“A good big man will beat a good little man” (boxing adage)

“A good big man is better than a good little man” is a boxing adage, popular mostly in the heavyweight division. All other things being equal, the heavier man with the longer reach will win the fight, the adage goes. The adage is less popularly used in other weight divisions, where the fighters are roughly the same weight.
 
“A good big man is better than a good little man” was used in boat racing in 1863, cricket in 1884, and cycling in 1889. The saying’s use in boxing dates to at least 1883.
 
     
Google Books
May 1863, London Society, “University Boat Races,” pg. 458:
Certainly, the Oxford men do manage their affairs very well, and then, too, whatever luck attends a match proverbially falls to their lot Mindful that, especially over so long a course, a good big man must be better than a good little man, since 1856, when the match became annual, they have five times sent the heavier crew,—disregarding the coxswain’s weight.
         
Google Books
The Oxford and Cambridge Boat Races:
A chronicle of the contests on the Thames in which university crews have borne a part, from A.D. 1829 to A.D. 1869. Compiled from the university club books and other contemporary and authentic records ; with maps of the racing courses, index of names, and an introduction on rowing, and its value as an art and recreation.

By William Fisher MacMichael
Cambridge: Deighton, Bell, and Co.; London: Bell and Daldy
1870
Pg. 268:
Over the former, “a good big man is better than a good little man,” but it seems that this is not the case at Henley.
 
17 May 1883, Macon (GA) Telegraph and Messenger, pg. 1. cols. 8-9:
MITCHELL AND SULLIVAN.
The Plucky Little Man Overpowered
By the Slugger.
N. Y. Special to Cincinnati Enquirer.

(...)
Good judges said that Mitchell was overmatched. The old adage, a good little man can’t whip a good big man, was exemplified in this set-to.
 
8 June 1884, New York (NY) Times, “A Hero of Cricket,” pg. 12, col. 6:
Alfred Mynn was a good big man, a being notoriously better than the best of good little men.
 
Chronicling America
17 January 1888, New York (NY) Sun, ‘The Kilrain-Smith Fake,” pg. 2, col. 4:
With a laugh he replied: “Well, every now and then. But Sullivan will win, if he will only get down to training. He must do that, as Mitchell is in first-class condition. A good big man can lick a good little man.”
 
Google Books
10 May 1889, The Wheeling and Cycling Trade Review, pg. 252, col. 1:
“With such men as Synyer, Osmond and Illslon, Crist and Windle have very little chance on account of their small size. A good big man is better than a good little man every time, you know.”
   
Google News Archive
29 September 1907, Pittsburg (PA) Press, “Ketchell May Pepper Gans” by Jimmie Mason, pg. 21, cols. 4-5:
There is an old saying that a good big man is better than a good little man. and I have yet to see where it does not hold good in the boxing game.
 
1 December 1912, Cleveland (OH) Plain Dealer, pg. 4C. cols. 1-2:
NEW RING STYLES
RULES OUT ADAGE
Good Big Man Cannot Al-
ways Whip Good Little
Man Nowadays.

BY W. W. NAUGHTON.
(...)
Among the time honored adages of the prize ring is one that says in effect, “A good little man cannot be expected to defeat a good big man.”
 
It is doubtful if the argument holds good in modern pugilism.
 
Google News Archive
19 June 1941, New London (CT) Evening Day, “The Sports Docket” by Jimmy Watterson, pg. 20, col. 7:
A good little man cannot beat a good big man. This is a boxing phraseology we have heard since we were knee high to a grasshopper. But a good little man can lick a good big man and that little man is Billy Conn. The big man is Champion Joe Louis.
 
Bad Left Hook
Classic Fight Series: When Carmen Basilio Beat the Greatest of All-Time
by Bad Left Hook on Nov 23, 2011 8:35 PM EST in Boxing History
(...) 
The “good big man beats good little man” cliché apparently trumped “guy in his prime vs. guy in the twilight”.