## The Value of 1st Down and 5 Situations

In a recent post I illustrated how to decide whether to accept or decline a penalty based on expected point (EP) values. I compared 1st down and 5 situations, often resulting from a defensive offside, 2nd down situations.

I had to assume a roughly linear point advantage for the 1st and 5 situations because there weren't nearly as many in the data as other situations. But when I actually plotted out the empirical average EP values for 1st and 5s and each yard line, I noticed something strange. Compared to the curve of 1st and 10 values (for which there is an abundance of data), the curve of 1st and 5 EP values was oddly shaped. As we'd expect, there is a fair advantage for 1st and 5s from a team's own 20 through the opponent's 45 or so. But from there all the way to the opponent's 5, the value of a 1st and 5 is apparently lower than that for a 1st and 10.

Here is a graph of what I'm talking about. The raw 1st and 5 average values are red, and the smoothed curve is blue (the chart legend has them swapped by mistake). The 1st and 10 values are green. Normally, you'd expect the blue line to be slightly above the green line throughout the field.

My first instinct is that it's just due to noise, but the graph above shows some pretty clear trends in the raw average EPs. I grouped the values into 10-yard increments and replotted the 1st and 5 values along with their standard errors. The red and green lines represent +/-2 standard error bands.

It looks unlikely that the shape of the curve is due to sample error. There would have to be a number of 2-standard error deviations for it to fit. So maybe there is some systematic reason why 1st and 5s are less valuable after an offense gets past midfield. Is there a bias where certain types of teams draw offside penalties in different parts of the field? Unlikely. Do coaches suddenly make dumb play calls on 1st and 5 inside midfield? I wouldn't put it past them, but it's hard to imagine any scenario that would make a 1st and 5 less valuable than a 1st and 10 at the same yard line.

The only viable theory I have is that there is a systematic bias based on offensive strength. Say there are bad offenses and good offenses. Good offenses get bigger gains on first down and would tend to decline the penalty. So we are left with bad teams accepting more than their share of 5-yd penalties. But, bad offenses would also tend to have the ball more often on their own side of the field than good offenses do. So I'd expect the values on 1st and 5 to be lower in an offense's own side of the field, not the other way around.

Ideas?

### 8 Responses to “The Value of 1st Down and 5 Situations”

1. Dave Archibald says:

You established yesterday that the conversion rate was the same between 2nd-and-2 and 1st-and-5, but the EP was greater for 1st-and-5. Your theory was that the offense had an extra down to convert a big play. The closer the offense gets to the opposing goal line, the less chance of a big play (as the defense doesn't have to cover as much of the field) and the less value in the big play (since it doesn't produce as many yards / as dramatic a field position shift). This brings the value closer to just the conversion rate, without the EP bonus.

2. Rob Eisler says:

Two things:

1. For a good offensive team, 1st and 5 is not a big advantage over 1st and 10, because they're good enough to get the ten yards anyway. 1st and 5 is more helpful for teams who have trouble getting ten tards.

2. The 1st and 5 situation comes about when a team just failed to have a good play on 1st and 10, so they had to accept the penalty. So by looking at 1st and 5, you're selecting for failure on the previous play. For a good offensive team, the value of the successful 1st and tens is higher, and you're selecting those out.

So 1st and 5 is more valuable compared to 1st and 10 for bad teams, and bad teams are a higher proportion of the data closer to the offense's own goal line.

Rob

3. Alex says:

I assume that most 1st and 5s occur due to a defensive offside penalty, and this happens more often on pass plays due to hard counts and the like. Is there something that changes about runs and passes in this situation? Maybe teams change their run to pass ratio on 1st down or when they cross midfield, or passes become less advantageous (similar to the first comment)?

4. Z-Dog says:

I suspect that this has something to do with play selection. Right in that band of midfield to about the opposing 20 is a spot on the field where teams like to take a deep shot at the end zone. This is espcially true when teams feel like they have a 'free play' the can spend on that high-probability, high-reward play.

Maybe when teams get that 5-yard penalty, and figure they won't need more than two downs to convert, they chuck it deep, and hurt their efficiency compared to 1st and ten.

5. Anonymous says:

It seems to make sense that teams wouldn't succeed in hitting big plays as they get closer to the goal line, and that means they are just trying to convert after spending a down trying to go deep. This might lead to more minimum conversions (i.e. getting the first down in 5-7 yards) which leaves you with first and 10 in less favorable field position than a conversion on first and 10 from the same field position would have.
I also wonder if negative plays are more probable in that area of the field. If a defense knows the offense is going to take a shot downfield, do interception/sack rates increase dramatically?

6. Happy says:

From the noise to signal ratio, I'd say that there is no statistically distinct relationship here.

If I accepted the proposition, however, I would consider it related to one of your prior posts on how teams run too much. A team is probably more likely (not that they should be) to run on 1st and 5 than on 1st and 10.

It would be interesting to look at the same statistics for a hand-picked group of offensively aggressive coaches. I would expect to see them take more shots downfield on 1st and 5 and end up with a higher EP.

7. Mike says:

If you assume a rationality to offsides (defenses which are better at stopping the run go offsides more because they use the timing to get the initial push [don't know if it's true probably an interesting thing to look at]) then near the goal line where run defense becomes more valuable due to selection bias you should see worse results from the offsides.

8. Anonymous says:

To come up to an answer to this question, I'd first ask the question why do teams have 1st and 5 to being with? If we assume the answer an overwhelming majority of the time is a defensive offsides (as you do), then there are two reasons why the offense is in a 1st and 5 situation:

1) The "offsides" play on first down netted the offense 5 yards or less, and accepting the penalty is obvious.

2) The "offsides" play on first down netted the offense 6 or 7 yards, and the coach accepted the penalty to get 1st and 5 over 2nd and 3 or 4.

The first one is a no-brainer, but the second one would have a bias towards bad offenses, where the need for an extra down offsets the couple of yards of field position.

Now, when you take the times that this penalty is called but not accepted, you're taking a very good gain (7+ yards) and dropping it in the "1st and 10" bucket. These can (and do) include plays where the QB detects the offsides and throws a consequence-free bomb down the field.

So, in short, "offsides" plays skew the stats in that any good play will register in the averages for the 1st and 10 bucket, giving it an advantage. Add to this that bad offensive teams will have a bias towards having more 1st and 5 situations (assuming all teams draw offisdes calls equally), and you see some of the difference.

Now, why only in enemy territory? I don't have a good answer for this, but I think another poster mentioned that the defense has less field to cover, allowing them to play tighter up front. This is a bigger disadvantage for bad offenses, who are more likely to get into 1st and 5 situations to begin with. This might explain it.