This guy's a real slime ball. Just look at him: a "short, somewhat popeyed gent" who goes around questioning everyone about their lives, trying to make a living off of telling their secrets to the whole world. And this was even before People magazine turned that into a full-time endeavor. Bump warns Roy about him:
"Most newspaper guys are your pals and know when to keep their traps shut, but to Max a private life is a personal insult Before you are here a week he will tell the public how much of your salary you send to your grandma and how good is your sex life." (2.100)
Roy doesn't need to be warned. He's already worried about Max, and his worry's justified:
He had tailed Roy from the dressing room and had spent a frustrated hour thinking I know this guy but who is he? It was on the tip of his tongue but he couldn't spit it out. He saw the face as he thought he had seen it before somewhere, but what team where, in what league, and doing what that caused him to be remembered? (4.91)
The exception was Max Mercy, who continued to concern himself with Roy's past rather than his accomplishments. He spent hours in the morgue, trying to dredge up possible clues to possible crimes, […] wrote for information to prison wardens, sheriffs, county truant officers, heads of orphan asylums, and semipro managers in many cities in the West and Northwest. (8.18)
It seems like Max won't be happy until he sees Roy go down. He constantly badgers Roy about his past, but Roy won't give it up.
Max is a sportswriter, but he also seems to be involved in some shady dealings. He's always hanging out with Memo and Gus, who turn out to be crooks. He also seemed to know ahead of time that Roy had agreed to fix the playoff game, because he had an article about it already printed as soon as the game was over.
Apart from Roy, Max is the only character present throughout the whole novel, and he works as a constant reminder of where Roy came from. Even if Max himself doesn't know, he senses that Roy has some secret and dedicates his life to trying to uncover it. Max saw him when he was a young phenom but doesn't quite recognize him now. He's a savvy enough sportswriter to know that people like Roy just don't come out of nowhere. He finally figures it out, to Roy's disgrace, and the photo of Roy's shooting is front-page news.
Max's effort to figure out Roy is a source of constant dramatic tension in the novel. Keep in mind that Malamud was able to create this story line because it took place in the 1950s. Today, anyone with an internet connection could have located all this info in about two seconds. But Max has to write thousands of letters and search through old newspapers. We're always wondering (and so is Roy) when one of his sources will come through and he'll discover the truth.