Roy Scheider did not receive an Oscar nomination for portraying Chief Martin Brody in Jaws.
Scheider acts as the embodiment of our feelings toward the events of the film. He plays him very well by just handling the part in a purely down to earth fashion. There is not style or flamboyance to Brody he is just a guy who is terrified of the idea of the shark as anyone would be. Sheider rightfully leaves these types of performances to Richard Dreyfuss and Robert Shaw whose characters fit that type of portrayal. He does very well to make it so we can easily empathize with Brody throughout the film and he carries us through both the terror and adventure found in the film.
This is a very reactive performance as Brody has to deal with not only the shark attacks but as well as the public reactions whether it be hysteria or denial. Scheider finds the right pitch in the way he handles each and every moment in which Brody deals with the problems presented with them. He in fact through his very grounded reactions amplifies the effectiveness of every scene. For example when the Shark kills the boy on the beach, the thing I remember most from that scene actually is Scheider absolutely perfect in that single shot of his reaction bringing the full weight of the moment through that terror in his eyes.
Scheider also does manage to create Brody into a likable character particularly through the adventure scenes late in the film. His chemistry with both Shaw and Dreyfuss is great bringing so much more to the film. Scheider makes Brody almost the straight man of the three and makes the dynamic between all three of them work. And again it must be stressed how Scheider way of just being there contributes so much like during Shaw's magnificent delivery of the Indianapolis Speech Scheider succeeds by taking the right place within it. The scene of course belongs to Shaw that is unquestionable, but Scheider does contribute through the dread he brings to Brody's face.
As Brody Scheider mixes in both the right strength and hesitations in Brody throughout and he quite excellent in really internalizes the guilt and fears of Brody. He is really great because he makes Brody a man who does have the strength to keep it together, but at the same time still definitely feels the pains from the situation particularly when he is accused of allowing more of the Shark deaths to occur. He adds the layer with subtly and it really is quite powerful because he keeps it contained without seeming a repressed man either, rather the way an honest man would deal with it.
Jaws is a one of the greatest thrillers ever made and Scheider is the perfect hero for the film. His reactionary performance is just brings so much to the film, and Scheider deserves a great deal of credit for the strength of the film as well. The best example being when we first see the shark where Spielberg is (rightfully) credited in making the scene so effective being doing the joke than cutting it off with scare. Scheider though also enjoyably delivers that joke, than is amazing as he instantly switches to just about frozen in terror, then tops it all off with his absolutely brilliant ad lib "We're Gonna Need a Bigger Boat".
This might not be your traditional "great" performance in that he does not really have a really any individual scenes just to express his character, he has to move right along with the whole story and has to express his character quickly as the film moves along. Scheider does it incredibly well though never letting us forget Brody's own personal stake while we are taken in by all that surrounds him as well. Scheider's work he adds that extra emphasis to every scene Scheider brings to us even more fear in the early attacks, and perhaps even more importantly makes feel the joy right along with him when Brody finally gets the shark.