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

As we’ll find out throughout this year, it’s not always Josh McDaniels who has to make the tough decisions. Sometimes it’s the other team’s head coach. This was the case against Seattle last week when Pete Carroll, down 7-24, faced a 4th-and-2 late in the 3rd quarter. The Seahawks were at the Denver 20-yard line and had just moved the ball quickly down the field from their own 20. Carroll had the following options:

1) Go for the 1st-down

2) Kick the field goal

The first option was certainly attractive from a risk/reward standpoint. If the Seahawks were going to recapture the momentum from the Broncos, who had been playing a great game thus far at home, they needed something big. Settling for the field goal seemed somehow deflating. And 7 points would have given the Seahawks more flexibility in the 4th quarter. Instead of needing two touchdowns, they could settle for a field goal later if necessary.

In contrast, 3 points would get the Seahawks on the scoreboard, and it would make the game a two-score affair anyway. And if, for some reason, Seattle didn’t get the 2 yards they needed, then the Broncos would still have a three-score advantage going into the 4th quarter. Perhaps getting the 3 points was the right move. The announcers seemed to agree, and on air, expressed their feelings that Seattle should settle for the field goal.

So what was the right call? We know from our 20/20 hindsight that the Seahawks didn’t convert the 4th down and indeed, from that point forward, faced a three-score gap in a game that was never really in doubt. Does that mean Carroll was wrong?

### Stats to the Rescue

What does the math tell us? As we do each week, we can use some reasonable assumptions about probability and Expected Points Value (EPV) to help us come to grips with what was probably the correct decision.

This week, I’ll be utilizing Brian Burke’s EPV over at Advanced NFL Stats. I often use another set of EPV from Professor Wayne Winston. But we are big fans of Burke’s research, and given that his EP values show similar trends, the data set is close enough for The Dude’s work.

First, however, we need to make a few (very reasonable) probability assumptions using data from all NFL teams during the entirety of last season. Here, one might also consider using data from the previous Seahawks season. But since the Seahawks changed their offense, scheme, and many of their players from last year, this year’s team doesn’t resemble last year’s squad. Thus, one is inclined to use overall NFL averages from 2009:

The reason we’re using these two assumptions is that we’re treating the decision of Seattle as mutually exclusive. The Seahawks either decide to go for 2 yards (a 4th-and-2) or the team decides to kick the field goal.

Now, using Brian Burke’s EP values, we can make a few other assumptions about the expected value of the different scenarios:

Now, without boring you with the math, we’ll apply a probability equation (using our previous percentage assumptions) to both going for the 1st down and going for the field goal:

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

(.8362 x 2.3)+(1-.8362) x (-.72) = **1.81 Expected Points **

*Here we assume there’s a 83.62% chance of making the field goal.

**2. Going For The 1st Down:**

(.6215 x 4.21 )+(1-.6215) x (-.34) = **2.49 Expected Points**

*Here we assume there’s a 62.15% change of getting the 1st down.

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 EPV of going for the 1st down is indeed higher than going for the safer field goal.

Why? That’s debatable, but for starters, the conversion rate on 4th-and-short in the NFL is quite high. And the EPV of being that far into your opponents’ territory is high as well. And even though there’s an 83% chance that Seattle would have made the field goal, the expected value of those points, when accounting for the 17% possibility of a miss along with the expected value of Denver’s kickoff return (on average, the 27-yard line), are just not enough to warrant the conservative call.

So Carroll’s call, at least from my view, was the right one, despite the fact that the Seahawks didn’t convert. You might not like Carroll’s fraternal style of coaching, but you can at least appreciate the math behind his call on Sunday.

As they say, “Sometimes you eat bar, and sometimes, well, he eats you—37.89% of the time.”

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