Almost Kicking Away a Chance at the Playoffs - Green Bay at Chicago - December 29, 2013

With the NFC North title on the line, the Green Bay Packers came back from a 28-20 deficit against the rival Chicago Bears.  Quarterback Aaron Rodgers, in his first game back from a fractured collarbone, drove the Packers from their own 13 yard line for the winning touchdown to receiver Randall Cobb, also back from injury.  A thrilling finish, one which I watched alongside many Packers fans in a bar in Wisconsin.  (Also at the same time, the Chargers were completing their own comeback, also for a playoff spot)

The Packers comeback almost didn't happen.   Coach Mike McCarthy almost prevented his own team from this comeback by sending out the punt team on a 4th-and-1 situation in their own half of the field. His offense had to talk him out of punting and go for it.  The linked nfl.com article calls it a gamble.  Many others in the bar thought it was an obvious play.

So was it a gamble, the right call, or could it go either way?

The Situation

Losing by 1 point, 28-27, with 4:41 to go in the game, the Packers face a 4th-and-1 at their own 22 yard line. This game is basically a playoff game, with the winner earning a spot in the playoffs as NFC North Champions, and the loser going home.  What should the Packers do in this spot?  To figure this out, we need to see what the Win Probability (WP) of each decision, to punt or to go for it.  We need to look at several factors to see what the right decision is.

The Factors

Coaches and fans can talk about "trusting their defense" or "pinning the other team back", but it basically comes down to several probabilities:

1. The probability of success on this 4th down and 1.
2. The probability of winning the game, given a conversion on this 4th and 1.
3. The probability of winning the game, given a punt to the Bears.

While we might not be completely accurate with these numbers, we can put in some estimates and see which decision gives the best chance of the Packers winning.  To get some ballpark figures, we will once again go to our friends at Advanced NFL Stats.

Success on 4th and 1

A 4th down conversion is likely with the Packers high powered offense.  Indeed, most of the time, the decision not to go for it on 4th and 1 (in most situations) is not because of lack of confidence in the offense, but because coaches are reluctant to turn the ball over in poor field position if the offense fails.  Coaches think this is a disaster if they fail to make the line to gain but never consider the upside of succeeding.

According to the 4th down calculator from advancednflstats.com, the average team has a 74 percent chance of converting in a 4th and 1 situation.  We will use that number for now, but assuming the conservatism of NFL coaches, we will look at what happens when this number changes.

Winning the Game After Converting this 4th and 1

The Packers only need to get a field goal to go ahead.  If they do so, it will also be likely there will be under 3 minutes left in the game for the Bears to mount their own comeback.  Of course, the Packers, with their offense, are also likely to score a TD here as well, making it even more difficult for the Bears to win.

The calculator gives the Packers a 50 percent chance of winning the game, if they convert this 4th down try.  This takes into account the chances of the Bears mounting a comeback as well, but is really based on average NFL data.  We can also adjust this number later to see how it affects the decision.

Winning the Game After Punting

If the Packers punt, they will be giving up the ball to the Bears, barring some fluke fumble.  The Bears would then be able to take down the clock again, though the Packers did retain one timeout.  Even on a 3-and-out, the Bears would still be able to take the clock down 80 seconds, leaving less than 3:20 left in the game before the inevitable punt.  That's of course if the Packers were able to stop the Bears on 3 plays.  The Packers defense rank in the bottom 10 of NFL teams as far as yards given up.

Also, the Bears have top return man Devin Hester returning the punt, a sure bet the Bears chances in this situation would be more than that of an average NFL team if they received the ball.

These factors would make it less likely the Packers win if they punt, but for now, we can go with the calculator's estimate of a 27 percent chance of winning the game if they punt.

Other Assumptions

There is one assumptions that we haven't stated yet, but we can safely make.  If the Packers fail on this 4th and 1, they will lose the game 100% of the time.  This assumption overstates the worst case outcome should the Packers fail.

It also really makes our calculations a lot simpler.  In the actual game, the actual chance of winning would not be 0, but pretty low, probably below 10% depending on how fast the Bears scored.

