Origins of the sports idiom "playing 500", meaning same number of wins/losses

Solution 1:

Playing 500 turns up in Google Books mainly in reference to the card game 500 until the mid-20th century, when it begins to turn up in reference to American sports. This leads me to propose that the convention derives from baseball statistics, which in turn became more widely known thanks to television and to the influence of the 1952 series of Topps baseball cards.

Statistics were already an important part of baseball fandom. Many of these specific stats, and their method of calculation, had been formulated by an Englishman, Henry Chadwick. A statistician raised on cricket, he is the one, who decided, for example, that the batting average (BA) would be defined as the number of hits (H) divided by the number of at-bats (AB), and to express the ratio as a decimal to the thousandths place.

This is the origin of the idiom batting a thousand, one of numerous expressions originating in baseball. A perfect batter would hit once every at-bat, hence have a BA of 1.000 (one thousand thousandths). Various other baseball statistics, like the misnamed fielding percentage (FP), winning percentage (WPCT), or caught stealing percentage (CS%) are also expressed as a ratio to three decimal places (and not as a percentage).

The earliest example I could find in Google Books of an application outside of baseball is a passing reference from Official Foot Ball Rules, published in 1937:

Playing .500 ball were Wooster, under the veteran L.C. Boles, and the Doc Spears directed Toledo University Fliers.

Its appearance in the langauge outside of sports jargon probably relates to sports broadcasting and, not to be underestimated, the influence of the 1952 Topps baseball card series, which included numerous design updates, among them listing key player statistics on the back. Here is an image of the 1953 Jackie Robinson card from the National Museum of American History website:

Baseball cards remained extremely popular for around four decades thereafter. There is scarcely an American boy from that era who would not have been familiar with them, whether he was a baseball fan or not.

Solution 2:

As a longtime fan of mediocre baseball teams and of Bill James, I am very familiar with the term "playing .500," meaning to win as many games as you lose over a specified period of time—81–81 over a full 162-game season, for example. The .500 is a simple fractional figure, indicating a win rate (or "winning percentage") of .500 out of 1.000—or 1 out of 2. As AlanCarmack notes in a comment elsewhere on this page, baseball is especially prone to calculate three-digit "percentages" that begin with a decimal point. More often than not, sportswriters and sportscasters use the longer expression "plating .500 ball" or "playing .500 baseball."

Instances of 'playing .500 ball' from Google Books

A Google Books search doesn't find many very old instances of the longer phrases. One early instance is from Richard Waters, "Athletics of the Week," in The Princeton Alumni Weekly (May 15, 1936):

Ball Team Breaks Even in Dartmouth Games

Our baseball team played .500 ball last week, winning two and losing two games. In view of our record so far this average is nothing to complain about. We managed to keep out of the league cellar for another week at least and at times played some excellent baseball.

Fom Harold Kaese, The Boston Braves, 1871–1953 (1954):

The first World War not only overshadowed baseball, but it caused the 1918 season to be terminated September 2. This was all right with the Braves, who finished seventh [in an eight-team league]. In mid-June they were third, but even then were not playing .500 ball. The war season ended on a glorious theme, however. After losing their first fifteen games with the Giants, the Braves beat McGraw's team in the season's very last contest.

Likewise, from Joseph Reichler & Ben Olan, Baseball's Unforgettable Games (1960):

The day before, against Mel Harder of the Cleveland Indians, DiMaggio had been hitless in three official times at bat. The Yankees then were in fourth place, playing .500 ball. It wasn't until two months and three days later that Joe went hitless again. Ironically, it was Cleveland pitching again that stopped him.

From Irving Marsh & Edward Ehre, Best Sports Stories (1961):

Some experts gifted with the infallibility of hindsight believe that the Yankees' decline goes back to the closing stages of the 1958 season when after piling up an overwhelming lead, the team failed to play .500 ball in the last fifty-five games.

(Of course, no one can play .500 ball in an odd number of games...)

From New York Magazine, volume 1 (1968):

Hodges has set a goal of winning 70 games this year and perhaps playing .500 ball next year. "These boys have it in them. They're fine boys."

(Historical note: instead of playing .500 ball in 1969, the Miracle Mets won the World Series over my team, the Baltimore Orioles.)

And here's a later instance from Bill James, The Bill James Baseball Abstract 1987:

I don't see the [White] Sox as being a contender in 1987. While I'm generally impressed by Fregosi's approach to the team, the pitching is unproven and the offense, unfortunately, is proven. I would give the Sox perhaps a 3% chance of winning the division and a 25% chance of playing .500 ball, and those would be the lowest percentages for any team in the division.

But lest you think that "playing .500" was exclusively used in the context of baseball in the old days, here is an instance from Official Foot Ball Rules (1937), referring to U.S. collegiate football:

A third group playing exceedingly creditable ball were the Rosy Starn directed Kent eleven, Bill Stobb's Wittenberg Lutherans, and Harris Lamb's Polar Bears of Ohio Northern. Closely pressing this third group come Harry Ockerman's Bowling Green outfit, Capital University with another good season under Bernlohr, and Ted Turner' Heidelberg Student Princes. Playing .500 ball were Wooster, under the veteran L. C. Boles, and the Doc Spears directed Toledo University Fliers.

Instances of 'playing .500 ball' from Library of Congress newspapers

The earliest instance of the phrase from the Library of Congress's Chronicling America newspaper database is from "Hough Again to Lead Galesburg: Profiting by Hannibal Experience He Can't Be Released if Team is Over .500," in the [Keokuk, Iowa] Daily Gate City (October 14, 1909):

The [Galesburg baseball] association agreed last night to hold Hough as manager, and not dispense with his services, if the team was playing .500 ball or better, or if it was in the first division.

