“Winning is the best deodorant” (or “winning is a great deodorant”) means that everything smells better with winning. With losing, everything stinks.  “Winning is a great deodorant. When you win, all these things go away,” was said in August 1993 by American football coach and television color commentator John Madden. Although Madden popularized the saying, he denied coining it and called it an old sports saying. As Madden wrote in a 1997 book:
 
“There’s an old saying in sports: ‘Winning is a great deodorant.’”
 
American actress Elizabeth Taylor (1932-2011) said “There is no deodorant like success” in 1964 (and “Success is a great deodorant” in 1977).
 
   
Wikipedia: John Madden
John Earl Madden (born April 10, 1936) is a former American football player in the National Football League, a former Super Bowl-winning head coach with the Oakland Raiders in the American Football League and later the NFL, and a former color commentator for NFL telecasts. In 2006, he was inducted into the Pro Football Hall of Fame in recognition of his coaching career. He is also widely known for the long-running Madden NFL video game series he has endorsed and fronted since 1988. Madden broadcast with Pat Summerall in the 1980s and 1990s, on CBS and later Fox. He was also the last color commentator for ABC’s Monday Night Football, teaming with Al Michaels, before it moved to ESPN in 2006. His last regular role was as a commentator for NBC’s Sunday Night Football, also with Michaels. During his career, he worked as the main color commentator for all four major networks.
 
Madden has also written several books and has served as a commercial pitchman for various products and retailers. He retired from broadcasting on April 16, 2009 in order to spend more time with his family.
 
17 August 1993, Fort Worth (TX) Star-Telegram, “Sports People,” Sports, pg. 2:
SWEET SMELL OF SUCCESS
“I have this theory,” said John Madden, the CBS football analyst. “Winning is a great deodorant. When you win, all these things go away.”
 
9 January 1994, Philadelphia (PA) Inquirer, “Who wants to become an Eagles exec?”, Sports, pg. E9:
“Winning is a great deodorant,” Madden said.
 
20 January 1994, Dayton (OH) Daily News, “Bombers can’t figure out how to win; Time running out in answer search” by Marc Katz, City, pg. 1D:
“When you’re winning, you’re not worried about anything,” Derek Donald said. “When you’re winning, you don’t look for anything. When you’re losing, you look for something.
 
“Winning is the best deodorant. It covers up everything.”
   
New York (NY) Times
PRO FOOTBALL; Breakup of Cowboys’ Team Leaves a League in Wonder
By FRANK LITSKY
Published: March 30, 1994
(...)
“I don’t know if Johnson’s waiting for Shula to leave,” Madden said. “Dallas was so good for the last couple of years that I don’t like to see this happen.
 
“But you know, it’s hard to be an owner. An owner has to have a big ego. It’s easy to stay in the background with a big ego when you’re losing, but a lot tougher when you’re winning Super Bowls. Winning is a great deodorant, but sometimes it’s got problems. Sometimes, it’s not enough of a deodorant.”
 
Google Books
All Madden:
Hey, I’m Talking Pro Football!
By John Madden with Dave Anderson
New York, NY: HarperPaperbacks
1997
Pg. 125:
There’s an old saying in sports: “Winning is a great deodorant.” Winning usually solves whatever problems exist. Winning usually stops whatever smells exist.
 
23 December 1997, St. Petersburg (FL) Times, “My, how Bucs’ fortunes change” by Ernest Hooper, South Pinellas, pg. 1A:
Football analyst and former NFL coach John Madden loves to say winning is the best deodorant.
 
21 April 1998, The State (Columbia, SC), “Goody’s 500 Notes, Sports, pg. C5:
“Winning is the best deodorant there is,” John Andretti said Monday. “It covers up a lot of stink.”
 
31 October 2003, Indiana (PA) Gazette, “Treatment of coaches real mess” by Matthew Berglund, pg. 15, col. 1:
As is often said, winning is the best deodorant.
 
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adcontrarian‏
@AdContrarian  
“Winning is the best deodorant” John Madden
12:13 PM - 26 Jan 10
 
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Steve Herring
‏@ManCaveQB  
“Winning is a great deodorant, everyone smells better.” - John Madden #GoIrish This is fun.
3:17 PM - 29 Oct 11