When rosters expand to as many as 40 next week, Pittsburgh’s Gregory Polanco is one of several players who could alter playoff races. (Rob Foldy/Getty Images)

On Sept. 3, 2013, the Cincinnati Reds were teetering on the edge of playoff contention, facing a key home game against division rival St. Louis. In the seventh inning of a scoreless game, lumbering left fielder Ryan Ludwick poked a leadoff single up the middle. Dusty Baker, then the Reds’ manager, looked down his bench and inserted a player who had never before appeared in a major league game, outfielder Billy Hamilton.
In 2011, Hamilton stole 155 bases at two minor-league levels, a professional record. And he was on the Reds’ roster in the midst of a pennant race for one reason – to steal bases. He could be in such a position for only one reason, too – the fact that, at the most crucial time of year, baseball allows its teams to play by completely different rules, expanding rosters on Sept. 1 from 25 to as many as 40.

It’s as if the Miami Heat could add a three-point specialist in May, as if the Green Bay Packers could designate a kickoff returner in December. What impact did Hamilton have? That night against the Cardinals, he stole second on the next pitch, then scored the only run in a 1-0 victory. In his first 11 games, nine of which he entered as a pinch runner, he swiped 13 bases without getting caught. The Reds won nine of those games and clinched a wild-card berth.

Which contenders, then, could benefit this fall – beginning Monday, when rosters expand – by this peculiar roster rule? A breakdown of some potential impact call-ups:

Joc Pederson, outfielder, Dodgers: Wait, with Carl Crawford, Andre Ethier, Matt Kemp and Yasiel Puig, don’t the Dodgers already have more than enough outfielders? Sure. But Pederson, who became the first player in the Class AAA Pacific Coast League to steal 30 bases and hit 30 homers in 80 years, could be a key defensive replacement. Manager Don Mattingly is already on record with his belief that Pederson is Los Angeles’s best option in center going forward.

Terrance Gore, outfielder, Royals: Potentially this year’s Hamilton, light. Kansas City bumped the 23-year-old from high Class A to Class AAA, where he has 10 stolen bases in his first 15 games. In his minor-league career, he has 167 steals in 184 attempts – a success rate near 91 percent – and it’s not hard to imagine Manager Ned Yost using him in the late innings of a tie ballgame.

Gregory Polanco, outfielder, Pirates: Yes, Polanco was in a 1-for-30 skid when he was sent down to Class AAA Indianapolis earlier this week in the interest of getting more at-bats. But he remains one of the game’s top prospects, he did hit .338/.416/.441 in his first 16 major league games, and it’s not crazy to think he couldn’t eventually win an outfield job back from, say, Travis Snider.

Marco Gonzales, left-handed pitcher, Cardinals: The 2013 first-round pick made three starts for St. Louis earlier this year and turned in a 7.07 ERA, but he blitzed through the minors from high Class A through Class AAA with a 2.43 ERA and 117 strikeouts to 27 walks in 21 starts. St. Louis is likely to get Michael Wacha back sometime in the next few weeks, but the rotation’s ERA in August (4.65) is the third-worst in the N.L. Help is needed.

Jacob Lingren, left-handed pitcher, Yankees: No player taken in this June’s draft has yet appeared in the majors, but Lingren – a second-round pick out of Mississippi St. – could help a shaky Yankee bullpen after recording a 0.73 ERA at four minor league levels this summer, recording 48 strikeouts in 24-2/3 innings.

Aaron Barrett, right-handed pitcher, Nationals: It’s easy to forget that in his first 30 major league appearances, Barrett had a 1.67 ERA and 33 strikeouts in 27 innings. After giving up runs in five of his next 10 appearances, he was sent down, but in Class AAA he has righted himself with 8-1/3 scoreless innings and a 0.720 WHIP. He could pitch some key bridge innings in Washington.

There are some others worth watching, too. The Mariners could turn to hard-throwing right-hander Taijuan Walker, who started three games for Seattle earlier this summer. Detroit outfield prospect Steven Moya is huge (6-6, 230 pounds), has hit 34 homers and slugged .549 at Class AA, and the Tigers have no pop off their current bench. First base prospect Christian Walker has 25 homers in Class AA and AAA for the Orioles and could provide right-handed power off the bench.

But whatever the names, some race for some playoff spot somewhere will be impacted by a player not currently on a major league roster.