2nd Down and 1

Al Michaels: “First and 10 from the 30. Campbell back to pass…it’s a screen to Portis. Right sideline…a 9-yard, no make that a 10 yard gain with the spot. It’ll be 1st and 10 for the Redskins at the 40.”

John Madden: “Yeah, Al. That’s just a totally Portis thing. He just knows where the first down marker is by instinct. See, right here [during the replay], he just --BAM!—reaches across the line for the first down. It’s like he’s got radar, Al.”

Actually, in a strange way, 'Sherriff Gonna Getcha' may have just unwittingly cost his team almost a point.

Portis may have cost his team almost a point (on average) because he passed up the juiciest down-and-distance situation of all: the 2nd and 1.

It must give defensive coordinators across the league nightmares. An offense can do anything on 2nd and 1. It can run, and probably pick up the first down, but they could just as easily take a shot down the field without much risk. The QB has the luxury of a no-pressure down. He doesn't have any need to force the pass and can throw it away if needed. An incompletion still leaves a very manageable 3rd and 1. And failing that, an attempt on 4th and 1 may not be out of the question (especially if it's a short 1).

A look at the expected points for 1st and 10 situations shows there is statistical evidence that a 9 yard gain is actually preferable than a 10-yard gain. The graph below shows the average expected points for most 1st and 10 plays in the 1st half of all regular season games from 2000 to 2007. (I excluded plays inside field goal range (the 35) and plays within 2 minutes of halftime. This limits the data to normal football situations, when teams are neither desperate nor nursing big leads, and when time is not a consideration. It also removes any bias in the data due to having the option to play very conservatively inside FG range.)

We can see a fairly clear drop in expected points from a 9-yard gain to a 10-yard gain from 2.3 points to 1.6. That's about a 0.7-point drop in the average number of points scored between having a 2nd and 1, and actually getting the first down. It may not sound like a lot of points, but it's a relatively large difference for a single yard on a single play.

There is, however, some noise in the data. So how can we be sure that the sudden discontinuity between 9- and 10-yard gains isn't just a very large random blip? First, the blip is fairly large. In fact, it's the largest jump between any two yardage gains. Second, it goes in the opposite direction we'd expect it to go. Further, the graph indicates that on 1st down, a 9-yard gain is not only better than a 10-yard gain, but it's better than anything up to a 16-yard gain. It also indicates that a 2nd and 3 is notionally just as good as converting 1st and 10. Lastly, we have a good theoretical basis as to why we'd see such a result.

So am I actually suggesting that ball carriers should intentionally try for a 9-yard gain instead of try for the extra 1 or 2 yards? It might be a hard sell, but yes, the evidence is there. On the other hand, the first time anyone actually did it intentionally, and his team failed to convert the 1st down, the criticism would be merciless and it would never be done again.

However, it appears that it may already be happening, at least unintentionally. The graph below plots the frequency of each gain (or loss) from a 1st and 10. Notice the the divot at exactly 10 yards. There is an unnaturally low number of 10-yard gains compared to 9- and 11-yard gains. This could be due to how refs spot the ball or how defenses guard the 10-yard marker, but it's intriguing.

So if 2nd and 1 is really that valuable, are NFL offenses taking advantage when they get one? Are they actually taking shots down the field? After all, the advantage is only as big as offenses make it. Perhaps it could be even larger if coaches properly exploited the situation. I'll take a look at that in the next post.

Edit: I hope no one thinks I'm suggesting untouched ball carriers should spontaneously drop after 9 yards. I'm only suggesting that the outstretched arm/second effort thing can be strangely counterproductive. But mostly I'm just illustrating how the rules of football sometimes create counter-intuitive effects.

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16 Responses to “2nd Down and 1”

  1. Anonymous says:

    Outstanding analysis! However will Michaels, Madden, and NBC ever survive without you as the third man in the booth?

  2. Edward says:

    I actually noticed something similar during the Bears-Colts game last night.

