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# Lions-Cowboys: 4th-down decisions key

DeMarco Murray’s score came on a fourth-down play; the Cowboys rarely went for it on fourth this season. The Detroit Lions decision to punt on a fourth-and-1 play after the controversial incomplete pass to Brandon Pettigrew wasn’t the only crucial fourth-down decision in Sunday’s wild-card playoff game. Whereas the Lions’ decision to punt on this play lowered their probability of winning, the Dallas Cowboys increased their chance of winning by attempting two fourth-down conversions.

Lions: Fourth-and-1 from the Cowboys’ 46

#### Decision Analysis Calculations

The equation to calculate the expected win probability of a decision is as follows:

Expected Win Probability = (Win Prob if Successful)*(Likelihood of Success) + (Win Prob if Failure)*(1 - Likelihood of Success)

In the case of the Lions’ fourth-and-1 decision, the relevant numbers are as follows:

Likelihood of success: 62.2 percent

Win Probability if Successful: 74.1 percent

Win Probability if Failure: 53.9 percent

Go for it:

Expected Win Probability = (.741 * .622) + (.539 * .378) = 66.5 percent

Punt:

Expected Win Probability = 63 percent

With 8:25 remaining and the Lions leading 20-17, Detroit faced a fourth-and-1 play from the Dallas 46. With a long field goal (63 or 64 yards) likely not an option, the Lions had two choices: try to convert the first down or punt.

Go for it: Road teams convert 62 percent of fourth-and-one plays in the fourth quarter in similar field positions. If the Lions had gained the yard they needed, their win probability would have been 74 percent. Had they failed (and not lost any yardage), their win probability would have fallen to 54 percent.

Punt: An average punt probably would have given the ball to the Cowboys at about the 15-yard line, and the Lions’ win probability would have been 63 percent. (Instead, after a delay-of-game penalty and a shanked punt that went 10 yards, the Cowboys had the ball at their 41; that put the Lions’ win probability at 55 percent, 8 percentage points lower than in a “likely” scenario.)

With all of the statistical risks considered, the Lions made the wrong decision; their chance of winning fell by about 4 percentage points.

Cowboys: Fourth-and-goal from the 1

With 2:55 left in the third quarter, the Cowboys faced fourth-and-goal from the 1. Trailing 20-7, the Cowboys went for it and scored on DeMarco Murray’s rush touchdown. That cut the Cowboys’ deficit to six points and increased their chance of winning by 9.5 percentage points. Here is the analysis of their decision:

Go for it: Home teams have converted 52 percent of fourth-and-goal plays from the 1 since 2001. When the Cowboys gained the yard they needed, their win probability was 23 percent. If they had failed, their win probability would have been 9 percent.

Kick FG: Every field goal of that distance (about 18 yards) has been made this season. Assuming Dallas had made the field goal, its win probability would have been about 12 percent.

The Cowboys added to their win probability by about 4 percentage points by going for it on fourth and goal.

Cowboys: Fourth-and-6 from Detroit’s 42

With six minutes left and the Cowboys trailing 20-17, they faced a fourth-and-6 in Lions territory. During the regular season, the Cowboys attempted the second-fewest fourth downs (six) in the NFL. But they went for it here, and a pass from Tony Romo to Jason Witten gained 21 yards, increasing the Cowboys’ chance of winning by 18.5 percentage points.

Go for it: Since 2001, teams have converted 45 percent of fourth-and-6 plays in the fourth quarter from around that field position. If the Cowboys had gained seven yards (instead of 21), their win probability would have been 53 percent. If the Cowboys had not converted, their win probability would have been 28 percent.

Punt: By punting, assuming the ball landed on the 10-yard line, the Cowboys’ win probability would have been 37 percent.

The Cowboys added about 3 percentage points to their chance of winning by going for it on fourth and 6.

Overall, considering the Cowboys going for it twice on fourth down and the Lions not going for it on fourth-and-1, the Cowboys gained about 11 percentage points in win probability based on fourth-down decisions. That controversial play on which a flag was picked up? That was a swing of 12 percentage points in win probability - not much more than the effect of the fourth-down decisions.