alligator arms n.pl. in American sports, especially football, arms that are not sufficiently extended to catch a ball; generally, short arms on a player. (source: Double-Tongued Dictionary)
Further reading
For at least three centuries, declaring I’ll eat my hat! has indicated that the speaker is so certain they’re right, that if they’re not, they’re willing to swallow their chapeau. Variations of this phrase include I’ll eat my boots, I’ll eat my cap...
The phrase throw in the towel meaning “give up,” stems from boxing competitions in the late 19th. If a boxer’s team wanted to stop the fight—usually because their fighter was taking too much punishment—they would literally throw a towel into the air...
There is a definite irony to this, considering that the Florida Gators have produced a lot of good receivers.
also used to describe someone who is cheap. their arms are too short to reach their wallet.
This definition is misleading. The term “alligator arms” refers to a receiver who is afraid of taking a hit while trying to catch a pass. Because of this fear, the receiver does not extend his arms as far as he could or should. He keeps his arms closer to his body to protect himself. The term has nothing to with the physical length of a player’s arms, so the second part of the definition is way off base.