"I said, 'What Laveranues did last year, you have to do this year," Martin recalled about the conversation earlier this season. "He looked me in the eye and said, 'All right.' And he's been performing."
Moss leads the team with 38 receptions for 580 yards and seven touchdowns, emerging to fill the role Coles had last season. He is coming off one of his best games, when he had 10 catches for 121 yards and three touchdowns against the New York Giants last week.
That explosive game came against Will Allen, whom he faced annually in the Big East when Moss played for Miami and Allen played for Syracuse.
When the Jets play at Oakland on Sunday, there will be another familiar face staring back at him: former Miami teammate Phillip Buchanon.
"It's going to be fun," Moss said. "I went against him a lot in practice. He's a pretty good talent. He uses his skills the best he can. You know you have a guy that can run with you and that probably will take chances sometimes because of his speed."
Until now, the 2001 first-round pick has primarily been known as a punt returner. It has taken three years for the 5-foot-10, 185-pound Moss to show how valuable he is as a receiver. After injuries curtailed his rookie season, Moss entered last season stuck behind Coles.
And boy did Coles shine. He led the Jets with 89 catches for 1,264 yards and five touchdowns.
But he left as a free agent in the offseason after the Jets would not match an offer sheet to keep him. With Coles gone, Moss, Wayne Chrebet and Curtis Conway saw a chance to fill the void. Moss participated in an offseason strength program at Miami, where he worked out for two hours every morning.
He came into training camp stronger and bulkier. But with Chrebet and Conway as the starters, Moss did not have many opportunities.
That changed during the bye week. Following an 0-4 start in which the offense stagnated and the loss of Coles was glaring, coach Herman Edwards announced Moss would replace Conway.
Good move. Moss has a touchdown reception in each of the four games he has been a starter and has become more productive than Coles recently. His seven touchdown receptions puts him two behind league leaders Torry Holt and Randy Moss.
"He needs to be the guy that makes the big plays for us," Edwards said. "I think he feels that. We talked about that. He wants the ball, and we'll find a way to get him the ball."
Moss already has career-high numbers through just eight games, bettering the 30 catches for 433 yards and four touchdown receptions of last year.
As for Coles, he started the season with three 100-yard games, but has not reached that mark since Sept. 21. He has two touchdown receptions this year -- five fewer than Moss -- and is averaging 14.3 yards a catch, less than Moss' 15.3 average.
Moss recalls the talk with Martin, and realizes everyone knew he had to start showing his ability to make big plays.
"I'm aware of guys looking at me knowing what I have," Moss said. "But I'm one of those patient guys. If you go out there trying to break your neck to be something that you aren't, that's when you mess up and do things that you're not supposed to do."
Last year on special teams, Moss had two punt returns for touchdowns and averaged 16.5 yards a return. Though his numbers have dipped slightly this year, he still is a threat every time he touches the ball.
His speed and shiftiness make him exciting to watch no matter where he is playing.
"He's awesome. He's so much fun to watch," Chrebet said. "The more time he has out there, the more repetitions, the better he's going to be."
Moss is aware of his success this season and plans to keep building on it. He already has proven he is just as valuable as Coles.
"When you're aware of things, you just like to know about it and keep trying to get better," Moss said. "You can't just sit on them."
This story is from ESPN.com's automated news wire. Wire index
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