A few weeks ago, the global tennis community left Canada dazed and exhausted after a ridiculously absurd yet entertaining week crammed with surprises and plot twists.

One of the basic themes of that week, however — lurking beneath headline-grabbing events from the likes of Nick Kyrgios, Belinda Bencic, and Andy Murray — was that the players who thrived in lower-tier tournaments the week before Canada were not able to perform as well in the great North.

Attacking The Net had this to say:

Some professional tennis players are in positions where their talents are best used in the pursuit of mid-level tournaments. That’s where they can maximize paychecks and derive the most satisfaction from playing. Other players want to be the very best, but they have to play more events in the attempt to try to get rankings points and match-play experience. They’re caught in between the competing desires to win and to season themselves for the future.

Other players, though, have arrived at points in their careers where they’re not playing for the money (they have more than enough of it) or the mid-level titles. A number of tennis professionals have displayed the talent, the toughness, the stamina, the cleverness, or any or all of the above — enough to show to themselves and others that they are capable of winning major titles. A subset of the larger community of tour-level players can be regarded as the top tier of the top tier.

Yes, if you’re one of the 100 best in the world at your profession, you’re very good, but the cruel and unforgiving realm of professional tennis puts the top six (or 10, or 12) in a separate category.

This is why winning Washington and Stanford will mean different things to different people. Canada and Cincinnati are bigger.

This is why winning Canada and Cincinnati will mean different things to different people. The U.S. Open is bigger.

Do athletes want to win any tournament, or do they want to win the tournaments that matter? They get to make the choices and live with them. They also know — as all athletes do — that their choices help determine (though not necessarily guarantee, for better or worse) how history will remember them.

The following statements are opinions, not facts, and you can certainly disagree with their locations on a spectrum of tennis thoughts, but they generally fit into a discussion in which tennis players are distinguished — some by their desire to establish themselves competitively; some by their desire to establish themselves financially; some by their desire to win the biggest events on the calendar, the majors:

Sloane Stephens’s Washington title rates as a much more impressive accomplishment than Kei Nishikori’s Washington title, and also more impressive than Kerber’s Stanford title.

Belinda Bencic’s Toronto title rates as a more significant and meaningful accomplishment than Andy Murray’s Montreal championship… but Murray’s championship will grow in stature if it leads to a U.S. Open title.

Simona Halep valued this Toronto title enough to keep playing through the second set, but in doing so, she showed a lack of regard for the U.S. Open at a time in her career when the majors are what she should be thinking about.

Similarly, Kei Nishikori — by playing in Washington — left himself spent in the latter stages of Montreal. He should be aligning his schedule for (and around) the majors, but he hasn’t reached that stage in his thought process yet. (In that sense, he’s the new Nikolay Davydenko… although unlike Kolya, Kei has already made a major final.)

Those are opinions, not facts, but they merit thought as a wild week in Canada can be seen in the rearview mirror.

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Two weeks later, those ideas resonate ever more deeply.

Kei Nishikori, even though he didn’t play in Cincinnati and rested for the U.S. Open, was still not good enough to get out of the first round. Full credit goes to a deserving Benoit Paire, who toughed out a difficult five-set win and saved two match points in a fourth-set tiebreaker. Yet, it remains that Nishikori — as great as he can look in best-of-three-set matches — doesn’t own the stage in best-of-five competition. At this tournament, he had a soft draw through the quarterfinals and had a chance to show that he could back up his run to the 2014 U.S. Open final.

Instead, Nishikori’s early exit — beyond costing him nearly 1,200 rankings points — reinforces the reality that he’s not ready for prime time at the biggest tournaments of the year. Sure, he won Washington, but players of Nishikori’s ability shouldn’t make Washington a priority. How they play in New York (and Melbourne and Paris and suburban London) — that’s what should count for a No. 4 player in the world, soon to drop out of the top five in all likelihood.

What about Sloane Stephens, also a winner in Washington? She broke through and won her first title this past summer, an occasion well worth celebrating at the still-young age of 22. (Nishikori, as a point of comparison, will turn 26 just before New Year’s Day.) However, that event merely raised a fresh obstacle for her: How to react to being a champion and, therefore, more of a target on the WTA Tour?

Stephens didn’t handle that pressure very well in subsequent weeks, and her first-round U.S. Open loss to a pioneering CoCo Vandeweghe continues the “one step forward, one step back” pattern of her career. It’s still a young career, mind you; Stephens’s journey is not imperiled nearly as much as Grigor Dimitrov’s career, and this setback is nowhere near as substantial as Nishikori’s. However, Stephens is very much entering a two- or three-year window in which this sort of progression needs to begin to become less commonplace. If it’s still happening at age 24, a lot of potential will have been wasted. Stephens has shown too much to be a player who only wins Washington and not the bigger events on tour.