The Calculations

To figure the chance of winning if the Packers go for it, we must multiply the probability of 4th down success by the chance of winning the game if they convert.  Normally, we would also do the same for the probability of failure by the Packers WP if they fail, however our assumption makes this calculation easier.

The full calculation:

WP(Go for It) = P(Convert)WP(Conversion success) + P(Failure)WP(Failure)

WP(Go For It) = (.74)(.50) + (.26)(0)

WP(Go For It) = .37

The Packers have a 37% chance of winning the game if they go for it, not a great chance of winning, but given the fact they are behind, something expected.

However, we need to compare this number to the probability of winning the game if they punt. We figured that earlier as a 27% chance of winning. 

Conclusion

With these numbers, Mike McCarthy was going to give up 10% chance of winning the game, something that's not a trivial matter in today's NFL.  Thank goodness his players talked him out of it.  Though coaches like to talk about "playing the percentages," a lot of times they have no idea what those percentages actually are.

The verdict: Given these assumptions, it's obvious to go for it in an attempt to win the game and the NFC North.

Alternate Calculations

Maybe you think kicking was the right move and the Packers got "lucky" to win.  Maybe you think the Bears are awful and don't have that much of a chance to win, or maybe the Packers offense isn't good enough to convert this 4th down any regularity.  Let's look at a couple of situations which will require some math.  We'll look at the 3 numbers we've calculated before, and try to change each one to see what how bad it would have to get before it's the right decision to punt.

1. How bad does the Packers' chance of converting the 4th down have to be to make punting the right decision?
2. Changing the Packers' chance of winning the game, even after they convert the 4th down.
3. How bad does the Bears offense have to be to make punting the right decision?

Hopefully it's clear, the better the Packer offense is here, the more often they should go for it.  This of course is partly because there's a higher chance in converting this particular 4th down, but also increases the chance they can come back if the Bears score on the short field.  Note, this means a non-zero chance of winning the game, even if they fail this 4th down try.

Changing the Offensive Chances

If we make the Packers' chance of converting this 4th down worse, it makes it more right to kick the ball away and try to stop the Bears on defense.  Making this number smaller simulates a coach's pessimism on how well his offense will perform here.

How bad does this number have to be?  We will use our previous assumptions, but change the chances the the Packers will convert this 4th down.  Let's let x represent the chance of converting this 4th down.

It then becomes right for the Packers to punt IF:

WP(go for it) < WP(punting)

(x)(.50) < .27

Dividing both sides by .50 gets

x < .54

Given all other factors the same, it becomes right on punt only if the chances of conversion are less than 54%.  The Packers have a high enough powered offense that the chance of conversion is much greater than that.

Changing the Probability of Winning if Successful

Now, instead of changing the chances of converting, let's change the Win Probability of the Packers if they do convert.  Making this number smaller reflects a coach reliance on playing the field position game and the pessimism of scoring from deep in their own territory.

Again, we will use our previous assumptions, but this time change the probability the Packers will win, even if they convert.  Let's let x represent the chance of winning if they convert.

It then becomes right for the Packers to punt IF:

WP(go for it) < WP(punting)

(.74)(x) < .27

Dividing both sides by .74 gets

x < .365

The Packers should punt only if their chances of winning the game even if they convert is less than 36.5%.  Since they only need to kick a field goal in order to go ahead (driving 50-60 yards instead of the full 80), the chances of winning are surely more than that.

Changing the Probability of Winning on a Punt

The Packers defense is also one of the worst in the league, but if we assume they're better (or the Bears offense worse), the better the chances are of the Packers winning the game after punting.  How much better must their chances be to justify punting?  

Again, keeping the same assumptions as before, we let x this time be the chances the Packers will win after punting the ball away.

WP(go for it) < WP(punting)

(.74)(.50) < x

Completing the expression of the left gets us:

.37 < x

The chances of the Packers have to be greater than 37% even after they punt the ball away.  To look at this the other way around, the Bears would have win the game less than 63% to make punting correct.  Even if you think Jay Cutler isn't so good, and even if you have no faith in the Bears offense (even against the Packers defense), being ahead with less than 5 minutes to go is surely a position I'd want my team to be in.

Comments?

Again, if you disagree, please feel free to leave me a comment!