By Andrew Mooney, Boston.com Correspondent

Sunday was vintage Tom Brady. Two minute drill, down by three, the game on the line. And for the 32d time, he delivered a fourth quarter comeback victory.

Yet, had the previous two Cowboys possessions played out differently, Brady may never have had that chance. As Chad Finn pointed out on Monday, the choices of Dallas' coaching staff down the stretch "proved ripe for second guessing." Did the Cowboys’ conservative decision-making swing the game in the Pats’ favor?

With about 5:35 left in Sunday’s fourth quarter, the Cowboys faced the first of two critical decisions. Staring at 4th and goal on the New England 8 yard line, the safe choice was to kick the field goal, though it would mean giving the ball back to Tom Brady, up by only three. A Cowboys touchdown in this situation certainly would have put severe pressure on the Pats, who had managed only one touchdown the entire game.

One way to decide the optimal course is to compare the Expected Points (EP) of each decision, here measured according to the system compiled by advancednflstats.com. Every yard line on the field has an Expected Point value: the amount of points, on average, a team can expect to gain, possessing a 1st and 10 at that spot. For example, having a first down at midfield is worth two EP; in other words, averaging all the points scored on drives with a first down at the 50, a team can expect to score two points for each such trip.

On 4th and goal from the eight, the Cowboys’ probability of scoring a touchdown was about 30 percent, and the probability of converting a field goal was approximately 96 percent. Failing to convert either, and giving the Patriots the ball around their own 10, would yield an EP of -0.2; the Patriots, from that field position, can expect to score 0.2 points on average. We can find the total EP value of each decision by multiplying the probability of each outcome by its EP and adding them together.

(Note: under the Expected Point system, a touchdown (and extra point) is not actually worth seven points. The scoring team must also kick off to the opposition, giving them, in turn, about 0.4 Expected Points, which is the value of a possession beginning at their own 20 yard line.)

Aggressive Strategy
(Probability of TD)(EP value of TD) + (Probability of no TD)(EP value of no TD)

.30 * 6.6 + (1-.30) * (-0.2) = 1.84 EP

Conservative Strategy
(Probability of FG)(EP value of FG) + (Probability of no FG)(EP value of no FG)

.96 * 2.6 + (1-.96) * (-0.2) = 2.49 EP

Since, in a tie game, it is in the team’s best interest to maximize Expected Points, Cowboys head coach Jason Garrett made the right decision to kick the field goal.

The results seemed to vindicate Garrett, as the Cowboys’ defense again stifled Brady and the Pats, forcing a 3-and-out and a Zoltan Mesko punt. Less than four minutes remained on the clock, and Garrett once more had to make a game-changing choice: would he open up the offense and try to ice the game with a first down via the pass, or would he resign himself to three simple running plays and a punt, forcing the Pats to use their remaining timeouts?

This one is a little trickier to calculate, requiring a few rough estimates. Considering the outcome of this choice likely would determine the result of the game, it's better to use Win Probability (WP) here – the percent chance a team has of victory, given a certain game situation.

For a series beginning with a 1st and 10, a team has a 66 percent chance of earning another first down, assuming they use their regular offense, and not the “play it safe” approach of three runs. A first down for the Cowboys at this stage in the game forces the Patriots to use all their remaining timeouts and, in the best case scenario, the Pats get the ball back deep in their own territory with less than a minute remaining. For simplicity’s sake, let’s put the Cowboys' Win Probability in this case at 90 percent.

In running the ball three times, the Cowboys would essentially give up the chance of gaining a first down, especially against a defense that’s expecting the run. But the probability of a first down is not zero; there’s always a chance a running back could break a tackle and move the chains. Let’s put the chance of a first down here at 15 percent.

Now we need to figure out the Cowboys' Win Probability if they fail to get the first down – the outcome that was actually observed. According to this graph provided by advancednflstats.com, the Cowboys' chances of victory upon punting the ball back to the Patriots with just over 2:30 on the clock stood at 82 percent.

However, this estimate is based on a league-average opposing offense and quarterback, and Brady is anything but average. In reality, the Cowboys' Win Probability was much lower – let’s say, 65 percent. Had the Cowboys attempted to pass for the first down and thrown an incompletion, their Win Probability would be lower still – perhaps another five percent – as the Patriots would have held an additional timeout.

Now that we have all the appropriate probabilities, or at least reasonable proxies for them, we can calculate the relative merit of each strategy.

Aggressive Strategy
(Probability of first down)(WP) + (Probability of no first down)(WP)

.66 * .90 + (1-.66) * .60 = .80 WP

Conservative Strategy
(Probability of first down)(WP) + (Probability of no first down)(WP)

.15 * .90 + (1-.15) * .65 = .69 WP

Again, this second series of calculations is based heavily on estimates. Tweaking some of the percentages might give you a narrower margin, but, for practical purposes, the conclusion remains the same: the Cowboys made a mistake in playing it safe the second time. Their strategy failed to maximize their odds of winning, and they ultimately paid for it with a heart-breaking road defeat.

There's a growing body of evidence that NFL coaches are far too conservative in the manner in which they manage games: they shouldn't clam up in the fourth quarter, and they should attempt more 4th down conversions, for example. Yet many coaches fear the sort of public backlash Bill Belichick received after his infamous decision to go for it on 4th and 2 against the Colts in 2009, even though the statistics supported his call.

If you asked Belichick about that choice, he'd probably tell you he'd do it again, if he had the chance. Sure, sometimes it comes back to bite you, but you'll come out ahead in the long run if you play the percentages. In the future, Jason Garrett would do well to learn from his example.