It is interesting that Santiago is so interested in a team sport like baseball when his own profession as a fisherman is a solitary one. The only sense of being on a team is when Manolin is with him but that is significant. In general, Santiago appreciates baseball because it is a competitive sport and he is a competitive fisherman.
Perhaps more significant is Santiago's admiration for Joe DiMaggio. Santiago was once a great and certainly more consistent fisherman. Now he is older, has more health problems, and struggles to compete/fish at the level he did as a younger man. DiMaggio is also in the twilight of his baseball career, no longer the dominant player he once was. Santiago identifies with DiMaggio in this way: they are both older, trying to recapture the successes of their younger days, and in the end just trying to continue in their respective professions.
So, not only does Santiago identify with DiMaggio, DiMaggio is a role model for the old man. Santiago also notes that DiMaggio's father was a fisherman, another way for him to identify with DiMaggio. Even when the Yankees lose, Santiago never loses faith.
"In the American League it is the Yankees as I said," the old man said happily.
"They lost today," the boy told him.
"That means nothing. The great DiMaggio is himself again."
Since Santiago identifies with DiMaggio, to lose faith in DiMaggio would mean Santiago would lose faith in himself. Santiago continues to fish despite his bad luck of having gone 84 days without a fish. Santiago wants to be himself again; to be a successful fisherman again. He wants DiMaggio, his role model and parallel, to be himself as well. If DiMaggio can return to his former glory, so can the old man. In this way, DiMaggio resembles a figure with Christ-like potential: the potential to resurrect a career and/or to rise again. Santiago believes in the aging DiMaggio in order to believe in himself.
Also note that Santiago wants to get back to a consistent level of fishing. He has gone 84 days without a streak. One of DiMaggio's greatest records is that he went on a 56-game hitting streak in 1941 (The Old Man and the Sea was written in 1951, the last year of DiMaggio's playing career, and published in 1952). Santiago has faith that DiMaggio can at least approach the same sort of success and Santiago uses that faith to give himself the motivation to go on.