*Note: Each Wednesday, we take a look at a critical coaching decision from the prior week’s game that had an impact on the final score—from a statistical point. *

It is rumored that during the Battle of Waterloo, Napoleon yelled to his generals, “We get the ball to start the 2nd half!” Of course, we all know how that ended. I don’t have the stats from that game, but I think the French missed a late field goal and turned the ball over 3 times, while committing stupid penalty after stupid penalty.

Fans also love talking about getting the ball to begin the 2nd half—thousands of times in front of thousands of televisions across America. It’s uttered so much, in fact, that one might assume that getting the ball to start the 3rd quarter was worth actual points.

Unfortunately, opportunity just isn’t enough in the NFL. You still have to score.

And if you do, you’ve got something the football gods are slow to lavish out on any team—momentum.

So last week when the Broncos opened the 2nd half with the ball, their own hooded Napoleon, Josh McDaniels, was looking to put the Ravens back on their beaks, take control of the game, and narrow the score to 14-17.

What happened between the looking and the kickoff is our huge decision of the week.

This decision itself came at the 13:19 mark of the 3rd quarter. Denver had just scored to end the half and were driving quite nicely. But they stalled after crossing the Ravens’ side of the field. And before you could say all-out blitz, the Broncos faced a 4th-and-7 at Baltimore’s 37-yard line.

The Broncos sent out the punt team.

The announcer (I dare not speak the name Fouts on a Broncos blog) seemed a bit astonished that Josh McDaniels wouldn’t kick the field goal in this situation with a guy like Matt Prater waiting in the (raven’s) wings.

The subsequent play resulted in a 15-yard punt for the Broncos, which I can assure you was not what McDaniels had envisioned. He was hoping to pin the Ravens deep in their own territory.

But does this make Fouts right? In hindsight, yes, the Expected Points (EP) value of where the Ravens got the ball (at their own 22) was -0.42 for the Broncos. As we’ll soon find out, going for the Field Goal had an EP value of 0.40.

But using hindsight is a really lazy way to analyze this decision. And if you you are a reader of these weekly columns, you know that it’s not hindsight we care about, it’s whether the decision was right at the time the decision was made.

And for this, we are armed with our usual suspects, probability and expected value.

So, let’s ask again. Who was right? Josh McDaniels? Or a Chargers quarterback that I hate almost as much as Philip Rivers?

Let the stats begin. Or as one of the finest poets of his generation—Kip Winger-said, “I can’t get enough, it’s never enough…”

### The Decision

For the decision McDaniels was facing, I’m using the following probability assumptions:

- 60% of punts in the midfield area land inside the 20-yard line, with the average yard-line being the opponent’s 10.7-yard line.
- 22% of the punts in the midfield area end up as touchbacks.
- 18% of the punts in the midfield area end up on the wrong side of the twenty, with the average being the opponent’s 28.7-yard line.
- Teams were 53.39% when attempting field goals of 50+ yards

A few observations about these probabilities. First, for the punt numbers and probabilities, I went back to an old article at Pro Football Reference by Jason Lisk, which you can find here. Second, I used all kicks from 50 yards and behind from 2009. One might argue for using Prater’s actual numbers from 2009 beyond 50 yards, but as many of you know, kicking percentages from kicker to kicker fluctuate wildly from year-to-year. In addition, the sample size from Prater from 2009 is simply too small.

We’re also using Brian Burke’s EP values over at Advanced NFL Stats (A quick note: visit Burke’s site one time and you will immediately be 2 standard deviations smarter than Al Davis).

Burke’s EP values tell us that we can expect the following values under our scenarios:

- EP Value of pinning the opponent at the 11-yard line (our average from the study): 0.16
- EP Value of shanking the the punt and our opponent getting the ball at their own 29-yard line (our average from the study): -0.85
- EP Value of getting a FG: 2.3 (due to the Colts’ subsequent EP value after kickoff
- EP Value of missing the Field Goal and seeing the Ravens take over with a 1st-and-10 at their own 45-yard line (where the ball is placed during the missed kick) : -1.77
- EP Value of the Ravens facing a 1st-and-10 from the their own 20-yard line: -0.34

Now, let’s apply a probability equation (using our previous percentage assumptions and Burke’s EP values) to both going for the FG and punting with the hope of pinning the Ravens inside the 20-yard line:

**1. Going For the Field Goal:**

(0.5339 x 2.3)+((1-0.5339) x (-1.77) = **0.40 Expected Points **

*Here we assume there’s an 53.39%% chance of making the field goal.

**2. Punting:**

(0.60 x 0.16) + (0.22 x -0.34) + (0.18 * -0.85) = ** -0.132 Expected Points**

*Here we assume there’s a 60% chance of getting the pinning the opponent at the 11-yard line, a 22% chance of getting a touchback, and an 18% chance of shanking the kick and putting the ball at our opponent’s 29-yard line.

Admittedly, this analysis is both complex and requires several assumptions (yes, it does make an ass out of you and the Black Hole). First, one has to determine the probability of making the field goal. Second, one has to determine the probability of getting a touchback, pinning the opponent, and lastly, shanking the punt (as Colquitt did). Lastly, one has to make a reasonable guess as to the likely yard line in which to measure the Expected Points. Hence, the averages.

Still, I’m satisfied, and I think the analysis provides a framework for such decisions. In both of these equations, we are simply applying the percentage chance of each event likely happening by the expected value of each event. We can see that the EP Value of going for the field goal was greater. In fact, punting in this situation, one could easily argue, is a losing proposition.

But McDaniels did punt, even though he should have, I would argue, gone for the points. And after the ill-fated drive, the momentum got ugly yet again, and the Broncos faced their own Waterloo at the hands of the bad-ass blackbirds from Baltimore.

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