With 5:52 left in the 4th quarter and the score tied at 13 in Sunday’s game against the Patriots, the Cowboys faced and 3rd-and-goal from the NE 5. The play Dallas ran was a shovel pass to Tashard Choice that was stuffed for a 3-yard loss, forcing the Cowboys to kick a FG for a 3-point lead instead of going ahead by a touchdown.

The Patriots eventually drove down for the winning TD and won the game by a margin of 20-16. Because of this, many have questioned Jason Garrett’s decision to call the shovel pass, which can be seen as conservatively “playing for the field goal” instead of aggressively going for the TD, especially when going up against a strong Patriots offense that would have 5+ minutes to get either a tying FG or a winning TD.

**A mathematical look at this play call using ESPN Stats & Information’s win probability estimates and NFL success rates on various play types in goal-to-go situations shows that this shovel pass was not that bad of a call. At most, the play call (not counting the actual execution of it) cost the Cowboys about 1-2% in terms of expected win probability, well within the margin of error based on the individual tendencies of his own offense or the opposing that a coach might pick up on leading up to or during the game.**

Since the Cowboys had 5 yards to go, we can assume they would pass (runs are rare in this situation), but we can see how the numbers move based on their decision to throw a pass behind the line of scrimmage (as the shovel pass was) as opposed to throwing one into the end zone (like a back-shoulder fade or slant to Dez Bryant, as some have suggested).

We will consider three possible outcomes for each type of pass play: 1) touchdown, 2) no touchdown, but maintain possession, and 3) an interception (assuming a touchback). To assign payoffs to each of the possible outcomes, we will use ESPN Stats & Information’s win probability estimates for each of these situations:

Cowboys win probability if TD: 80%

Cowboys win probability if no TD but maintain possession: 62%

Cowboys win probability if Int (assuming touchback): 45%

Now, we can look back at NFL success rates on 3rd-and-goal pass plays from the 4-6 yardline by distance thrown using video-tracked data since 2008.

**Throw Pass Behind Line of Scrimmage**

Chance of Outcomes Based on NFL Averages Since 2008

Chance of TD: 31%

Chance of no TD, keep possession: 69%

Chance of Int: 0%

**Expected Win Probability for Pass Behind Line of Scrimmage: (0.31)*(0.80) + (0.69)*(0.62) + (0.00)*(0.45) = 68%**

**Throw Pass into End Zone**

Chance of Outcomes Based on NFL Averages Since 2008

Chance of TD: 40%

Chance of no TD, keep possession: 58%

Chance of Int: 2%

**Expected Win Probability for Pass Into End Zone: (0.40)*(0.80) + (0.58)*(0.62) + (0.02)*(0.45) = 69%**

As you can see, choosing to pass the ball behind the line as opposed to into the end zone does not make a huge difference in this situation – the Cowboys’ expected win probability is roughly the same in each case (68-69%). Essentially, Dallas forfeited a larger chance of a TD to avoid the increased cost of a possible turnover via interception. Even though the chance of an interception is so low when throwing it into the end zone, the huge cost in terms of win probability is enough to make throwing it into the end zone only slightly better than throwing a pass behind the line of scrimmage.

Even if you assume the Cowboys could call a pass play into the end zone that would have ZERO chance of being intercepted but still have a 40% chance of success (maybe like a back-shoulder fade?), then the expected win probability for such a pass would be higher than that of a pass behind the line, but again not by that much.

The actual play resulted in a 3-yard loss and dropped the Cowboys win probability to about 61%. You could blame the poor execution on Tony Romo for not changing the play, Tashard Choice for not picking up more yardage, or the Cowboys blockers for not giving Choice any space. But according to this analysis, the play call itself had a much smaller impact on the Cowboys’ chances of winning the game.