I wonder if you ever noticed this about Radar in MASH? Once you do, you’ll never be able to stop noticing it. Radar, played by Gary Burghoff, always keeps his left hand carefully and cleverly hidden. For example, he makes a fist or puts his hand in his pocket. More specifically, he keeps the fingers of his left hand hidden. He only ever uses his right hand to reach out to take something. And often, his left-hand fingers are hidden underneath a piece of mail or clipboard. Many times, his left hand is held down at his side, just off camera. Why did Radar always hide his left hand?
Radar kept his left hand hidden because the fingers of his left hand were significantly shorter than his right hand and two of them are partially fused together. Gary Burghoff was born with a birth defect called Poland’s Syndrome, which affected the development of his fingers on that hand. You can see this in the photo below, clearly showing his left fingers while holding a football in his very first scene on the show.

In this scene, the football is thrown to Radar by Spearchucker Jones, just before he speaks the first real line of dialogue in the show.
But, Really, Why Hide His Left Hand?
I haven’t adequately answered the question, have I? He could have still shown his left hand. Well, Burghoff didn’t hide it because he was ashamed or embarrassed. Although Radar was supposed to be around 19, Gary Burghoff was in his thirties and had lived with his deformity his entire life. While he has rarely opened up about it, he surely had time to learn to deal with it. No, there are practical reasons for hiding the hand.
One reason is because Walter O’Reilly never would have been drafted given this condition. This may have been a less important reason to hide his hand since the show was fictional and the audience probably wouldn’t have picked up on it. However, the audience would have been distracted. Gary Burghoff wanted audiences to see the character and not have his left hand become a focal point. Once you start noticing him hiding his hand, it does become a focal point!
What Is Poland Syndrome?
Poland syndrome is a congenital disease characterized by unilateral (one-sided) underdevelopment of the chest wall and pectoral muscles along with upper limb abnormalities. As well, the latissimus dorsi and serratus anterior muscles are missing, along with the nipple. The arm on the same side (ipsilateral) is hypoplastic (incomplete or underdeveloped), characterized by a small hand with syndactyly, brachydactyly, or both. Gary Burghoff has both on his left hand. His fingers are shorter and two are fused together.
Radar takes his shirt off more than once on MASH, including while suntanning and it is clear that Gary Burghoff has no chest deformity. As well, the fingers on his left hand are not nearly as deformed as happens in some cases. It seems that he was not a greatly affected by Poland’s Syndrome as is possible. See my source.