A wise man once said the credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly; who errs, who comes up short again and again. For years, the Washington Nationals knew only dust and sweat, trampled by their opponents and overlooked across their sport. Wednesday afternoon, Game 162 brought an endpoint for the majority of baseball and, for them, the triumph of high achievement.

Before a roaring crowd, the Nationals’ 5-1 victory over the Philadelphia Phillies enabled the Nationals to finish with the best record in the majors and gave them the top seed in the National League playoffs. They will begin their best-of-five, first-round series Sunday at the winner of Friday’s one-game wild-card playoff between the Atlanta Braves and St. Louis Cardinals.

Their 98 wins marked an 18-win improvement over last year, a 29-win increase from 2010 and a 39-win leap from 2009. The Nationals gathered in February as an upstart and emerged seven months later as a juggernaut, primed to take on Washington’s first major league postseason since 1933.

“You knew the potential was there, but we’ve played beyond everyone’s expectations,” said starter Edwin Jackson, who earned his 10th win with 62 / 3 innings of one-run ball. “It’s just a matter of how you approach it. If you come out expecting to win games rather than hoping to win games, then you win games. You don’t hope. You take the field knowing that you’re going to beat every team you’re playing.”

The Cincinnati Reds could have tied the Nationals at 98 wins if they won their regular season finale later Wednesday night, but the Nationals earned the top seed by virtue of beating the Reds, 5-2, in the season series. The Nationals, then, will avoid a cross-country flight to play the San Francisco Giants and will play the first playoff game at Nationals Park next Wednesday.

For the first seven years after baseball’s return to Washington, the 162nd game would have ended their season. Now the reminders of October baseball, of more to come, surround them. Wednesday morning in the Nationals clubhouse, players were fitted for new hats with the official “Postseason” logo patch on the side.

“This is a great season, a great team, a good group of guys, and we accomplished a lot that we should be proud of,” third baseman Ryan Zimmerman said. “But we have a lot more to accomplish, hopefully.”

In the other dugout, the Phillies came to grips with an 81-81 record that snapped a string of nine winning seasons and five division titles. They, like the Nationals, absorbed injuries all season. Unlike the Nationals, their depth did not allow them to contend. But they still have three top-shelf starters, and the rivalry may reach new hostility in 2013.

“It’s all coming together for them,” shortstop Jimmy Rollins said. “So, that’s great for them. But with us being healthy, they’re still in second place. But we weren’t.”

It is not the critic who counts. The Nationals seized their final victory of the season, and sealed a 9-9 split with the now-former NL East champion, behind Jackson’s rebound start. After recording four outs Friday in St. Louis, Jackson allowed six hits and walked one while striking out six. He left his final regular season start to a standing ovation, waving to the crowd with his right hand.

“After the last start in St. Louis, to go into the postseason with some confidence and come off a great outing, that was big for him,” first baseman Adam LaRoche said. “For all of us.”

The Nationals’ offense came after rare inspiration. Phillies left-hander Cliff Lee allowed the Nationals no runs for the first three innings. In the middle of the fourth came the daily Presidents Race, the moment when so often the home crowd pointed out how the strong man stumbles.

The crowd still buzzed as the Phillies took the field after the racing Teddy Roosevelt won for the first time. Zimmerman, the franchise third baseman who had watched more of the mascot races than any other National, stepped to the plate.

After he fell behind Lee, 1-2, Zimmerman roped a 92-mph fastball down the right field line and into the Nationals’ bullpen, a solo homer that tied the game at 1. The next hitter, Michael Morse, blasted a double off the very top of the right-center field wall, inches from another homer. Tyler Moore roped a double to left, and Morse raced home. In the immediate aftermath of the Presidents Race, the Nationals ripped three consecutive extra-base hits and took a 2-1 lead.

Behind Jackson’s powerhouse start, they needed no more offense but piled on, anyway. Moore added an insurance, solo homer off Lee in the sixth inning, his 10th this season in a part-time role despite spending a chunk of the year at Class AAA Syracuse.

The blast let the Nationals relax. Bench coach Randy Knorr made the pitching changes as Manager Davey Johnson underwent tests for numbness in his left leg, caused by a pinched nerve in his lower back. In the eighth, Zimmerman drew a leadoff walk. Bryce Harper pinch ran for him, and as Zimmerman walked backed to the dugout he doffed his helmet to the roaring 37,075 fans. They helped set a new Nationals Park attendance record with 2,370,794 on the season.

With Harper on first, Morse crushed a home run deep over the scoreboard in right-center field. The exulting crowd would not stop cheering until Morse emerged from the dugout, helmet in one hand, and raised both arms over his head.

“I like where we’re sitting headed into the postseason,” right fielder Jayson Werth said. “This is what it’s all about. This is what you play your whole life for to get to this point and we’ve got a chance to do something special here. We’ve got a good team and a good group of guys, and I think the city can be proud of that.”

After the ninth, the Nationals emerged from their dugout, finished with one season and ready to start another. They shall never be with those cold and timid souls who neither know victory nor defeat.

But, with a magical season behind them and another ride ahead, they have come to find victory suits them awfully fine.