It turns out that if a team is on the fringe of the playoff race, a good way to get back in is winning a whole bunch of games in a row. The St. Louis Cardinals confirmed that by clinching a playoff spot on Tuesday night with their 17th consecutive victory.

After the games of Sept. 10, the Cardinals found themselves with a record of 71-69, 15 games behind the Brewers in the National League Central and in fourth place among wild-card candidates, three and a half games out of the second spot. Through Tuesday, they were 88-69, still six games behind the high-flying Milwaukee Brewers but safely qualified for the playoffs.

At the start of the streak, the Cards were one game ahead of a certain New York team in the standings. Now they are 13 games up on them. Sorry, Mets fans.

With an offensive attack that includes three 30-homer players (Nolan Arenado, Tyler O’Neill and Paul Goldschmidt) and with a pitching staff that includes a 40-year-old starter, Adam Wainwright, who has 17 wins and a 3.05 E.R.A., the Cardinals will be a stern challenge in the wild-card game, even though they will be underdogs to either the Los Angeles Dodgers or the San Francisco Giants (depending on which team wins the N.L. West).

Significant winning streaks are not uncommon in baseball: Since 1900, almost 400 teams have won at least 10 in a row, for example. (No slight to the St Louis Maroons or Providence Grays, but we’re sticking with the modern era.)

But as the streaks grow longer, they grow much rarer. The Cardinals are just the 14th team since 1900 to win 17 a row, and the record streak is only 26. Or is it 22?

Should the Cardinals keep winning, beginning with Wednesday night’s game against the Brewers, they could join some truly elite company.

At 18 wins are two New York teams. The 1904 Giants won 106 games, but declined to play in the newfangled “World Series” that had been relaunched the previous season as a championship between the National and American Leagues. The 1953 Yankees had no such qualms: After sweeping to an easy pennant behind Mickey Mantle and Yogi Berra, they beat the Brooklyn Dodgers in the Series.

At 19 wins are two more World Series-winning teams, Joe DiMaggio’s 1947 Yankees and the White Sox of 1906, who beat the Yankees (then called the Highlanders) to the pennant. Oddly enough, none of the longer streaks belong to World Series winners.

At 20 wins are the 2002 Oakland Athletics, a streak immortalized in the film “Moneyball.” Game 20 was won on a pinch-hit homer by Chris Pratt, er, Scott Hatteberg.

At 21 wins are the 1935 Chicago Cubs. The streak started in September with the team two and a half games out of the pennant. The Cubs rode the streak to a four-game margin in the final standings but lost the World Series to the Tigers and wound up waiting until 2016 for a championship.

At 22 wins is Cleveland in 2017. The best team in the American League with 102 wins, the team was defeated by the Yankees in the playoffs in an upset. The streak surpasses any from the 19th century, so that makes it the record. Unless you count …

At a mind-boggling 26 games are the 1916 New York Giants, and it was a weird streak for several reasons. The team started the season 2-13 and appeared poised for a stinker of a year. But then the team stumbled upon some bizarre, if temporary, baseball magic.

The team reeled off 17 straight wins and then … it started to stink again. Its record fell from 19-13 at the end of the streak to 59-62 in September. And then, improbably, the magic returned. The Giants went on another tear, this one a record-setter, winning 26 without a loss. When they finally lost, a New York Times headline read: “Braves End Flare of Giants’ Meteor.” The end result was an 86-66 record, and only a fourth-place finish. When the team wasn’t streaking, it was 43-66.

So why is there any doubt over whether this 26-gamer is really the record? In the middle of all those W’s there is an unsightly scar: a T. Ties were not uncommon in the early part of the 20th century, when sunset wrapped games up, and the Giants had a 1-1 draw against Pittsburgh in the second game of a doubleheader that at least somewhat marred the streak.

In the Elias Sports Bureau’s official record book, which recognizes the 26-game streak as the record, ties are ignored in the calculation of win streaks. But if you’re a stickler (or a Cleveland fan), you could choose to credit the 1916 Giants with a 12-gamer and a 14-gamer sandwiched around a tie.