Tom Brady put his stamp on the 2009 season so quickly that he could get a job processing passports at Terminal E if this quarterbacking thing doesn’t work out.

New England’s signal-caller overcame a year of rust, a shaky three quarters and a surprisingly spirited effort from the hard-luck Bills to spark one of the average, ordinary inexplicable victories that have defined his career.

You know the story from Monday night: Brady, with the help of a critical special teams turnover by Buffalo in the final two minutes, fired a pair of gorgeous late touchdown passes to Ben Watson to spark a 25-24 win over the Bills.

Brady has been on the winning end of improbable victories since the very beginning: In his very first NFL start, he helped deliver a stunning 44-13 win by the 0-2 Patriots over the 2-0 Colts that instantly changed the complexion of the 2001 season and, well, the complexion of an entire decade of pro football. Four months later, at the end of his very first season as an NFL starter, Brady led the only walk-off scoring drive in Super Bowl history.

Ho-hum. Little has changed since then, and Week 1 of the 2009 season provided another example.

While Patriots fans both celebrated the wild victory and mourned the fact that an expected blowout was so tightly contested, I stepped back to ponder the big picture.

Why do Brady’s Patriots win more often than any team in history — his 102-27 (.791) record as a starter (including playoffs) is easily the best ever — and why do they so often win in unexpected fashion like they did Monday night?

I found two reasons:

1. Brady generates big production with few mistakes

Brady produces points while limiting mistakes better than any quarterback in history.

As of Monday night, when he tossed two scores and one pick, Brady has thrown 199 touchdowns against just 87 interceptions in his career — a ratio of 2.28 TDs for every INT. It’s the greatest ratio of TDs to INTs in the history of football, and it’s critical to New England’s success under Brady.

In fact, few players are even close to this ratio. To cite some notable legends, here’s how Brady stacks up:

Brady — 2.28 TDs for every INT (199 to 87)

Steve Young — 2.17 TDs for every INT (232 to 107)

Peyton Manning — 2.01 TDs for every INT (334 to 166)

Joe Montana — 1.96 TDs for every INT (273 to 139)

Dan Marino — 1.67 TDs for every INT (420 to 252)

Brett Favre — 1.5 TDs for every INT (465 to 310)

Joe Namath — 0.79 TDs for every INT (173 to 220).

The benefit of throwing touchdowns is obvious: You put points on the board. Even Jets fans or our own Mike Adams can figure that out. The benefit of not throwing INTs is less obvious, but it’s so important that it deserves a bulletproof limo and Secret Service protection.

For example, over at Cold, Hard Football Facts, we’ve conducted an annual study of every playoff game in league history and found that every INT that a quarterback throws reduces a team’s chances of winning by about 20 percentage points.

Passers who throw 0 INTs win about 80 percent of the time.

Passers who throw 1 INT win about 60 percent of the time

Passers who throw 2 INTs win about 40 percent of the time, and so on.

Get the picture? There is no single play in football — and few plays in all of sports, period — that have such an obvious and immediate impact on a team’s ability to win like interceptions.

Brady has generated a lot of criticism in his career from ignorant football fans and pigskin “pundits” for what’s described as his “dink-and-dunk” style of play. But the truth is that Brady helps the Patriots pull out improbable victories every time he eats the ball or throws it away or dumps it off to Kevin Faulk rather than make a Brett Favre-esque risky pass downfield into triple coverage in a futile quest for the big payoff.

It’s this ability to swallow his pride and avoid mistakes rather than take wild risks that’s so critical to his historic success.

Remember the game-winning drive against the Rams in Super Bowl XXXVI? It was a classic example of the Brady style in action. Under a heavy pass rush and with the game riding in the balance, he dumped the ball off to little-used running back J.R. Redmond on three straight plays. Nobody was going to confuse his arm with a Howitzer, but the glorified handoffs led to a game-winning field goal and the only walk-off scoring drive in NFL history.

