After 10 rounds of matches in Serie A, Roma have both the best attacking record, with 22 goals, and the worst defensive tally, with 19 conceded.
They have scored in every game and kept a clean sheet only once, and their home game against Palermo on Sunday has the makings of another goal feast.
Roma have twice squandered two-goal leads at home, losing 3-2 on each occasion, but have also overturned a 2-0 deficit at Genoa to win 4-2, buttressing Zeman's reputation for producing teams who pay little attention to the small matter of defending.
They handed Inter Milan a footballing lesson at San Siro, winning 3-1, but were given one themselves by leaders Juventus in a 4-1 defeat.
It is already looking as if this season will determine whether the 65-year-old Zeman's career goes up in smoke, along with his trademark 4-3-3 system, or whether he will be acclaimed as the country's greatest exponent of attacking football.
After Wednesday's 3-2 defeat to Parma on a rain-soaked pitch, talismanic striker Francesco Totti said it was up to the players to put the Czech-born coach's ideas into practice.
"We have to stay united," he said. "At the moment, we are putting into practice only half of what the coach wants and things are not going well. That is why we are not getting the results.
"It depends upon us. Our aim is third place," he said. "I can't say that we are aiming to win the title because Juventus are so superior to everyone else.
"I don't want another year of transition, I'm tired of that." Roma made sweeping changes last season only for coach Luis Henrique to quit at the end.
"We have to follow Zeman and we will come out of this tunnel," added Totti.
Zeman, who has surprised Roma fans by leaving midfielder Daniele De Rossi on the bench, agreed with Totti.
"I continue to say we are a great team. We are just paying for the fact that we do not play well for the full 90 minutes," he said.
"With a little good fortune, and above all belief, we can prove that we know how to play football."
