By Ari Rubin and Daniel Granoff

With 1:40 left in last nightâ€™s Monday Night Football game, Bears fans prayed that their team wouldnâ€™t turn the ball over or continue its impressive skill of messing up on the goal line. Chicago had first-and-goal at Green Bayâ€™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 Rodgersâ€™ hands, down 7, with a chance to tie the game. McCarthy went with option A: he felt more confident in his defenseâ€™s ability to stop the Bears from scoring than in Aaron Rodgersâ€™ shot at a successful 2 minute drill (or perhaps he was just adverse to the less conventional route, but weâ€™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, â€śwhy donâ€™t the Packers just let the Bears score so they can get the ball back?â€ť 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 Forteâ€™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 1^{st} down)= P(Forte fumbles on 2^{nd} down)= P(Forte fumbles on 3^{rd} 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 theyâ€™d have with the ball on offense.

So, P(Bears not scoring)= P(Forte fumbles on 1^{st} D)+ P(Forte fumbles on 2^{nd} D and doesnâ€™t fumble on 1^{st} D)+ P(Forte fumbles on 3^{rd} D and doesnâ€™t fumble on 1^{st} or 2^{nd} D)+ P(Gould misses a 27 yard FG and Forte doesnâ€™t fumble on 1^{st}, 2^{nd}, or 3^{rd} 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 Forteâ€™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 nightâ€™s range have made 94% of their kicks. Â 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 Packersâ€™ 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. Rodgersâ€™ 1 for 5 career conversion rate for 2 minute drills to end a game fits pretty well with the league wide average. This, plus Rodgersâ€™ domination of Chicagoâ€™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 2^{nd} and goal at the 1, to maximize his teamâ€™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, â€śwhy did the Bears even give the Packers the option to choose?â€ť 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 McCarthyâ€™s and Lovie Smithâ€™s decisions last night, thereâ€™s a lot more that goes into play selection at the end of a game than just maximizing the probability of winning.

Speaking as both Packer fan and fantasy owner down 3 points at game’s end with only Forte left, you can believe I agree with your smart thinking. McCarthyyyyy….!

I think the conclusion is even stronger than you say.

First, I get P(Bears not score) = .063 just running your numbers. I don’t see where .077 came from.

Second, if Forte fumbles, there is a probability the Bears recover. so your method is conservative. The estimate for Forte fumbles and his team doesn’t recover is lower than .0147

Hey Anon-

Thanks for the correction.

It is difficult to assign probability to the Packers actually recovering the ball in the event that Forte fumbles. We gave it the most conservative estimate: a Forte fumble equates to the Bears not scoring, just to show that even in a Packers’ defense favored scenario they still should have let the Bears scored.

Found out about you guys in the Mag…love the attention you are giving to things like this.

I think the only one who didn’t get it was McCarthy

Does the probability for the Packers to win the game if Forte fumbles get factored into this equation? Meaning, if Forte fumbled the ball and the Packers recovered, what is the probability GB can get a FG after Forte fumbles on first, second or third down? Doesn’t that have to be included into this in some way to measure the probability of a GB win or tie in that situation.

The Bears probability of not scoring is 6.3% Meaning that they will score in some way 93.7% of the time. If we include all scenarios, what is the probability of the Packers winning the game? I am just curious if the chance for a GB FG after a Forte fumble on 1st down should be taken into account in the equation.

I think that’s a really good point Scott. There are definitely other scenarios to consider, and some of them make it seem like McCarthy wasn’t necessarily wrong.

I would also like to add that Gould’s FG % could have been adversely affected because he was in a high pressure situation. The FG % may be the most sensitive part of this post’s model. Using the framework from this post, I believe the breakeven point for a Gould made field goal is 88%. In other words, if McCarthy thought Gould had less than an 88% chance of making the field goal, his decision would have been correct.

When it comes down to it, I think Smith’s decision was just as questionable as McCarthy’s. Based on Forte’s fumble rate, the best thing for the Bears probably would have been to take a knee three times and let Gould take the field goal.

I think the Bears should have taken a knee on third and goal, but getting the FG closer was a good strategy, specially after seeing Hartlett miss for the Saints from the 11 yard line. It might be that Smith instructed Forte not to go in, since the run also eats up more clock. By running three times, they took at least 5 more seconds than if they had kneeled three times.

I like your point about Hartley. For all the statistical bashing we are giving McCarthy, it is important to remember that a day earlier both the Raiders and Saints lost a game because their field goal kickers couldn’t convert in crunch time from within the fifteen yard line. This certainly could have been running through his mind as the time ran down.

So, shouldn’t the natural conclusion to all of this be that the bears should have just taken a knee on all 3 downs to maximize their chance of winning?