What's more, they respond.
"The work ethic and intensity (under Belichick) is so much better than before," said quarterback Bernie Kosar, who has rebounded from a miserable 1990 season to rank among the league's passing leaders this year.
"The difference is like night and day, the attention to detail in meetings and the way we go over fine points that are important to winning and losing. Bill's approach really has turned things around."
The Browns took a shocking plunge last season, falling from AFC championship finalists in 1989 to a 3-13 team in 1990. Head coach Bud Carson was fired after the season and hired as defensive coordinator with the Eagles.
Belichick, the long-time defensive coordinator with the New York Giants, the brooding tactician known as "Silent Storm" by the Giant players, was brought in to overhaul the Browns.
Owner Art Modell showed his confidence in Belichick by signing him to a five-year contract worth an estimated $2.5 million.
Modell's investment is paying dividends already as the Browns have exceeded last year's win total (they are 4-5) and rejoined the AFC playoff hunt with the Eagles coming to town for a pivotal game on Sunday.
The Browns' improvement is remarkable when you consider the team has been hit hard by injuries.
Seven defensive backs have gone down along with Pro Bowl linebacker Mike Johnson. Leading rusher Kevin Mack has been nicked off and on and scatback Eric Metcalf went on injured reserve last week with a bad shoulder.
Yet the Browns have hung tough in almost every game, a far cry from last season when they were outscored, 462-228, and embarrassed by Buffalo, 42-0, and Houston, 58-14.
Most players credit Belichick with the team's grittier attitude. He ran the toughest training camp that anyone in the Cleveland organization had ever seen. Veterans referred to it as "Stalag Belichick."
When rookie guard Ed King reported to camp late following a contract dispute, Belichick took him directly to the practice field for wind sprints - at 11 p.m.
The gate surrounding the field was locked so Belichick, King and strength coach Jerry Simmons climbed the fence in the dark. The man means business, obviously.
"Bill's work ethic is astonishing," Modell said. "I've reached him at 7 o'clock in the morning at the office and at 11 o'clock at night. He has been waiting for this opportunity all his life and he's going to make the most of it.
"I think we have a real winner, but only time will tell."
The Browns were the consensus pick to finish last in the AFC Central this season, but they blanked New England, 20-0, and nipped Cincinnati, 14-13, in Weeks 2 and 3 to generate some early momentum.
They have been competitive in every game except one, a 42-17 loss to unbeaten Washington.
The Browns still haven't beaten any of the NFL's elite teams and they are 0-3 against the NFC East with the Eagles coming up on Sunday. Cleveland lost to Dallas, 26-14, and the Giants, 13-10, before stumbling in the fourth quarter against the Redskins.
Last Sunday, Belichick's team suffered its most disappointing loss of the season, 23-21, to previously winless Cincinnati.
The Browns had four chances to win in the final five minutes, but a fumble by Mack, a dropped pass in the end zone by wide receiver Brian Brennan and two missed field goals by Matt Stover (one bounced off the upright) left them beaten and dispirited.
It will be interesting to see how the Browns respond this week facing an Eagles team that was revitalized by its 30-7 thrashing of the Giants on Monday night.
"I don't think last week's game will have any effect on us," Belichick said yesterday. "It was a disappointing loss, but it's gone now and we have to focus on the Eagles."
Ah yes, the Eagles.
Belichick knows them well.
As an assistant coach with the Giants the last 12 seasons, he developed an extensive book on their offensive personnel. Of course, a large chunk of that book became obsolete when Randall Cunningham went down and Jim McMahon took over at quarterback.
Most people would assume that makes Belichick's job easier this week as he prepares for the Randall-less Eagles. He doesn't feel that way, especially after scouting Monday night's game from the Veterans Stadium press box.
"The problems they pose (with McMahon) are different, but I don't know if they are lesser or greater," Belichick said.
"Randall made a lot of big plays by improvising. McMahon makes big plays by using his experience, reading the coverage and checking off. Big plays are big plays, no matter how you make them. Big plays are what win football games and both (quarterbacks) are capable.
"Jim McMahon has taken a team to an NFL championship," Belichick said, referring to the 1985 Chicago Bears, "and if he has done it once, he can do it again."
Bernie Kosar goes into Sunday's game with a streak of 293 consecutive pass attempts without an interception, one short of the NFL record set by Green Bay Hall of Famer Bart Starr in 1964-65 . . . This will be Kosar's first regular season appearance against the Eagles . . . Browns' No. 1 draft pick, safety Eric Turner, missed 10 weeks with a stress fracture in his left leg, but he played last week against Cincinnati . . . Veteran cornerback Frank Minnifield (shoulder) is listed as questionable.