# Not All Yards Are Created Equal

So yesterday (and the day before) I discussed game theory as it relates to 3rd down strategy, hilighting that it appears as though NFL teams should be running much more often on 3rd and 1 (and 3rd and 2 to a lesser extent).  I also believe teams are incentivized to run more often on 3rd and 3-5, but I’ll have to come back to that later.

Today we need to start looking at one of the potential reasons for the discrepancy we saw in the Call/Success rates for Run and Pass plays.  The overall “game” that we created assumes the goal is to get a 1st down.  On 3rd and 1, that’s obviously a very important goal, but it’s not the ONLY goal, complicating our game.

In the comments, I mentioned that a potential reason for the lack of efficiency is the fact that teams may not be valuing 1st downs as highly as I expect them to.  That raises an obvious question:

How valuable are 1st downs?

To get an idea, we are going to go back to the concept of “expected points”.  Some of you will remember that our 4th Down Strategy series (and the chart accessible off the main menu above) are built from this concept and largely derived from the work of Brian Burke at AdvancedNFLStats.com.  I’m not going to go through the explanation of expected points again, since most of you are already familiar with it.  If you aren’t, see this post, which is the initial post of the 4th Down Strategy Series.

Today we are looking at just one scenario: 3rd Down and 1 yard to Go.

Obviously, in this case, the FIRST yard is the most important one.  Put differently, we should expect the bulk of the value in any 3rd down and 1 yard play to result from gaining the initial yard.  Each gained yard after that also has value, but since you only need 1 yard for a first down, we should see diminished returns after getting the conversion.

That’s pretty logical, but now I want to quantify it.  To do that, I used the data from Advanced NFL Stats, found here.  At this site, you can actually download the Expected Points spreadsheet if you’re interested in exploring it yourself.

Methodology

From this spreadsheet, I put together a fairly simple analysis.  Remember this is only for 3rd and 1.

With every 3rd and 1 play, there are two major outcomes, a first down or a fourth down.  To gain the first down, you only need 1 yard.  So I compared the expected points value of a 1st down at each yard line with the expected value of a 4th down at each yard line.

I then offset them, to account for the gained yard and looked at the difference in expected points.  Here’s an example:

3rd and 1 at the 10 yard line:  A 1st down at the 9 yard line (so gaining 1 yard) is worth 4.83 expected points.  Conversely, failing to convert, resulting in a 4th down from the 10 yard line (original spot) is worth just 2.15 points.  Therefore, in that situation, the 1 yard gain is worth 2.68 points.

Simple enough?

From there, I looked at the marginal increase in value for each additional yard.  So gaining 1 yard in the above scenario gives us a 1st and goal at the 9 yard line, worth 4.83 expected points.  Gaining 2 yards gives us a 1st and goal at the 8 yard line, which is worth 4.94 points.  Consequently, the second yard gained in that scenario is worth 0.11 expected points.

I did the same thing for the third and fourth yard gained, then put them all in an area chart seen here:

As you can see, in a 3rd and 1, the first yard gained is worth A LOT more than each yard gained after it.  If we extrapolated further, it’d become clear that in any given 3rd and 1 scenario, there are TWO particular yards that are far more important than the others: the yard that get you the first down, and the yard that gets you the TD.  In fact, the yard that gets you the TD isn’t worth as much as you think, since being stopped just short would give you a 1st and goal at the 1 (itself worth nearly 6 points).

Pulling it Together

That’s a long way of saying that teams, in 3rd and 1 situations, should be valuing that one yard above all else.  I’ll do a more detailed analysis of this later, but choosing a less optimal play (lower odds of getting the first yard) in hopes of hitting a “big play” isn’t worth it, as least not in the offensive half of the field.

Not all yards are created equal.  Any yardage that gets you a First Down should be the absolute priority on 3rd down.  This will require another post, but I’ll leave you with another example.

Given 3rd and 1 and the 20 yard line, a 1 yard run is worth 2.39 expected points.  A 5 yard gain (presumably from a pass) is worth 2.65 expected points.

Let’s just assume for a second the odds of success for each are equal to the Run/Pass odds we saw yesterday (I know that isn’t right, but its instructive). That means the expected payout for each is:

Run: 2.39 expected points * 70.7% success = 1.69 Expected Points

Pass: 2.65 expected points * 54.6% success = 1.45 Expected Points

For that to be correct, that expected yardage for a run on 3rd and 1 would have to be 1 yard and the expected yardage for a pass would have to be 5 yards, neither of which is likely the case.  However, as you can see, the difference in expected yardage gained would have to be very big to account for the difference in success rates.

Administrative Note: I may or may not be going on vacation next week.  I have no idea if I will be able to post or not, so apologies in advance if I don’t get much up.