New York racing’s biggest day is upon us. Out at the big park in Elmont, there’s a buzz in the air and a bounce in people’s steps. Once again, the flowers have been freshened, the grass clipped, the bunting hung. Saturday morning, the trains will roll in, the fans will line up, and the Clydesdales will start marching, resplendent and proud. There’s $1 million in the pot for the 138th running of the Belmont Stakes, and another page of racing history to be written.

Which byline will head that page is anybody’s guess. All the horses we thought were stars in the spring have left the Triple Crown trail. The Kentucky Derby winner, Barbaro, broke his leg during the Preakness Stakes. The Preakness winner, Bernardini, needs a rest. What’s left is a solid, well-matched field. The shortest morningline odds on the board are the thoroughly bettable 3-1 on Bluegrass Cat.

The Belmont Stakes is the longest of the Triple Crown races, and it’s likely the longest race any of these 3-year-olds will ever run. To make the distance you need three things: You need a cool horse, you need a jockey who can keep his head together, and you need stamina.

In 2003, Funny Cide took the Kentucky Derby and the Preakness, and he came to New York to prove he deserved the hype. In retrospect, his chances of beating Empire Maker twice were slim. But he might have had a chance if he hadn’t gone rank around the first turn, ranging up on the outside, running too fast and too close to the front of the race. The horse lost his cool and never settled into a stride on the wet track.

The following year, it was Smarty Jones’s turn to take a shot at the Triple Crown. The horse looked as if he had the stamina to make it, but his jockey, Stewart Elliot, succumbed to the horses pushing him into the lead and made his move too early. With six furlongs left to race, Elliot pushed the horse through a quarter-mile in 23 seconds, like it was a sprint. Only steps from the wire, Smarty was still out in front, but Birdstone ran him down.

To win the Belmont, both horse and rider have to be in top form the whole way. Certainly there have been some long-shot winners in recent years – Birdstone went off at 36-1 – but each of the last three winners was deserving and capable. Birdstone, after all, was a homebred Whitney horse, exactly the kind of breed that hits the track less and less in this era of flashy auction horses bred to win short races as 2-year-olds. Reading Empire Maker’s pedigree is like reading a who’s-who of top thoroughbreds of the last few decades. And the 2005 winner, Afleet Alex, was head and shoulders above the rest of the field, a standout.

In Saturday’s race, there is no standout horse. So in trying to pick a winner, we’re left with the three criterion mentioned above: tractability in the horse, experience and cool in the jockey, and the bred-in stamina to make the distance.

Four horses qualify on these counts: Bob and John (5-1), Bluegrass Cat (3-1), Jazil (10-1), and Steppenwolfer (9-2). Each has the stamina to make it, and none is likely to ruin the race by running up on the muscle or jumping to the lead unexpectedly. What’s more, each of these jockeys is capable of putting together a strong ride. Garrett Gomez, up on Bob and John, is the leading rider in the country. Johnny Velasquez, in the irons on Bluegrass Cat, is back from an injury incurred before the Kentucky Derby; he’s downright deadly, especially in combination with trainer Todd Pletcher. Jazil’s Fernando Jara is a talented 18-year-old chasing a dream, though he lacks experience. RobbyAlbarado, up on Steppenwolfer, has been up in the money on 49% of his starts this year.

That said, it’s time to turn to the race and figure out how it will be run – and won.

These four horses divide neatly into two types. Bob and John and Bluegrass Cat both stalk the pace, up in the front half of the race, whereas Jazil and Steppenwolfer run from the back of the pack.

It’s usually an advantage at Belmont to run close to the pace, because it’s very easy to get trapped at the back. The distance of the race is such that if the pace is hot, your horse might not have the juice to make up a lot of ground. At the same time, your horse must be a monster to win it on the front. The trainers of Jazil and Steppenwolfer both know this and plan to have their horses slightly farther up in the race in the opening half.

The likely pacesetters in this race, High Finance and Double Galore, are weak horses: The former has never run anywhere near this distance, and the latter won his first race just a few weeks ago. They’ll give up the lead on the backstretch, which should leave Bluegrass Cat battling Bob and John out front earlier than is wise. Steppenwolfer typically doesn’t sink back as far as Jazil, and I expect him to inherit a perfect running spot as the early leaders fade.

When Jazil ranges up on the turn, Steppenwolfer will move with him. Steppenwolfer gets a small advantage here, simply by starting closer to the pace. The two of them will hook up and charge toward the leaders, Bluegrass Cat and Bob and John. The foursome will get shuffled around on the turn, leaving a tiring Bob and John to battle Jazil for third. Jazil might win that fight, but he won’t catch the two in front of him.

Entering the stretch, Steppenwolfer and Bluegrass Cat will engage in an all-out duel. But this is Steppenwolfer’s distance, and he’ll put his head in front with a furlong to go. When they hit the wire, it’ll be the gray’s race – and his page in the history books.

Mr. Watman is the author of “Race Day: A Spot on the Rail With Max Watman” (Ivan R. Dee).