From "Changes in the Baseball Fights," in the Grand Forks [North Dakota] Daily Herald and the Evening Times (May 11, 1914):

A week of contests with Cleveland and Chicago as opponents only served to increase Detroit's advantage in the American league race, the Tigers sustaining but one defeat in six games. Only one club did better than to break even, the trio playing .500 ball being Philadelphia, St. Louis and New York.

And from "Giants Tuning Up for World's Series," in the [New York] Sun (September 17, 1917):

For quite a stretch the Giants were in a pretty bad slump and had any team really been chasing them this slump might have proved dangerous. But the Phillies, in their slow, plodding way, were never able to go faster than about a .560 clip, so the Giants kept their big lead intact, though for a month they did little better than play .500 ball.

Conclusion

The idiomatic phrase "playing .500 ball" has been in use and in print since at least 1909. It probably arose in the context of U.S. baseball, but it has been in use in other sports as well for many decades. In any case the notion of "playing .500" is certainly more than a century old.

Update (4/224/2016): 'playing .500' without the 'ball'

A comment from Jim points out that all of the examples I offer above involve the phrase "playing .500 ball." Jim notes that the OP asked about the phrase "playing 500" by itself, and he argues that "There's a big difference." Examples of the phrase "playing .500" without the word ball following it are indeed less common than examples of the longer phrase. But they are hardly rare, and (I believe) they amount to a common short form of the same idea—that is, they truncate "playing .500 ball" to "playing .500" without altering the sense of the longer phrase. Here are some examples.

From "NBA: Knicks, Bucks Compete for 'Silver' Crown," in Ebony (January 1971):

The Seattle Supersonics started the season playing .500 and 6-foot-10 Bob Rule was scoring 30 points a game. He looked like he had finally found himself and was ready to lead the Supersonics to a winning season.

From Peter Gammons, Beyond the Sixth Game (1985):

"With the talent we have on this team, playing .500 is a disgrace," [Carl] Yastrzemski said the day—July 5—they finally got there, with a half-dozen potential all-stars hitting a collective .251. They had inched their way to within one game of .500 eight previous times and every time had lost the next game. Four days later [Red Sox owner Tom] Yawkey died.

From Mike Shatzkin, Baseball Explained (1987):

Games Behind is the number of games a team behind would have to beat a team ahead in order to catch up to them in games above .500. (A team is playing .500 when it has an equal number of wins and losses.)

From Chris Jaffe, Evaluating Baseball's Managers: A History and Analysis of Performance in the Major Leagues, 1876–2008 (2010):

Put in a desperate situation, they [the Red Sox] fell back on what they knew best—collapsing. After that home field deflation, they traveled to Chicago, where the White Sox swept them. That eight-game losing streak effectively ended Boston's season. The Red Sox limped along the rest of the season, barely playing .500 afterwards.

From Peter Stewart, Early Professional Baseball in Hampton Roads: A History, 1884–1928 (2010):

The Builders posted 41 wins and but 13 losses, six games better than Portsmouth, with Rocky Mount and Petersburg playing .500 or one game above it. Portsmouth reporters grumbled about losing that one game to the "Make Believers" out of Norfolk and also a forfeit victory given to the Builders by the league when Petersburg failed to show up for a game in its own park. ...

...

After falling far back of the Builders just after the start of the second half of the year and barely playing .500, Portsmouth markedly improved its record. But although they closed the gap, they could not overtake the Builders, especially after the Petersburg protests were overturned and even though they swept their opponents in a late-season series.

From Kevin Nelson, Baseball's Even Greater Insults: More Game's Most Outrageous & Irreverent Remarks (2011):

"I like to call the American League East the Fortune 500. Because they are spending a fortune and playing .500." —Syd Thrift, former AL East general manager

(Thrift's comment also appears in a collection of quotations in a 1990 issue of Scholastic Coach magazine.)

From Robert Gordon, Then Bowa Said to Schmidt...: The Greatest Phillies Stories Ever Told (2013):

The Phillies tanked quickly after that incident. They went from a contending team playing at a .655 clip for the preceding month and picking up steam to also-rans barely playing .500.

From Gary Peterson, Battle of the Bay: Bashing A's, Thrilling Giants, and the Earthquake World Series (2014):

The [Ernest] Riles experiment as among many things that went wrong in a 4–1 loss to the Mets He was indecisive on two balls that fell for doubles and was charged with an error. The Giants struck out 11 times. The team's play was so lackluster that [Roger] Craig thought something needed to be said. "I decided in the seventh inning to have a meeting," he told writers after the game. "We got to 20 games over .500 and we're playing .500 ever since. We've got to play with more intensity and fire."

From Steve Kettmann, Baseball Maverick: How Sandy Alderson Revolutionized Baseball and Revived the Mets (2015):

From June 14 onward, over the last one hundred games of the season, the Mets played .500 ball. Merely playing .500 is not enough to satisfy fans, nor is it enough to satisfy Sandy Alderson and the front office, or the owners, or anyone in the organization.

From John Thorn, Pete Palmer & David Reuther, The Hidden Game of Baseball: A Revolutionary Approach to Baseball and Its Statistics (2015):

The 1982 Card[inal]s won the pennant not by "playing .500 on the road and fattening up at home," which is the axiomatic road to success, but by playing so well on the road that the difference between their home and road records was smaller than the league average, not greater—which happens to be the true, documentable path to success.

In each of these instances, you could add the word ball immediately after the phrase "playing .500" and not change the meaning at all. It follows that "playing .500" and "playing .500 ball" are interchangeable expressions.