*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. *

Mike Singletary may be old school, but he sure does need some schooling.

Why? His decision to kick a field goal in the 1st half of Sunday’s game helped the Broncos. It may not have factored into the final analysis, but it easily could have.

Singletary would probably remark, like Raheem Morris in Tampa Bay, that stats are for losers.

So be it. Eventually the stats—and the expected points values—catch up to everyone (more on this later).

So, let´s get right to it, or as one of the finest poets of his generation, Dr. Dre, said, “It ain’t nuthin’ but a stat thang, baby.”

### The Setup

Singletary faced a 4th-and-1 from the Broncos’ 17-yard line with 47 seconds remaining in the first quarter. He could either:

1) Kick the relatively easy field goal.

2) Go for it.

In order to conduct our analysis, 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 49ers season. But since the sample size is somewhat limited for one team, one is inclined to use overall NFL averages from 2009:

- Teams were 62.15% on 4th downs in which they faced 1 to 2 yards
- Teams were 83.62% when kicking field goals from 30-39 yards

The reason we’re using these two assumptions is that we’re treating the decision of the 49ers as mutually exclusive. The 49ers either decide to go for 1 yard (a 4th-and-1) or the team decides to kick the field goal.

As usual, I’ll also be utilizing Brian Burke’s EPV over at Advanced NFL Stats. I often use another set of EPV from Professor Wayne Winston and Jeff Sagarin. But we are big fans of Burke’s research, and given that his EP values show similar trends, it’s fun to promote Burke (not that he needs it).

Now, using Burke’s EP values, we can make a few other assumptions about the expected value of the different scenarios the 49ers faced:

- EPV of getting a field goal: 2.3 (due to Denver’s subsequent EPV after kickoff)
- EPV of getting a first down and facing 1st-and-10 at the 16-yard line: 4.33
- EPV of turning the ball over and facing a Broncos 1st-and-10 from Denver’s own 17-yard line: -0.22
- EPV of missing the field goal and facing a Broncos 1st-and-10 from the Broncos’ own 25-yard line: -0.58 (Denver gets the ball where it’s placed, not snapped)

### The (Non-LeBron) Decision

Now, without boring you completely, 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 (-.58) = ** 1.82 Expected Points **

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

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

(.6215 x 4.33 )+(1-.6215) x (-.22) = **2.61 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. Sure, Singletary put points on the board, but even without the field goal, over the long-term, the numbers say he would have put them up anyway. Better to be aggressive in this situation.

(Note: A quick note on my opening, in which I said that over the long term, the stats catch up to everyone. This isn’t quite true. In a theoretically infinite season, Singletary would get burned; just like in poker, though, one can outdraw an opponent over and over and over, spit in the face of the odds, and do just fine. I should also point out that stats don’t pet your dog, don’t factor in whether or not your kicker just sprained his ankle, and don’t know if your QB is preoccupied with sexting. Other than that, we’re good!).

If you like to see The Dude slack off 24/7, you can always find him on Facebook and Twitter. Or you can email him at: tjthedudejohnson@gmail.com. He assumes you are following It’s All Over, Fat Man! on Facebook and Twitter, but if you are not, that’s nihilistic.