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:

Rank | Name | Year | TM | G | Rec | RecYd | TD | ACY | TM ATT | ACY/TMATT | VALUE |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | Brandon Marshall | 2012 | CHI | 16 | 118 | 1508 | 11 | 2318 | 529 | 4.38 | 1067 |

2 | Andre Johnson | 2012 | HOU | 16 | 112 | 1598 | 4 | 2238 | 582 | 3.85 | 861 |

3 | Calvin Johnson | 2012 | DET | 16 | 122 | 1964 | 5 | 2674 | 769 | 3.48 | 855 |

4 | A.J. Green | 2012 | CIN | 16 | 97 | 1350 | 11 | 2055 | 586 | 3.51 | 669 |

5 | Demaryius Thomas | 2012 | DEN | 16 | 94 | 1434 | 10 | 2104 | 609 | 3.45 | 664 |

6 | Michael Crabtree | 2012 | SFO | 16 | 85 | 1105 | 9 | 1710 | 477 | 3.58 | 582 |

7 | Vincent Jackson | 2012 | TAM | 16 | 72 | 1384 | 8 | 1904 | 592 | 3.22 | 504 |

8 | Wes Welker | 2012 | NWE | 16 | 118 | 1354 | 6 | 2064 | 668 | 3.09 | 484 |

9 | Dez Bryant | 2012 | DAL | 16 | 92 | 1382 | 12 | 2082 | 694 | 3 | 441 |

10 | Roddy White | 2012 | ATL | 16 | 92 | 1351 | 7 | 1951 | 643 | 3.03 | 430 |

11 | Reggie Wayne | 2012 | IND | 16 | 106 | 1355 | 5 | 1985 | 669 | 2.97 | 403 |

12 | Victor Cruz | 2012 | NYG | 16 | 86 | 1092 | 10 | 1722 | 559 | 3.08 | 400 |

13 | Steve Smith | 2012 | CAR | 16 | 73 | 1174 | 4 | 1619 | 526 | 3.08 | 375 |

14 | Percy Harvin | 2012 | MIN | 9 | 62 | 677 | 3 | 1047 | 290 | 3.61 | 362 |

15 | Eric Decker | 2012 | DEN | 16 | 85 | 1064 | 13 | 1749 | 609 | 2.87 | 309 |

16 | Steve Johnson | 2012 | BUF | 16 | 79 | 1046 | 6 | 1561 | 541 | 2.89 | 281 |

17 | Julio Jones | 2012 | ATL | 16 | 79 | 1198 | 10 | 1793 | 643 | 2.79 | 272 |

18 | Pierre Garcon | 2012 | WAS | 10 | 44 | 633 | 4 | 933 | 297 | 3.14 | 231 |

19 | Brian Hartline | 2012 | MIA | 16 | 74 | 1083 | 1 | 1473 | 541 | 2.72 | 193 |

20 | Dwayne Bowe | 2012 | KAN | 13 | 59 | 801 | 3 | 1156 | 418 | 2.76 | 166 |

21 | Randall Cobb | 2012 | GNB | 15 | 80 | 954 | 8 | 1514 | 571 | 2.65 | 164 |

22 | Danario Alexander | 2012 | SDG | 10 | 37 | 658 | 7 | 983 | 361 | 2.73 | 130 |

23 | Marques Colston | 2012 | NOR | 16 | 83 | 1154 | 10 | 1769 | 697 | 2.54 | 120 |

24 | Sidney Rice | 2012 | SEA | 16 | 50 | 748 | 7 | 1138 | 438 | 2.6 | 102 |

25 | Mike Williams | 2012 | TAM | 16 | 63 | 996 | 9 | 1491 | 592 | 2.52 | 91 |

26 | Golden Tate | 2012 | SEA | 15 | 45 | 688 | 7 | 1053 | 411 | 2.56 | 82 |

27 | Danny Amendola | 2012 | STL | 11 | 63 | 666 | 3 | 1041 | 407 | 2.56 | 78 |

28 | Cecil Shorts | 2012 | JAX | 14 | 55 | 979 | 7 | 1394 | 557 | 2.5 | 78 |

29 | Davone Bess | 2012 | MIA | 13 | 61 | 778 | 1 | 1103 | 440 | 2.51 | 63 |

30 | Jordy Nelson | 2012 | GNB | 12 | 49 | 745 | 7 | 1130 | 457 | 2.47 | 50 |

31 | Antonio Brown | 2012 | PIT | 13 | 66 | 787 | 5 | 1217 | 496 | 2.45 | 43 |

32 | Anquan Boldin | 2012 | BAL | 15 | 65 | 921 | 4 | 1326 | 561 | 2.37 | 0 |

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.

{ 6 comments… read them below or add one }

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.

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

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.

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.

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.

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

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