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We know how this story will end.

We know how this story will end.

Regular readers know that one of my projects this off-season is to come up with a better way to grade wide receivers. I first attempted to rank every wide receiver four years ago. That study, which I will reproduce this week, has some positives and negatives. My goal is to eventually come up with four or five different ranking systems, so consider the series this week to be the first of several ranking systems to come.

The first step in this system is to combine the three main stats — receptions, receiving yards and receiving touchdowns — into one stat: Adjusted Catch Yards. We know that a passing touchdown is worth about 20 yards, so I’m crediting a receiver with 20 yards for every touchdown reception. Next, we need to decide on an appropriate bonus for each reception.

We want to give receivers credit for receptions because, all else being equal, a receiver with more receptions is providing more value because he’s likely generating more first downs. I looked at all receivers over a 12-year period who picked up at least 30 receiving first downs. I then used the number of receptions and receiving yards those players had as inputs, and performed a regression to estimate how many first downs should be expected. The best-fit formula was:

Receiving first downs = 4.9 + 0.255 * Receptions + 0.019 * Receiving Yards

There is nothing magical about the number 30, although the R^2 was pretty strong at 0.81 and both variables were highly significant. If we use 40 receptions, the R^2 is still strong (0.69) and best-fit formula is:

Receiving first downs = 10.0 + 0.261 * Receptions + 0.016 * Receiving Yards

There is no doubt that receptions are highly correlated with receiving first downs. So what do we do now? The coefficient on receptions is 13.2 times the coefficient on yards in the first equation and 16.6 times larger in the second formula. So if first downs were the only thing that mattered, we’d give a bonus of between 13 and 17 yards for each receptions. But, of course, first downs aren’t the only things that matter, since receivers do more than just catch passes that result in first downs. Gaining seven yards on third-and-six is great. But gaining eight yards on third-and-six is better. Gaining twenty is better still. You can think of 13 as the upper limit on the size of the bonus we should give for each catch, but in reality, receptions are quite a bit less valuable than that.

But take a step back and think about what the value is of a first down. Possession of the ball is generally worth about four points. If you have 1st-and-10 at the 50, you are in a state of +2.0 expected points, which means that if you fumbled the snap and your opponent recovered, they would be in that same +2.0 position.  So we know that by losing possession, you lose four points. We know that first-and-10 from your own 1 is worth -0.53 expected points, and 1st-and-goal from your opponent’s 1 is worth 5.96 points, which means the 98 yards in between is worth 6.5 points; that means a point is roughly equal to 15 yards. So if possession is worth 4 points, then it is also worth 60 yards. If you average 35 net yards on a punt, the value of a first down that comes on third down is then a net loss of 25 yards to the punting team. The regression says a catch is worth .26 first downs, so that would make a catch worth 0.26*25, or 6.25 yards.

Those are, of course, broad, sweeping generalities. Some catches are worth much, much more than others. But we can’t, at this point, track down all of Harold Carmichael’s third down catches and try to assess the value of each one. So we have to estimate. And it’s worth remembering that not all first down catches come on third downs, so even if a first down may be worth 6.25 yards on third down, that doesn’t mean  the average first down is that valuable. In the end we are left having to make a pretty rough estimate, but I’m happy to give that number a slight haircut and make each reception worth five yards.

So we have our formula for Adjusted Catch Yards: 5 * Receptions + Receiving Yards + 20 * Receiving Touchdowns.  What’s next?

If you’re a frequent reader of this site, then you know we can’t simply use counting stats for wide receivers. Having a 1200 yard season is more impressive when your team throws 400 passes than when it throws 550 passes. It’s also a lot more valuable. On the other hand, we don’t want to give too much credit to just the “high rate” guys.  How do we find a middle ground?

First, I divided each wide receiver’s ACY by his team’s total number of pass attempts (sacks included). Once I have an ACY/A average for each receiver, I then had to come up with a baseline. I decided to use the worst starter method, so this means the 32nd best wide receiver in modern times; in other eras, the baseline also equals WR N, where N equals the number of teams in the league. Let’s use a real example to show how the formula works.

Most people would say Marques Colston had a much better year in 2012 than Sidney Rice. Colston caught 83 passes for 1,154 yards and 10 touchdowns, which looks a lot better than Rice’s 50-748-7 stat line. But the Saints had 697 pass attempts while Seattle only had 438 pass plays, making it hard to compare the receivers based on raw numbers. Rice averaged 2.60 ACY/A, narrowly edging Colston’s 2.54 average. In 2012, the thirty-second ranked wide receiver in ACY/A was Anquan Boldin at 2.37. Rice gets credit for averaging 0.23 ACY/A over the baseline for 438 plays, so he’s credited with being 102 ACY over average. Colston was 0.17 ACY/A over the baseline for 697 passes, giving him 120 ACY over average. So Colston does get credit for beating out Rice, but not nearly as much as the raw numbers would indicate. Here are the top 32 wide receivers in 2012:

