With 1:40 left in last night’s Monday Night Football game, Bears fans prayed that their team wouldn’t turn the ball over or continue its impressive skill of messing up on the goal line. Chicago had first-and-goal at Green Bay’s 9 yard line with the score tied, 17-17.
With the Bears closing in on victory, Packers coach Mike McCarthy had two options: A) play out the series and hope for a Bears fumble or a missed field goal, or B) let the Bears score and put the ball in Aaron Rodgers’ hands, down 7, with a chance to tie the game. McCarthy went with option A: he felt more confident in his defense’s ability to stop the Bears from scoring than in Aaron Rodgers’ shot at a successful 2 minute drill (or perhaps he was just adverse to the less conventional route, but we’ll let the behavioral economics guys take that one). Many Packers fans, cursing their 18 penalties on the night, and Madden players alike, must have been wondering, “why don’t the Packers just let the Bears score so they can get the ball back?” Well, HSAC was wondering too.
Based on our probability calculations, we believe that the Packers should have let the Bears score on first-and-goal. This decision would have increased the probability of extending the game into overtime by at least two fold.
To figure out the answer to this question, we calculated the probability of the Packers scoring a touchdown after they let the Bears score vs. the probability that the Bears would not score on their goal line series.
A couple of assumptions first:
1. The Bears would run all three plays with Forte, rather than passing the ball or taking a knee (the Bears did in fact put the ball in Forte’s hands three times rather than giving it to interception prone Cutler).
2. Each run is independent of one another. That is, the P(Forte fumbles on 1st down)= P(Forte fumbles on 2nd down)= P(Forte fumbles on 3rd down). While there may be some factors making these events not independent (Forte gets more tired after his first run, thus making him more likely to fumble), we can generally assume the difference in this probability is negligible.
3. We will use the baseline scenario that the Bears had first down on the 9 yard line with 1:40 to play. If the Packers had let the Bears score, they would have done it on the first play, thereby maximizing the amount of time they’d have with the ball on offense.
So, P(Bears not scoring)= P(Forte fumbles on 1st D)+ P(Forte fumbles on 2nd D and doesn’t fumble on 1st D)+ P(Forte fumbles on 3rd D and doesn’t fumble on 1st or 2nd D)+ P(Gould misses a 27 yard FG and Forte doesn’t fumble on 1st, 2nd, or 3rd D).
Since the P(Forte fumbles)=.0147, and we believe P(Robbie Gould misses a 27 yard FG)=.02, the P(Bears not scoring)=.063
A couple notes here. To calculate P(Forte fumbles), we used Forte’s career rushing fumble rate. To calculate P(Gould missing), we first found that Robbie Gould is 40/40 on kicks inside of 30 yards. Historically, kickers at Monday night’s range have made 94% of their kicks. We cannot assign 0% probability to Gould missing his kick, however, we feel his past performance is good enough to push his probability of making the kick to 98%.
Also, we used the P(Forte fumbles) as the determinant of the Bears not scoring. We did not take into account the P(Packers force a fumble). Although the Packers would be looking for a difficult goal line strip, Forte would be ultra aware of the need to hold on to the ball. We would expect just a slight change in P(Forte fumbles) in either direction, depending on the skill of the Packers’ defense.
To find the P(Packers score a TD), we used Advanced NFL Stats’ Win Probability Calculator. On average, if a team gets the ball with 1:35 left with 1 time out remaining at the 25 yard line (assuming this as the average starting point), then:
P(scoring a TD)=.16
The Packers under Aaron Rodgers are much better than an average NFL offense, which would likely bring the P(Packers score a TD) even higher than .16. Rodgers’ 1 for 5 career conversion rate for 2 minute drills to end a game fits pretty well with the league wide average. This, plus Rodgers’ domination of Chicago’s defense that day (only three drives stalled outside of field goal range) means the likelihood of him driving down the field is pretty good. In addition to this, the one 2 minute drill that the Bears defense has faced this year was an 83 yard drive by Shaun Hill and the Detroit Lions in week one, where the lack of a score should be accredited to Calvin Johnson rather than the Bears defense. Based on this evidence, the .16 figure could very well be higher.
Since P(Packers score a TD)=.16 and P(Bears not scoring)=.063, it seems giving the Bears a free touchdown would have paid off for the Packers.
A strikingly similar situation happened in Super Bowl 32, when tied with 1:47 left on the clock, Mike Holmgren told his Packers to let the Broncos score on 2nd and goal at the 1, to maximize his team’s time with the ball. While Favre was unable to drive his team down the field to score, he at least had the opportunity to get on the field, unlike Rodgers last night. While it is interesting that the probability of Green Bay scoring is much higher than Chicago not scoring, the real question is, “why did the Bears even give the Packers the option to choose?” The Bears could have taken a knee for the entire series (remember Maurice Jones-Drew last year) thereby reducing the P(Bears not scoring) to P(Robbie Gould misses the FG). As seen with both Mike McCarthy’s and Lovie Smith’s decisions last night, there’s a lot more that goes into play selection at the end of a game than just maximizing the probability of winning.