NEW ORLEANS -- They will be like two wacky scientists, hidden away in their respective laboratories with no one else around and theories racing through their head at time-warp speed trying to come up with that important secret formula.

Mike Martz will be the guy trying to come up with the offensive plan; Bill Belichick the defensive plan to stop Martz and his St. Louis Rams.

Bill Belichick is a defensive genius, but his biggest decision for Super Bowl XXXVI might be which quarterback to use.(AP)

A Super Bowl matching the Rams against Belichick's New England Patriots might not be the marquee matchup many had wanted, but it does have the best possible coaching match. When the two teams meet Sunday at the Superdome in Super Bowl XXXVI, it should cap what will be a week-long debate about which of these minds will get the better of the other.

Martz is the offensive wizard and Belichick is the defensive czar.

"We won't get much sleep this week," Martz said after beating the Philadelphia Eagles on Sunday in the NFC Championship Game.

Belichick's defenses can do that to a team. They are hard to figure out, hard to decipher. He is perhaps the best defensive mind of all time, a guy who goes against the grain in scheming opponents.

But his biggest decision might be made on the other side of the ball this week. If quarterback Tom Brady, who left Sunday's AFC Championship Game victory over the Steelers with a high-ankle sprain, isn't 100 percent, will Drew Bledsoe start against the Rams?

Even if Brady is ready to go, is there a chance that Bledsoe, who lost his job in the third week to an injury, will start? Should Bledsoe start?

He came off the bench Sunday to impressively lead the Patriots to the 24-17 upset. He looked calm in the pocket, throwing a key touchdown pass to put the Patriots up 14-3 just before half. For a guy who hadn't played since September, he looked sharp, although his numbers were not that impressive. He was 10-of-21 for 102 yards, but was effective at the right time.

Brady, though, is the guy who got the Pats into that position, going 12-3 as a starter. Even though he hadn't played great over the final month of the season, the Patriots won games and Brady didn't cause them to beat themselves. That's the way Belichick likes to play the game. Keep it close with his defense and let the offense score just enough to win.

Can that work against the Rams? Perhaps, but if Bledsoe plays, they have a better chance of keeping up with Kurt Warner and the Rams' high-scoring attack. At this point in their careers, Bledsoe offers a better passing option than Brady. That isn't to say Brady isn't on his way to a big career, but for one game Belichick might be wise to start Bledsoe.

Belichick couldn't make the move when the Patriots were rolling to the playoffs, but now he has an out. Brady is hurting and Bledsoe played well coming off the bench.

It appears it's the right time to make the move, although Belichick was non-committal Sunday.

The Vegas linesmakers have established the Rams as 16-point favorites heading into the game, no matter who starts at quarterback. It is the third-highest spread in the history of the Super Bowl, which means there aren't a lot of believers in New England's ability to win this game.

When the two teams arrive here Monday, opening a week of being swarmed by the media, the Rams will do so as a clear favorite, while the Patriots will have to deal with the reality that most think they have no chance.

New England has played in two previous Super Bowls, both on the Superdome turf, and lost both. Will the third time be the charm for the team that looks to be charmed?

Or are the Rams, who have not played a playoff game outside of a dome the past three seasons, on their way to their second Super Bowl title in three seasons? With only a week between the championship games and the Super Bowl, it will be up to the two coaches to come up with something special in a hurry that can help their teams win.

Will it be the innovative and forward-thinking mind of Martz that comes up with the right formula? Or will it be the cerebral approach of Belichick that digs up the secret formula the league has been searching for the past three seasons as they try to stop the Rams?

Both teams have won eight consecutive games, with the Rams the last team to beat the Patriots 24-17 on Nov. 18. That night Warner threw for 401 yards, but he also was intercepted twice and one was returned for a touchdown.

Martz had the answers the first time. Can Belichick pay him back in the biggest game of both their coaching careers?