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Know Your Phrase - The Meanings For Common Phrases and Idioms > T-Letter Sayings
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Phrases and Idioms - The Meanings and Origins For Several Common Idioms and Phrases
It is likely that this phrase comes from sports, where groups of players come
together as a team to accomplish a specific goal. The oldest writings of this
saying that I could find come from the 1960s, and it looks to nearly always be
used in the context of sports. For example, in the Daily Review newspaper,
1960, it mentions a particular rule that a pitcher named Verron Law from the
Pirates baseball team had:

"One of his most famous rules, although Law would be the first to admit it did not originate with him, is
'There is no 'I' in team.' Perhaps that one rule is the reason why the Pirates are out in front, winning the
pannant, not backing into it."

From the other newspapers I've looked at, this phrase is frequently used by coaches, players, and even newspaper writers to imply how victory is achieved not by any single individual, but through the players coordinating their efforts together. Another example comes from Titusville Herald, 1960, where it says:

"It is refreshing to see St. Joe realize there is no 'I' in teamwork."
* Stu wanted to make a delicious dinner for his family but he wasn't such a good cook, so his wife told him 'there's no I in team' and decided to help him prepare the meal.

* Bronson Dash does not know the meaning of 'there's no I in team,' because he's always hogging the ball and denying his own players an opporunity to score!
Note: A phrase's origins are, much of the time, completely unclear. The origins you see listed are the plausible theories floating around for how or where an idiom came from, but may not necessarily be accurate. The quotes which have the phrase in them are the oldest written forms of the phrase I could find, but keep in mind that older recordings are probably out there somewhere. If you find an earlier citation than what I have, feel free to let me know!

Also, remember that just because you see a saying in an old book or newspaper, let's say from the year 1893, it does not mean the saying originates from that source. In all likelihood, if an expression is already in use in a book or newspaper, then it's probably older. Nevertheless, these old quotes serve as a way to show the reader how far back in history some of these sayings go.
The common saying There is no I in team!
Sports, in this case, it's baseball.
To not work alone, but rather, together with others in order to achieve a goal.