The history of the phrase, "to drop the ball." [closed]
Dropping the ball
Christine Ammer, The American Heritage Dictionary of Idioms (1994) offers this entry for "drop the ball":
drop the ball Make an error; miss an opportunity. For example, She really dropped the ball when she forgot to call back, or He dropped the ball, turning down their offer. This expression comes from sports where a player who fails to catch a ball is charged with an error. Its use for more general kinds of mistakes dates from about 1950.
To this description, I would only add that "drop the ball" has come to be used (in my experience) especially in connection with neglecting to perform or follow up on a task that one is supposed to be responsible for doing—much as in Ammer's first example above.
One of the earliest examples that a Google books search finds of "drop the ball" in its idiomatic sense is from Marcus Goodrich, Delilah (1941):
Lieutenant Fitzpatrick and Ensign Snell were startled. Even with danger hanging overhead like a sword on unravelling thread, the Captain never interfered with his three officers, never failed to give them a chance to go through with it, unless, as Ensign Snell phrased it, they were "about to drop the ball."
Also, from U.S. Senate Subcommittee of the Committee on Appropriations, Hearings on the Labor–Federal Security Appropriation Bill for 1947, volume 6 (1946) [snippet view]:
Senator OVERTON. Is it a departure from the usual appropriation?
Admiral HUSSEY. Had we not dropped the ball between us this item would have been included in the items presented to the House Appropriations Committee.
Richard Calhoon, Moving Ahead on Your Job (1946) [combined snippets] uses the idiom multiple times, although his imagery seems to vacillate between football and baseball:
Every time you drop the ball or assignment and someone else has to pick it up, the boss loses a little confidence in you. Again, it is a matter of getting things done and his being able to depend on their getting done.
...
When you drop the ball, fail to clean up an assignment with dispatch, or have your costs all wrong in a report, you will certainly get another chance. You can erase your mistake too. But your reputation is built according to the way you carry the ball. If you make enough fumbles, they will begin to add up. From then on, every failure will cast some doubt on your future possibilities.
...
Failures of this type hurt you as far as the boss is concerned. If in a number of cases you have dropped the ball or died on third [base], he may think of you as one of those fast starters who do not finish anything.
The California Folklore Quarterly (January 1946) [combined snippets] notes the polar opposition between "dropping the ball" and being "on the ball":
Rule Number One in any sport played with a ball is "Keep your eye on the ball." Hence, anyone who is on the ball is alert, alive, thinking clearly, and performing efficiently. The diametric opposite of this is to drop the ball, or the more popular flub the dub.
Waiting for the ball to drop
As for the ball in Times Square that drops as the New Year arrives, that event, I think, is unrelated to the idiom for committing a blunder of omission or commission. However, it may well be associated with the phrase "waiting for the ball to drop," meaning waiting for something predicted or highly anticipated or very likely to happen to come about. (In this respect the "ball" is much like the "other shoe" of a somewhat more familiar idiom.)
"Time Signals" in Papers and Proceedings of the Royal Society of Tasmania (May 1865) has an interesting item on an early "Time-ball apparatus":
The Time-ball apparatus was erected at the Royal Observatory at Greenwich in the autumn of 1833. This ball, which is five feet in diameter, is raised half-mast high at five minutes before one o'clock as a preparatory signal for the public to watch ; it is then raised to the top of the mast, and at the precise moment of one o'clock it is dropped suddenly and resumes its first position till the following day. ...
It was found at Edinburgh, that under some circumstances there was time wasted in waiting for the ball to drop, and in the event of any delay the exact time was lost. Thus the gun which could be heard everywhere effected an economy of time.
One place where this idiom occurs is in Yozo Hasegawa, Japanese Business Leadership (2011):
But Ogura balanced these concerns [about potentially inefficient service] against the potential upside. "On the other hand, homemakers wouldn't constantly be asking for rate discounts like commercial clients do. It would be a cash-based operation. The idea that cash could be earned on the spot made it all exceedingly attractive. Plus our business as it was would only get worse, and I much preferred to try something new than to sit around waiting for the ball to drop.”
The drop or descent of the ball, an old custom that dates back to the 19th century, used to indicate the time ( 1 pm or noon) to which people could set their clocks. The idea of a descending ball was adopted by Mr. Adolfo Ochs, the owner of the New York Times, to celebrate the New Years Eve from the roof of the newspaper's building in Times Square.
Time balls had been a favored way of broadcasting the time to sea travelers in the 19th century. The first one was built in 1829 by inventor Robert Wauchope. These soon became regular features in ports across the world. When the ball began its descent (1 pm in many parts of the world and noon in the US), people would set their clocks to match the ball. By the beginning of the 20th century, with the advent of radio and other more advanced technologies, the time ball became obsolete. In 1907, the time ball, while not completely considered archaic yet, was beginning to become something people just enjoyed watching.
Even without fireworks, Ochs found a new way New Yorkers could celebrate the incoming new year in style and with glorious light. In 1907, Ochs commissioned the building of an electrically-lit ball to be lowered on the flagpole of the roof of One Times Square (the new name of the newspaper’s building). A “time ball” had been the suggestion of the newspaper’s head electrician, Walter Painer, who had seen one in use on top of the close-by Western Union building.
(www.todayifoundout.com : WHY WE “DROP” THE BALL ON NEW YEAR’S EVE)