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:

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.