    The Colts had 1st-and-10 in Bears territory, near midfield. Manning threw a pass down the right sideline that drew an illegal contact penalty on Charles Tillman.

    Now, the penalty for illegal contact is 5 yards and an automatic first down. This is different from, say, an offsides penatly, which is 5 yards and a replay of the down.

    The illegal contact resulted in the Colts advancing 5 yards and having a 1st-and-10 situation. If the penalty on the Bears had been offsides, which is considered to be a lesser pentalty (I base this on the fact it has a lesser punishment, no automatic first down), the Colts would have advanced 5 yards and had a 1st-and-5 situation.

    Granted, this issue only comes up if there's an illegal contact penatly on 1st-and-10, but it still is odd that a harsher penalty on the defense would be less beneficial to the offense than a lesser penalty.

  3. Ryan J. Parker says:

    Does this really make football sense? If it does then it's passed me, as you say:

    "Lastly, we have a good theoretical basis as to why we'd see such a result."

    So, what is this theoretical basis?

    Also, what's a 95% CI for that 10 yard result? Just like to get a little more context.

  4. Brian Burke says:

    Hi Ryan. The theoretical reason is the (almost) free shot an offense can take on 2nd and 1.

    The 95% CI is +/-0.15 points (1SE=0.075) for 9-yd gains, and it's +/-0.25 points (1SE=0.125) for 10-yd gains. So I believe the difference of 0.7 points is statistically significant.

  5. Phil says:

    Always interesting, I remember being annoyed as a kid when anything other than a deep bomb was called on 2nd and 1, kind of like being annoyed when the QB would throw it away after get a DLineman to jump offsides. Being a little older it occurs to me that that viewpoint was at least somewhat naive, but its always nice to see the offense take a shot on second and 1.

  6. Phil Birnbaum says:

    Brian, I linked to you on my site here, and Ted suggested the reason there's more 9- than 10-yard gains is because a 9.8 yard gain has to be rounded down to 9. What do you think of that theory? It sounds very plausible to me.

  7. Ryan J. Parker says:

    Thanks for the clarity Brian. I see now how it makes good football sense. The probability is so high of converting anyway that the offense can do a lot with that 2nd and 1, yes.

    Also, thanks for the CIs. That is a distinct difference that can't be ignored. Time to call Coach Fox.

  8. Matt Matros says:

    "It also indicates that a 2nd and 7 is theoretically just as good as converting 1st and 10."

    You meant 2nd and 3, right? Otherwise, great article.

  9. Mark Kamal says:

    Very frustrating when teams get 2nd and 1 and waste by handing to a fullback to dive for a one yard gain.

    Does your data account for position on the field?

    For Portis' situation, at their own 39 or 40, we compute the expected points to be 3.27 for 2nd & 1 from the 39, and 3.17 for the 1st & 10 from the 40. I think the differences you computed may be too extreme. Thoughts?


  10. Mark Kamal says:

    oops. I ran this from the NYG territory, not WAS. From WAS territory the numbers are 2.07 and 2.39 (advantage still to 2nd and 1)

  11. Brian Burke says:

    Phil-Thanks for the write-up. I agree with Ted.

    Matt-Good catch.

    Mark-I think the differences in our numbers could be due to a few things. My silly narrative was just an attempt at an entertaining intro. My graph portrays the average for all 1st down gains outside FG range, not just from that part of the field. Also, I'm only including plays from the first 28 minutes of games.

    One other difference could be due to the fact that I'm basing the analysis on the result of previous first down plays. So, technically, I'm not comparing a 2nd and 1 from the x yd line to a 1st and 10 from the x+1 yd line. I'm comparing a 9 yd gain from 1st and 10 at the y yd line to a 10 yd gain from a 1st and 10 at the y yd line. There might be a difference in that the 1st and 10 in your analysis could have been due to a change of possession and not due to a previous 10-yd gain. Or it could have been due to a longer gain on a previous play.

