## Accept or Decline: 1st & 5 vs 2nd & Short

Your team has just run the ball for a hard-fought 8-yard gain on 1st down bringing up a 2nd and 2. The defense was flagged for offsides giving you the option of making it 1st and 5. Should your team accept or decline the penalty or take the gain?

To simplify things, let’s only consider situations between the 20-yard lines. Looking at each option in terms of the probability of converting for a 1st down, you should be indifferent. Both situations convert equally as often at an 85% rate. But 1st down probability isn’t the whole story.

We can also look at each option in terms of Expected Points, the average point advantage an offense can expect given a particular combination of down, distance and field position. In this case, the 1st and 5 is the better option. Between the 20s, where the EP curve is nearly linear, the average value of 2nd and 2 situations is 0.2 EP less than the average value of 1st and 5 situations (accounting for being 3 yards further back).

The advantage for the 1st and 5 holds throughout the range of field positions between the 20s. As an example, a 1st and 5 at midfield is worth 2.5 EP. A 2nd and 2 at an opponent’s 47, is worth 2.3.

The 1st and 5 is so valuable simply because it gives you an extra down. It’s essentially an opportunity for a free shot downfield, which is likely why the conversion probabilities are equal but the EP values are not. The defense is really in a bind because it has to guard equally against any play type. That’s true of 2nd and short as well, but the 1st and 5 gives the offense an additional down of unpredictable abandon.

Coaches should accept the penalty on gains anything short of 8 yards, simply on the basis of the probability of conversion. And on an 8-yard gain, coaches should accept the penalty on the basis of expected points. A 9-yard gain is essentially a wash, and a 2nd and 1 can be very lucrative if taken advantage of.

One caveat: This analysis is based on the assumption that between the 20s, 1st and 5s are roughly equally advantageous over a 1st and 10 at the same field position. (There just aren't that many 1st and 5s to be certain.) But as I'll show in a future post, it's possible this hasn't been the case. In fact, the data might suggest that 1st and 5s have actually been less valuable than a 1st and 10 at the same field position.

Note: Data are from the 1st and 3rd quarters of all 2,400 non-preseason games from 2000 through 2008.

### 6 Responses to “Accept or Decline: 1st & 5 vs 2nd & Short”

1. Andy says:

Brian,
I went back and read your 2nd and 1 analysis arguing that coaches fail to take advantage. The question in the comments was whether defenses adjust to stop the long pass, opening up a good run play. You said that there was no public dataset on defensive formations in a given situation, but perhaps you could look at the average yards per run on 2nd and 1 compared to 3rd and 1. This might give us some indication of what the defenses are doing.

2. Brian Burke says:

Good idea. Or compare Expected Point values.

3. Anonymous says:

Can you do this analysis for accepting a holding penalty or taking the sack.

4. Brian Burke says:

You take the sack, almost always. But yes, I'm drafting a post on that.

5. Jay Paradise says:

Hey Brian,

The only place I know that has public defensive formations available is profootballfocus.com. It would take some time to go through their player participation data and put together formations, but might be an interesting study.

The only other option is to buy football outsiders charting data, but probably not worth it.

6. James says:

If you have a list of ideas, would you consider a study on when a defense should accept a penalty on a 3rd play that didn't convert for a first down? I imagine the length of the penatly and where on the field would be significant factors to consider.