1Brandon Marshall2012CHI1611815081123185294.381067
2Andre Johnson2012HOU161121598422385823.85861
3Calvin Johnson2012DET161221964526747693.48855
4A.J. Green2012CIN169713501120555863.51669
5Demaryius Thomas2012DEN169414341021046093.45664
6Michael Crabtree2012SFO16851105917104773.58582
7Vincent Jackson2012TAM16721384819045923.22504
8Wes Welker2012NWE161181354620646683.09484
9Dez Bryant2012DAL169213821220826943441
10Roddy White2012ATL16921351719516433.03430
11Reggie Wayne2012IND161061355519856692.97403
12Victor Cruz2012NYG168610921017225593.08400
13Steve Smith2012CAR16731174416195263.08375
14Percy Harvin2012MIN962677310472903.61362
15Eric Decker2012DEN168510641317496092.87309
16Steve Johnson2012BUF16791046615615412.89281
17Julio Jones2012ATL167911981017936432.79272
18Pierre Garcon2012WAS104463349332973.14231
19Brian Hartline2012MIA16741083114735412.72193
20Dwayne Bowe2012KAN1359801311564182.76166
21Randall Cobb2012GNB1580954815145712.65164
22Danario Alexander2012SDG103765879833612.73130
23Marques Colston2012NOR168311541017696972.54120
24Sidney Rice2012SEA1650748711384382.6102
25Mike Williams2012TAM1663996914915922.5291
26Golden Tate2012SEA1545688710534112.5682
27Danny Amendola2012STL1163666310414072.5678
28Cecil Shorts2012JAX1455979713945572.578
29Davone Bess2012MIA1361778111034402.5163
30Jordy Nelson2012GNB1249745711304572.4750
31Antonio Brown2012PIT1366787512174962.4543
32Anquan Boldin2012BAL1565921413265612.370

You might notice that Minnesota’s Percy Harvin ranks 14th in value added. Harvin only played in 9 games, but he ranked 3rd in ACY/Team Attempt. For players who played in fewer than 16 games (during the 16 game era), I used a pro-rated number of team attempts for those players. Minnesota had 515 pass attempts last year, so we assume that they threw 56% (9/16) of their passes in the games Harvin was active. Therefore, in the team attempts column for Harvin, he’s credited with 290 team attempts. Of course, Harvin is also then only credited for being above average for 290 plays, too.

Tomorrow I’ll present a list of some of the best seasons ever, and on Wednesday, we’ll look at the career list. Let me close with some obvious flaws in this system.

1) Post-season stats are excluded. It’s not difficult to add playoff numbers, but for now, I’d rather refine the system before including those numbers.

2) Rushing data, passing data and fumble data were also excluded for the same reason. No data exists on blocking ability, so that is obviously left out of this system, too.

3) The quality of the quarterback, offensive line, and the system a team runs all heavily impact a receiver’s numbers. So does playing in Buffalo compared to playing in New Orleans. These are all important factors but I chose to leave them out of the system and let each reader subjectively tweak a player upward or downward based on their own thoughts.

4) Wide receivers who play with other great wide receivers are probably harmed in this system, at least slightly. That hurts people like Isaac Bruce and Torry Holt or Anquan Boldin and Larry Fitzgerald. In some ways, this system does a better job of measuring “value added” than actual talent, and a superstar receiver on a team of scrubs probably can add more value than a star receiver on a team full of stars.

  • Tim Truemper

    Regarding # 4. This gets to a point I made earlier about what the methodology actually measures- how well a receiver performs given their context or situation; too many variables regarding indoors/outdoors, QB and team qualitiy etc to say “whose the best” by any quantitiative metric. And the work being done with this method of measruing receiver quality makes me wish Larry Fitzgerald would get traded to someone with a decent QB before his career dwindles to nothingness.

  • Richie

    I have no idea what to make of the fact that Davone Bess and Brian Hartline both make the top 32.

  • Danish

    Re the pro-rating: I don’t know how big of a difference this makes, but I’m not sure I understand the straight up prorating-approach. We’re dealing with top recievers in the league so their absence will presumeably make their teams pass less. When Harvin isn’t there, handing off to Adrian Peterson is more tempting to the Vikings right? The run-pass value equilibrium i pushed towards the run when your reciever is sidelined.

    How complicated would it be to simply go back and see how many times the Vikings actually passed in the games Harvin actually appeared? Certainly there’s a tradeoff of precision, data availabillity and coding complexity to consider.

    • Chase Stuart

      Basically the trade-off is too annoying. It’s the right way, of course, but it’s a bit of a pain to code and I don’t think worth it. The other issue is that many times older receivers would simply not get a catch in a game, but that doesn’t mean they were hurt. At some point (Maybe GWROAT III) I will go back and do it, though.

      • Danish

        I’m totally fine with this, for the record. Sometimes the perfect way is simply to laborious – that’s just a fact of life.

        Also fine: I really enjoy how you come back and answer questions and respond to debates even if the post is a couple of days old (I had fallen behind on my reading). It’s definetely something that keeps me hanging around the blog.

        • Chase Stuart

          Thanks Danish. Hope you stick around for a long time!