Football, like just about anything in life (work, travel, choosing between a Vixen and Ratt concert), presents us with tough decisions. Often these decisions are complicated by different risks and rewards that we must evaluate side-by-side. Even more often, and without the necessary time to weigh all of our options, we simply go with what feels right at the time. If we are lucky, we try to have our cake and eat it too (Vixen opening for Ratt?). Usually, however, these decisions are mutually exclusive. In other words, it’s one option or the other.

On Sunday, Josh McDaniels was faced with such a decision. Down 24-17 and with 4:47 remaining in the 4th Quarter, the Broncos faced a 4th-and-3 from Jacksonville’s 14-yard line. McDaniels had three realistic options.

1. Go for a field goal, take the 3 points, and try to get the ball back for a score.

2. Go for the three yards and get the 1st down.

3. Go for the end zone and 7 points.

As McDaniels quickly did, I think we can all rule out option 1, the field goal. 3 points at the time was useless, and the Broncos would have had to still get the ball back and score a touchdown. So we are really left with options 2 and 3.

We all know he chose option 3, and the Broncos came within inches of tying the game.

But did he make the right decision? Should he have kicked the field goal or simply tried for the 3 yards?

Here’s how Kyle Orton felt about it:

”I love the play call. We’re going to be aggressive in those situations and let our best players have a chance to make plays.”

A few days ago, in the Denver Post, Woody Paige disagreed, and felt McDaniels should have simply gone for the 1st down because the probability of getting the 1st down was much much higher than getting the touchdown:

”...McDaniels picked the low-percentage, 20-yard pass from Orton to Lloyd. The chances of that particular play succeeding, with good one-on-one corner coverage, were minimal.”

Now, I don’t know how Paige defines minimal, but I think we can safely assume he meant squat (and no, I can’t define squat, but let’s say it’s very low).

So, again, who is right? MicDaniels/Orton? Or Woody Paige?

With a little math, probability, and Expected Points Value (EPV) we can figure this out rather quickly.

First, there’s a few assumptions we’ll need to make, based on numbers from last season:

Teams were 46.23% on 4th downs in which they faced 3 to 5 yards

Teams were 31.03% on 4th downs in which they faced 11 to 15 yards

The reason we’re using these two assumptions is that we’re treating McDaniels’ decision as mutually exclusive. He either decides to go for 3 yards (a 4th-and-3) or he decides to go for 14 yards (characterized by a 4th-and-14). We immediately note that a 31% is a much higher percentage than minimal, but clearly not as high as 46%.

Still, we can go even farther. Using EPV, we can make a few other assumptions:

EPV of getting a TD: 6.734 (it’s not 7 due to the EPV of the following kickoff)

EPV of getting a first down and facing 1st-and-10 at the 11-yard line: 5.137

EPV of turning the ball over and facing a Jags 1st-and-10 from their own 14-yard line: .645

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 touchdown:

**1. Going For the TD:**

(.3103 x 6.734) + (1-.3103)x(.654) = 2.54 EPV

*Here we assume there’s a 31.03% chance of getting the touchdown.

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

(.4623 x 5.137 )+ (1-.4623)x(.654) = 2.73 EPV

*Here we assume there’s a 46.23% change of getting the 1st down.

In both of these equations, we are simply applying the percentage chance of each event 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 more risky TD pass.

Does this mean Paige is right? Technically, yes, but not nearly by the margin he probably expected. The difference between the two choices is a rather slight 0.186 expected points. Is this enough of a difference to distinguish between the two choices in a significant way? Not really.

So we are left again with our instincts and two choices of almost equal value. Go for the TD? Or go for the 3 yards and a 1st down?

Personally, like Paige, I would have liked for the Broncos to go for the 3 yards (did I just agree with Woody Paige?). However, like McDaniels/Orton, I can understand the need to be aggressive in that situation, given that the Jags were expecting a short play. For all we know, McDaniels/Orton could have given the touchdown play a much higher chance of succeeding than 31%. Had McDaniels/Orton assumed that they had even a 50-50 chance at getting the TD, the EPV would have easily exceeded that of going for the 1st down.

One can immediately understand the trouble with using probability (outside of Raiders fans and incarceration rates) in human decision making. If the assumptions are flawed, the decision will be flawed as well. But in this case, I don’t think we were far off. The decision could have gone either way .

What do you think of this week’s “Huge Decision” by McDaniels? Did he make the right call? Feel free to back up your opinion with numbers (I hope not), emotions (I hope so), or just with your need to disagree with Woody Paige (preferred).