*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. *

Most coaches play it safe. Too safe. They’d rather make a decision that likely won’t be criticized versus making a decision that has even the slightest potential for criticism from media, fans, and bloggers who still listen to Whitesnake and write from their parents’ basement.

Josh McDaniels does not—nor will he ever—play it safe. A graduate of the Belichick School of Take-This-And-Shove-It, he’s never met a 4th-and-short that he wouldn’t spit on.

I, for one, wouldn’t have it any other way.

Last week against the Colts, McDaniels once again provided us with ample opportunities to second guess his decisions. And once again he provided us with a textbook example of why going for it on 4th down, deep in your opponent’s territory, is usually the right move.

In order to analyze McDaniels’ decision, as always, we’ll split wide our two diva receivers, probability and Expected Points Value (EPV). So let’s get right to it.

By far, the most talked about decision last week came at the 8:46 mark of the 4th quarter. The Broncos were down 20-13 at the time, facing a 4th-and-3 at the Colts’ 12-yard line. As we know, Josh McDaniels faced two mutually-exclusive (it’s one or the other) decisions:

1) Go for the 1st down

2) Kick the field goal

Should McDaniels have just taken the points? The conservative coach (let’s call him Marty Schottenheimer since we all hate the Chiefs) would have surely gone with the field goal in the hopes that it would give his team a morale boost over the possibility of being mentally deflated if the team didn’t get a first down. After the game, a guy like Marty might say, “You never take points off the board.”

That sounds nice—even almost quaint. But for the love of Don Dokken, let’s at least bring some of this coach-speak into the 21st century after looking at some good old-fashioned math.

### The Decision

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

As I mentioned last week, instead of using the average for all teams in 2009, one might want to consider the 4th-down percentage for an individual team. In this case, I could have chosen the Broncos’ 4th-down-and-short percentage from last year or this year. However, I chose not to because this year’s Broncos are not last year’s Broncos and I’m not totally comfortable with such a small sample size to draw from. So I’m sticking with the overall average.

And just like last week, let’s use Brian Burke’s EP values over at Advanced NFL Stats (A quick note: visit Burke’s site one time and you will already be several standard deviations smarter than the average Raiders fan).

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

Now, let’s apply a probability equation (using our previous percentage assumptions and Burke’s EP values) to both going for the FG and the 1st down:

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

(.8362 x 2.3)+((1-.8362) x (-.34) = **1.87 Expected Points **

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

**2. Going For a 1st-down:**

(.4457 x 4.83)+(1-.4457) x (.11) = ** 2.21 Expected Points**

*Here we assume there’s a 44.57% 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 higher than going for the safer field goal.

After three weeks of this, you probably don’t even need to ask why going for the 1st down is a better call. But I know there are some Raiders fans who frequent this blog, so let’s review again. What is essentially happening with these equations is that the conversion rate on 4th-and-3 in the NFL is somewhat high. And the EP value of being that far into your opponents’ territory is worth more than a field goal in the long run. Thus, the value of a field goal, even a field goal with an 83.62% chance of success, just doesn’t yield enough expected points.

### You Wanna Wear the Hoodie? Well, Do Ya, Punk?

Another way to think about this problem is from the perspective of McDaniels himself. So, put on your hoodie and baseball cap. Now ask yourself, “How sure would I need to be of getting the 1st down in order to justify going for it?”

Here what we do is simply take the same equation, but instead of plugging in our probabilities, we solve for it as a variable. Come on, Raiders fans, a little algebra never hurt anyone. We know that the percentage chance also has to yield a greater EP value than our alternative, which as we know is 1.87 EP. So here’s how we set up the equation:

(p*4.83)+((1-p)*(.11)) = 1.87

This equation can be further refined by stating 4.83p+1.11-.11p = 1.87

Now we simply solve for our probability. The answer, of course is 37.29%.

Yes, you read that correctly. If you are an NFL head coach, facing a 4-and-3 from your opponent’s 12-yard line, you would go for the 1st-down if you reasonably thought your team had a chance better than 37% of getting the 1st down.

Now how do you feel about McDaniels’ decision? Still think he made a bad call? I would hope not. If you don’t believe that Kyle Orton and Denver’s offense can get a 1st down in this situation at the approximate rate of once in three attempts, then you probably shouldn’t be a coach. Perhaps a blogger, but never ever should you think about buying a hooded sweatshirt, buddy.

Let’s not forget that the Broncos got the ball back on the very next drive and scored the field goal anyway. Why? The numbers were on their side. McDaniels made the correct call.

McDaniels wasn’t taking points off the board. He was trying to put the most points on the board when the odds were in his favor.

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