A player in a position similar to the one inhabited by Stephens? Karolina Pliskova, 23 and a half years old come late September. Though seeded eighth, Pliskova was not a serious threat at the U.S. Open, and she promptly showed why in a first-round no-show against a delighted Anna Tatishvili. Pliskova is 2 for 14 at the majors in terms of making the third round. (This is a No. 8 seed we’re talking about, a member of the WTA top 10.) She’s 0 for 14 in terms of making the fourth round. She’s collected some lower- and middle-tier accomplishments in her sport, but when the bright lights of the most prestigious events come calling, she’s not able to answer the bell.

Then, we have this statistic to show you:

This top-10 list is packed with stories about women’s tennis, for better and for worse. The greatness of the Williams Sisters — including their longevity — is part of the story. The ability of Maria Sharapova to get results out of her more monochromatic game is another very positive story found in the numbers above. Victoria Azarenka’s competitive chops shine through as well; if she can just get healthy and stay healthy, she’ll make a run at 200 wins at the majors.

Then, however, there are the sadder stories on this list, and four of them were painfully dragged into (and then out of) the New York spotlight on Monday afternoon.

How many major tournaments have the players above played? You can do the easy math. Each loss represents one major tournament played. Then add the number of major titles each player has won. That’s your number, not including Monday’s results (since the tweet was posted over the weekend).

For Svetlana Kuznetsova, Jelena Jankovic, Ana Ivanovic, and Daniela Hantuchova — all in the top 10 among active WTA wins leaders at majors — the comparatively larger numbers of match wins are basically products of longevity. Ivanovic — at 27 years and nearly 10 months of age — is the one partial exception to that claim, but in tennis, age 28 is not exactly young. More to the point, it is an age by which a player needs to have figured out the mental arts of the sport.

Without belaboring the point, all four players — Kuznetsova, Jankovic, Ivanovic, and Hantuchova — crashed out of the U.S. Open on Monday afternoon. Worlds of opportunity in a relatively softer section of the top half of the draw were left unclaimed. The parade of seeded players (Kuznetsova, Jankovic and Ivanovic were seeded; Hantuchova wasn’t) leaving New York in the first eight hours of the tournament was substantial.

The truly damning verdict about all these events: With the possible exception of Jankovic’s loss to Oceane Dodin, none really raised any eyebrows among commentators and analysts. On the men’s side, Nishikori’s loss might have drawn some gasps if only because Paire has been a notoriously erratic and unreliable player (unreliable, at least, unless you depend on him to provide a mixture of comedy and theatrics), but it’s nowhere close to an earth-shaking event.

As the tennis season’s final major tournament begins, many seasons — measured by their ability to reach previously unattained or rarely attained heights in the most important moments afforded by the sport — are already ending.

Who really, REALLY cares if Nishikori wins, say, Paris-Bercy in a few months? Who will REALLY regard it as a big deal if Ivanovic or Jankovic does well in the Asian autumn swing? Yes, qualifying for the WTA Finals or the ATP World Tour Finals possesses value in terms of prestige and money, but without winning a centerpiece event on tour or at least making a final every now and then, this question of tennis identity lingers.

The Gospels of the Holy Bible tell us, “For what will it profit a man to gain the whole world and forfeit his soul?”

Day one of the 2015 U.S. Open offers a tennis gospel verse:

“For what will it profit a player — beyond money, of course — to gain Washington and lose early in majors far more than one should?”

Let’s acknowledge this about the Ivanovices, Jankovices, and Nishikoris of the world: They’re making a great living off tennis. Measured strictly in terms of income and prowess relative to all the other people who play tennis on this planet, they’re still doing extremely well, better than 99.9 percent of other human beings.

Yet, what’s true about our lives is true about professional athletes’ careers, especially in a solo-athlete sport where team-based considerations (the quality of owner/general manager/teammates you have) don’t apply: We all want to be remembered. Not everyone will be, but a part of us — an ancient part of us deep in the center of our being — wants to know that when we die, something in us or about us will live on.

For tennis players, being remembered is achieved by mastering the majors, not the Citi Open.

For Kei Nishikori, Sloane Stephens, and other big names on both tours, this search for tennis identity remains as frustrating and elusive as ever, just one day session into a new U.S. Open.