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A couple of weeks ago, Brian Burke of Advanced Football Analytics (formerly Advanced NFL Stats) wrote a great post on the value of a first down. From that post, we concluded that the marginal value of a first down is 9 yards, and we’ve previously determined that the marginal value of a touchdown is 20 yards. Therefore, we can create an Adjusted Yards per Carry statistic, which can be calculated as follows:

Adjusted Yards per Carry = (Rushing Yards + 20 * Rushing TDs + 9 * Rushing First Downs) / Rushes

If we use this metric to analyze the 2013 season, how would it look? Last year, the Eagles averaged 5.13 yards per carry and 8.29 Adjusted YPC, courtesy of the fact that the team led the NFL in rushing first downs. Philadelphia also ranked 1st in the NFL in both of those metrics and in overall rushing yards.


So what are the biggest differences we see when using Adjusted YPC compared to general YPC?

  • The Dolphins ranked 17th in yards per carry, but just 25th in Adjusted Yards per Carry. One reason: Miami ranked last in rushing first downs with just 61. Lamar Miller may have averaged a respectable 4.0 yards per carry, but he gained just 27 first downs on 177 runs. For reference: Trent Richardson rushed for 27 first downs last year, too, on 188 carries.
  • The Jets ranked 6th in rushing yards and 10th in yards per carry, but just 17th in AYPC. New York ranked 5th in rushes of over 25 yards, which helps the team’s YPC average, but long runs aren’t as valuable in Adjusted Yards per Carry.
  • The Panthers ranked 16th in YPC but 11th in AYPC. That makes sense: Carolina loves to run in short-yardage situations, which tends to lower YPC averages. But if the team is successful, they pick up a 9-yard bonus, and Carolina ranked 2nd in rushing first downs in 2013.
  • Denver ranked 20th in yards per carry and 14th in AYPC. The Broncos ranked 10th in touchdowns per carry and 11th in first downs per carry, so that was enough to offset the team’s mediocre yards per rush average.
  • The biggest positive mover on the list was Detroit. The Lions ranked 22nd in yards per carry but 15th in AYPC. What gives? Detroit converted 19-of-24 times when running on 3rd- or 4th-and-1 or 2, the 6th-best rate in the league. The team was also 13th in touchdowns per carry. With Reggie Bush and Joique Bell, Detroit had a pretty effective running game in 2013 — well, let’s hold off on that statement for a moment — and the 22nd-place ranking in YPC doesn’t reflect that.

What if we bring in the Football Outsiders and Advanced Football Analytics rushing rankings? Take a look:


Football Outsiders was very down on the Jets running game relative to the team’s lofty YPC average; using Adjusted YPC helps in this case, although FO was even more negative on the team’s running game. The Panthers are another team where the use of Adjusted YPC helps bridge the gap between the team’s DVOA rank and YPC rank. Carolina ranked 16th in YPC, 11th in AYPC, and 4th in DVOA. In general, AYPC seems to “work”, if the goal is to make YPC look more like DVOA. One big exception is Detroit: Football Outsiders thought the Lions running game was even worse than its 27th-place YPC average. There’s a very good reason for that, but I’ll give you a minute to see if you can figure it out.

Using AYPC also helps converge the YPC rankings and the Advanced Football Analytics rankings. For example, Denver ranked 5th in AFA’s rankings and 20th in YPC, but 14th in Adjusted Yards per Carry. Carolina also ranked 4th in AFA’s rankings along with DVOA. In general, I find the evidence pretty persuasive — and this shouldn’t be a surprise — that if the intent is to mimic either DVOA or EPA, using Adjusted Yards per Carry is better than using Yards per Carry.

Of course, Detroit again is an outlier in the AFA metrics — the Lions ranked 24th in AFA’s rankings. So why do both FO and AFA place low grades on the Lions rushing attack, even though the team was better at gaining first downs and touchdowns than its YPC average would indicate? Because Detroit lost ten fumbles on rushing plays last year, the most in the league. In fact, the Giants, with 8, were the only other team to lose more than six fumbles in 2013.

  • This is fantastic, I’m all for expanding the principle of “adjusted” metrics that first really started with QB’s Y/A. Thanks Chase and Brian.

    • Chase Stuart

      Thanks Topher.

  • Nick Bradley

    DVOA corrects fumbles lost for league averages…recoveries are statistically random.

    Perhaps something else in FOs box.

    AFA doesn’t do that. So, they both penalize for different reasons?

    • Chase Stuart

      Yeah, presumably Detroit also had a lot of fumbles, too, but you bring up a good point. I believe the lost fumbles penalty would be more severe at AFA because they are not regressed.

  • Ian

    Carolina’ high rank in DVOA is probably also fumble-related, as they had the lowest rushing fumble rate in the league. One additional thing that DVOA incorporates is strength of schedule, which explains their rank of the Jets. New York’s VOA was more than 8% better than their DVOA, which by far the biggest disparity. That checks out, since they only played 4 teams with an above-average rush defense.

  • Tom

    Great post. Does it make any sense to include total fumbles, or fumbles lost into the equation, in the same way that interceptions carry a 45-yard penalty for passing ANY/A? I’m thinking “no”, since although some players may be prone to fumbling, the team that actually recovers the fumble seems mostly random, and is probably split down the middle between offense and defense (per a post you did on fumble recoveries here, http://www.footballperspective.com/the-definitive-analysis-of-offensive-fumbles/).