We saw a similar effort Monday night: With the exception of the two touchdowns to Watson, almost every attempt on New England’s final two drives was a short toss to Randy Moss, Wes Welker or Kevin Faulk underneath the coverage.

These two winning drives were right out of the Brady textbook. With the game on the line, the NFL’s most ruthless big-game assassin minimized mistakes, drew in the defense and lulled the Bills into a false sense of security. Then he found the soft spots in the middle of the coverage and drove two daggers into Buffalo’s defensive heart with all the professional detachment of Michael Corleone placing a pair of bullets into the heads of the Turk and Captain McCluskey.

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Most other quarterbacks and budding young gangsters in this pressure-packed situation would have fired wildly into the arms of a defender or against the restaurant wall. They would have missed the mark and blown the assignment — with a typically bad outcome.

Brady’s ability to avoid these mistakes while still producing results is his single greatest attribute.

2. Brady stays cool in bad situations

OK, the story of Tom Cool is well known in football circles. Nobody really doubts that he has that certain “it” that allows him to maintain his composure in critical situations. 

But there is statistical evidence that he’s better than any player in history in bad situations. In fact, the win against Buffalo on a night when he fired off 53 pass attempts was a historic rarity that few observers outside of the Cold, Hard Football Facts noticed.

Put most simply, Brady wins when his team feels hopeless and abandons the run and puts the ball in his hands. In fact, he wins in these situations more often and more consistently than any quarterback in history. Consider these numbers that include every NFL game since 1960:

Quarterbacks who pass the ball 40 times or more in a game win just 31 percent of the time.

Quarterbacks who pass the ball 50 times or more in a game, as Brady did Monday night, win just 22 percent of the time.

In other words, if things look bleak and you have to pass on virtually every down and you put the ball in the hands of your quarterback, chances are you’re going to lose. But Brady is a historic exception to both of these trends.

Brady is 18-8 (.692) when he attempts 40 or more passes — easily the best record in NFL history.

Brady is 7-2 (.778) when he attempts 50 or more passes — also the best record in history when his team is hopeless and turns the ball over to the quarterback.

Monday night provided a classic example of Brady winning a game that quarterbacks lose almost every single time.  

The Patriots couldn’t run the ball all night (23 attempts for 73 yards)

They abandoned the running game in the fourth quarter (New England’s final 16 offensive plays were all passes)

They were down by two touchdowns with five minutes to play

It was a recipe for disaster in most circumstances. Most quarterbacks with no running game and facing a big deficit panic. They make big mistakes. They force the ball into coverage. (Brett Favre, anyone?) They throw those critical INTs that ruin their comeback effort. They simply can’t make the plays their team needs to overcome the odds. In other words, they lose the game.

Brady simply does not follow this pattern — and the proof is in his unmatched ability to consistently overcome the historic odds and win games that teams typically lose.

Consider that only two other quarterbacks in NFL history boast as many as five wins when called upon to pass the ball 50 or more times: Hall of Famer Warren Moon went 5-5 — pretty good, actually. Hall of Famer Dan Marino went 5-11.

To cite some other notables:

“Gunslinger” Brett Favre is 3-8 when he attempts 50-plus passes.

Joe Montana went 2-3

Peyton Manning is 1-7.

Joe Namath went 0-4-1

In other words, even the best quarterbacks in history find it difficult to win when the game’s placed squarely upon their shoulders.

We got a glimpse of Brady’s ability to overcome the odds and wing his way to victory early in his career — in the controversial 16-13 overtime victory over Oakland in the 2001 playoffs. Brady attempted 52 passes on that snowy night and won the game. He pulled off a similar victory in the 2006 playoffs — a 24-21 victory over the top-seeded Chargers on a day in which he attempted 51 passes.

Throughout all of NFL history, teams are just 4-22 in the playoffs when forced to pass the ball 50 or more times. Brady’s Patriots are 2-0 in these games. All these games — the playoff wins over the Raiders and Chargers, the Monday night win over Buffalo, and a slew of other improbable Brady victories — have something in common: teams with other quarterbacks would have lost.