first tee, they take pictures next to the bronze statue of the golfer, which captures his distinctive, powerful follow-through. Spieth took a tour of Palmer’s museum-like office on Wednesday. Two years ago, the rising star Viktor Hovland, then 21, was guided around the grounds by Palmer’s longtime assistant, Doc Giffin.

Perhaps if Hovland had more time, he might have learned how Palmer, in part because of his blue-collar, Western Pennsylvania roots, had pried golf from its country-club origins and, for the first time, made the sport cool. Palmer had charisma, dressed with pizazz, played with white-hot emotion and struck evocative poses that seemed made for a television camera. Palmer’s life became a particularly mid-20th century American story as he launched multiple prosperous companies, earned scores of corporate endorsements and made himself a worldwide brand — all as a golfer who last won a PGA Tour event in 1973.

Palmer also magnanimously strayed from his designated lane. More than a dozen PGA Tour players who live near Orlando remarked this week that their children were born at the Winnie Palmer Hospital for Women & Babies, named for Arnold’s wife of nearly 50 years. It is across the street from the Arnold Palmer Hospital for Children.

It is likely that millions of people around the world know Arnold Palmer not for his golf but because of the popular soft drink, iced tea combined with lemonade, that bears his name. In the end, perhaps he most enjoyed his status as a beloved, wise elder who was constantly approached by advice-seeking pro golfers — young and seasoned — who knew that no one had persevered and succeeded in golf like Arnold Palmer.

It is in all these ways that Palmer’s life after his playing career might serve as an example for how Tiger Woods, if he chooses, could continue to deeply influence golf for decades to come. Woods has already taken multiple steps to do so, in modern ways that are tailored to his specific interests and causes.

But as Woods watches this weekend’s Palmer Invitational — and his social media accounts made it plain that he was watching the PGA Tour last weekend — it will be easy to note the homage paid to Palmer’s almost lifelong leadership role in golf. Woods, an idol to the current generation of players in the same way Palmer was to the golfers who came after him, has the platform to forge a similar legacy. The two had a warm relationship, and Woods knows plenty about the path Palmer deliberately chose.

And it appears he already knows his manners. Of Woods’s eight victories at the Arnold Palmer Invitational, one of the most notable came when he sank a twisting 24-foot putt on the final hole to win the 2008 tournament. What made the moment most memorable was Woods’s reaction to that clinching putt: Perhaps anticipating a walk back to the clubhouse, he grabbed his hat and flung it to the ground.