    A middle ground possibility would be penalizing a team (45 yards, etc.) for half of their total fumbles (whether lost or recovered), but this probably starts to get kind of goofy, and maybe not worth the effort.

    Would love to hear anyone’s thoughts on this, thanks.

    • Chase Stuart

      Yes, it does make sense to include fumbles in the equation. The problem, however, is that we don’t have historical data on which fumbles occurred on rushing plays, and which fumbles occurred on passing plays or special teams plays. For 2013 though, I agree it makes sense to include them, and we could debate whether to assign full value or not for fumbles lost.

  • Nick Bradley

    I really don’t understand all this reinvention of expected points added. its a non-proprietary formula.

    EPA variance would probably be a good stat for running back, like success rate.

    • Chase Stuart

      EPA may not be proprietary, but it’s not intuitive to some folks. More importantly, it doesn’t work for historical seasons (I agree that EPA is much better for 2013 than using AYPC).

      • Nick Bradley

        it seems pretty intuitive, and you should be able to easily control for historical seasons

  • Ty

    I think one thing that might have been pointed out by sn0mm1s (at least I think it was him), is that a huge difference between AFA Rush stats and DVOA rush stats, is that AFA assigns a positive run on first down as 5 yards, and DVOA assigns a positive run on first down as 4 yards. This might not seem like much, but it is significant in the grand scheme… An offense has to gain about 5 yards on first down to have a positive expectancy, and anything less than that would put the offense in a worse position. I’m not certain how this would affect the list, but it is something to think about.

    • Chase Stuart


  • Tom

    Nick – I’ll give you my reasons:

    1. Compiling EP data is cumbersome if you do it on your own. “Regular” NFL stats are easily available and much more simple.

    2. During my year of compiling my own EP data, using Brian Burke’s EP model, I came across at least three different EP models – PFR’s, Brian’s, and Keith Goldner’s. And ESPN has their own, along with probably a few more. Every time you use it, you’re going to have to reference which model you’re using. And believe me, they’re different.

    3. You don’t know what you’re looking at when you use EP data, unless you have the play-by-play data on hand, or have inside knowledge. For example, in some EP models,QB’s get EP credit for pass interference plays. If you disagree with this, and want to demonstrate why, good luck. You’re going to have to download play-by-play, etc.

    4. The present NFL data is easy to find, easy to download, easy to verify, easy to manipulate.

    Yeah, I’m a huge fan of having formulas like ANY/A that get us closer to an efficiency stat like EP. And don’t get me wrong, I love EP – it’s the best way to measure efficiency because it takes what happens on a play and converts it to points, meaning you can use it for anything.

    Until we have the “one model to rule them all” and it is transparent and easily verifiable, using EP will always be difficult due to the reasons I laid out above.

    What I’m saying is, keep going Chase.

    • Nick Bradley

      Thanks Tom. a couple points.

      1. the conversion tables should be available on the internet — where is the formula? Burke’s were. don’t know where they are now.
      2. didn’t Burke advise ESPN on their model?
      3. can’t they hammer out discrepancies? EPA should be on the screen during games
      4. I’m fine with QB credit for pass interference. I am not OK with WR fumbles.

      • Tom

        Nick –

        Comments to your comments (my apologies all, not specifically trying to detract from the actual post!):

        1. This is where it gets sticky…there is a “conversion table” (I created one myself in Excel from AFA’s data), but it’s not posted on the internet, and further, in many cases, it’s not a formula. Keith Goldner (Drive By Football) I believe does use some kind of formula, or at least some kind of hybrid. Brian (AFA) uses some kind of algorithm, but it’s definitely not a one size fits all…I believe Brian’s is more closely tied to historical outcomes than the other models. That being said, Brian does provide a calculator, which is awesome…you can just punch in whatever situation and it spits back EP and WP (Win Probability) data.

        2. Not sure about Brian advising ESPN but I wouldn’t doubt it.

        3. Yes, this is what would be cool. Basically, the NFL stepping in and saying, “Here they are everyone. These are the Expected Points for every down, distance and field position situation”. They’d give it a datum name, like we surveyors use for elevations….it could be called “2000-2013EP”, basically telling you to use that datum if you’re analyzing plays in those years. There would then also be “1970-1980EP” datum, etc.

        4. I’m OK with it too, for some things, but my point is, when you look at a model, you don’t know if that’s what’s going on, and there is no quick way to find out, unless you email the guy who created the model.


        • Nick Bradley

          Wonderful response, thanks.

          I think its rather ridiculous that the NFL doesn’t collect advanced stats. MLB Advanced Media does it for baseball (e.g. Pitchf/x)

  • Tom

    Chase – not trying to be picky, but AFA has the efficiency model using EP and then the efficiency rankings which combine success rate and other “regular” stats. Which one did you use for this post?

  • Dave

    The one thing I’ve always been annoyed by with AFA’s RB’s page: http://wp.advancedfootballanalytics.com/playerstats.php?pos=RB

    Is that it doesn’t break out RB’s WP/EPA into rushing and receiving.

  • steve

    Have you looked at the list, and asked what the affect of being an “open-air team” has had on the rankings?

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