  12. Anonymous says:

    "So how can we be sure that the sudden discontinuity between 9- and 10-yard gains isn't just a very large random blip? "

    I think there are a lot of problems with these arguements.

    1) There are 8 instances on that graph where the added yard decreases the expected points.

    2) The number of plays is likely not the same for each of these numbers, thus each point on that graph would have a different standard deviation (perhaps 9 yard gains are much less likely than 10 yard gains due to the players knowledge of where the first down is).

    3) theoretical basis, seems to be cheerypicking. WHat is the theoretical basis that says a 5 yard loss is better than a 4 yard loss? There is a 0.4 or 0.5 difference right there.

    4) the variation from point to point on that graph indicates a uncertainty on the order of 0.5 pts. So to assume that this one jumnp is 100% valid does not follow. It may be better to say the 0.7 difference is somewhat larger than the 0.5 average point to point change, and therefore perhaps it is worth 0.2 points.


  13. Brian Burke says:

    Bob-See the above comment regarding 95% confidence intervals. It's almost certainly not a random blip. (edited)

  14. Anonymous says:

    this is a great site, and lots of cool analysis. I would make the point though that anyone can calculate a confidence interval, but that it doesn't necessarily mean anything.

    For one, football variables are not independent, everything is highly correlated.
    Two, these are not normally distributed random variables. Three, past performance is not indicative of future results.

    Regarding the CI, i'd bootstrap this data. One simple thing to do would be to plot that graph (E points by gain) for each year from 2000 to 2007. If the 2nd-and-1 peak is genuine, we should see it in every year (or at least in most years).

    Also important to know is the number of plays that went into each point, as well as if each team is equally represented.


  15. Brian Burke says:

    Bob-You're fighting hard not to accept this. I appreciate being pushed and it's how I learn, but I'm not sure what you're getting at with a couple of your comments. I'm well aware things are interdependent in football, and that past performance doesn't prove future results, etc. Not sure how to take your tone.

    The bottom line is, over the 1,974 9-yd gains and the 751 10-yd gains in the past 8 NFL seasons, teams score significantly more points following 9-yd gains.

    It's a simple average, not some crazy regression. Nor am I necessarily making specific predictions. However, based on the number of plays in the sample and the size of the effect, it's perfectly reasonable to infer the effect is systematic and would continue.

    The CI doesn't 'necessarily' mean anything? The "next expected points" variable is actually very normal (obvious enough visually that it's not even worth calculating chi-squares), for every gain amount, including 9 and 10 yards. The CIs are very strong evidence, no? Heart medications and cancer treatments have been approved based on studies with less statistical rigor.

    Good idea about bootstrapping. One year, 2002, showed a very slight advantage for the 10 yard gains. One other year, 2005, was close, but otherwise each year showed a clear advantage for the 9-yd gain over the 10-yd gain.

    I'm not very concerned about biases from individual teams. Keep in mind that 'good' offenses that get lots of 9-yd gains would also be expected to get lots of 10-yd gains. So if there is bias from team strength, it would be there for both 9- and 10-yd gains. I could take 2 hrs and do the math to prove that I suppose, but something tells me you still won't be convinced! :)

    Glad you like the site.

  16. Anonymous says:

    Actually, i think it's obvious that 2-and-1 has an advantage.

    Thanks for the info on the the yearly variation.

    I am surprised how the other points behave though, for instance, the 8 other instances where a team is better off gaining less yards.
    Losing 3 yards is better than losing 1 yard; gaining 5 yards is better than gaining 6 yards. This is what the graph shows, and I think that is wrong from a common sense point of view.

    One other point, i think you stated that the 2-and-1 was better than a 1-and-10 for up to 15 yards down field (i.e. that 0.7 score difference would need a gain of 15 yards to be made up). Most plays at 2-and-1 I would guess, are less than 15 yards (since they are mostly run plays). So, does it then follow from this analysis that the play after a 2-and-1 (the resulting 1-and-10) is less likely to score than this 2-and-1?

    That would be interesting.


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