## True Receiving Yards, Part I

One of many Rams greats to wear #29.

As you guys know, Neil Paine is the man. Here’s the latest reason: he came up with a metric called True Receiving Yards, the latest in a long line of thoughts in our Wide Receiver Project. So, what are True Receiving Yards?

We start with Adjusted Catch Yards, defined as 5 * Receptions + Receiving Yards + 20 * Receiving Touchdowns.

1) Then, we convert each player’s Adjusted Catch Yards to the same scale as pure receiving yards using the following formula:

Adjusted Catch Yards * League Receiving Yards / League Adjusted Catch Yards

2) Next, we adjust for how often the receiver’s team passed.  We use the following formula:

[Result in Step 1] * League_Avg_Team_Pass_Attempts / Team_Pass_Attempts

For purposes of this post, Team Pass Attempts include sacks.

3) Then we adjust for the league passing environment, by using this formula:

[Result in Step 2] * by (214.54/Avg_Team_Receiving_Yards_Per_Game).

Why 214.54? Because that’s how many yards the average NFL team has passed for in each season since 1970.

4) Finally, we need to adjust for schedule length. This one’s pretty simple:

[Result in Step 2] * 16 / Team Games

As it turns out, the single-season leader in True Receiving Yards is….. Harold Jackson for the 1973 Rams. That will probably surprise some folks; heck, it surprised me. So let’s walk through Jackson’s season by comparing it to Calvin Johnson’s 2012. Jackson caught 40 passes for 874 yards and 13 touchdowns. That gives him 1,334 Adjusted Catch Yards, while Megatron’s 122-1964-5 translates to 2,674 Adjusted Catch Yards, more than twice what Jackson produced.

1) First, we need to convert those ACY numbers into receiving yards.  In 1973, that conversion ratio is 65.5%, and in 2012, it was 64.5%; this means Jackson is credited with 874 receiving yards (ironically, his actual number) while Johnson is pushed down to only 1,725 yards. This is because Johnson had a ton of yards but only five touchdowns.  In other words, based on his receptions, receiving yards, and receiving touchdowns, Johnson was more like a 1,725-yard receiver last year.

2) Jackson’s Rams had just 288 Team Pass Attempts, while the average team in 1973 averaged 373.3 pass attempts. So we need to bump Jackson up by 29.6%, which would give him 1,132 receiving yards. The 2012 Lions had 769 Team Pass Attempts compared to a league average of 592.4; therefore, we need to give Johnson credit for only 77% of his ACY, bringing him down to 1,329 receiving yards.

3) Next, we adjust for league environment. In 1973, the average team passed for 159 yards per game, which means we need to bump Jackson up by 34.6% (the result of 214.54 divided by 159); this gives him 1,524 receiving yards. For Megatron, since the average team in 2012 passed for 246 yards per game, we need to multiply his result in step 2 by 87.2%, leaving him with only 1,159 receiving yards.

4) For Calvin Johnson, that’s it: he is credited with 1,159 True Receiving Yards, after reducing his numbers for playing in a pass-happy offense, playing in a pass-happy era, and not having many touchdowns. For Jackson, his 1,524 gets pro-rated to a 16-game season, giving him 1,742 True Receiving Yards.

The table below shows the number of True Receiving Yards for the top 200 receivers since 1970. Let’s walk through Paul Warfield’s 1971 season, #4 on the list, as an example. That year, his 43-996-11 stat line translates to 1,431 Adjusted Catch Yards. The Adjusted Receiving Yards to Receiving Yards ratio for the entire league that season was 66.6%, so that translates to 953 receiving yards for Warfield. We multiply that number by the average number of pass attempts in the league that year (392) and divide it by the number of pass attempts by Miami (318) to get 1,174 yards. Next, we multiply that by 214.54 (the average receiving yards per game over the 43-year period) and divide by 174, which represents the low-octane era of 1971; that gives us 1,449 yards. Finally, we pro-rate to 16 games, and end up with 1,656 True Receiving Yards.

1Harold JacksonRAM19734087413133465.5%373288159141742
2Cliff BranchOAK197460109213165265.6%401359171141732
3Steve SmithCAR2005103156312231864.4%551477218161696
4Paul WarfieldMIA19714399611143166.6%392318174141656
5Michael IrvinDAL1995111160310235864.6%593512236161607
6Randy MossMIN2003111163217252764%550562214161587
7Marvin HarrisonIND1999115166312247864.9%581560228161569
8Cliff BranchOAK197646111112158165.8%403389173141523
9Otis TaylorKAN19715711107153566.6%392372174141518
10Gene A. WashingtonSFO197053110012160566.2%410391181141511
11Marvin HarrisonIND2002143172211265764%577614227161510
12Steve SmithCAR20087814216193164.4%549434224161506
13Jerry RiceSFO1994112149913231964.8%571546227161483
14Roger CarrBAL197643111211154765.8%403391173141482
15Roddy WhiteATL20088813827196264.4%549451224161473
16Jerry RiceSFO199398150315229364.9%552559215161466
17Ken BurroughHOU19755310638148865.7%418374183141465
18John StallworthPIT198480139511201566%559478228161461
19Brandon MarshallCHI2012118150811231864.5%592529246161460
20Wes ChandlerSDG19824910329145765.9%30735022191457
21John GilliamMIN1973429078127765.5%373330159141455
22Jerry RiceSFO198982148317223366.5%552528229161455
23Gary ClarkWAS199170134010189065.7%534456215161453
24Jimmy SmithJAX199911616366233664.9%581571228161450
25Terrell OwensSFO200193141216219764.5%561532221161449
26Eddie BrownCIN19885312739171866.4%542422218161441
27Yancey ThigpenPIT19977913987193365.1%566486219161432
28Jerry RiceSFO1995122184815275864.6%593677236161421
29David BostonARI20019815988224864.5%561555221161421
30Santana MossWAS20058414839208364.4%551512218161420
31Randy MossMIN200077143715212264.7%566530222161417
32Marvin HarrisonIND2001109152415236964.5%561587221161416
33Herman MooreDET1995123168614258164.6%593637236161413
34Sterling SharpeGNB1992108146113226165.3%520570205161406
35Mel GraySTL19754892611138665.7%418363183141406
36Michael IrvinDAL19919315238214865.7%534538215161399
37Fred BiletnikoffOAK1971619299141466.6%392372174141399
38Nat MooreMIA19775276512126565.9%384347162141393
39Torry HoltSTL2003117169612252164%550643214161384
40Bob HayesDAL19703488910125966.2%410336181141379
41Randy MossNWE200798149323244363.7%567607228161367
42Isaac BruceSTL1995119178113263664.6%593675236161362
43Stanley MorganNWE198228584378465.9%30720222191358
44Michael IrvinDAL19938813307191064.9%552504215161354
45Rod SmithDEN2001113134311212864.5%561553221161350
46Lee EvansBUF20068212928186264.4%549478219161347
47Rod SmithDEN200010016028226264.7%566599222161336
48Wesley WalkerNYJ19784811698156966.1%459431178161335
49Andre JohnsonHOU200811515758231064.4%549587224161332
50Drew HillHOU198872114110170166.4%542452218161332
51Jerry RiceSFO198686157015230066.1%560608226161330
52Michael IrvinDAL19927813967192665.3%520514205161328
53Dick GordonCHI197071102613164166.2%410455181141328
54Art MonkWAS198410613727204266%559533228161328
55Reggie WayneIND2007104151010223063.7%567574228161320
56Marvin HarrisonIND2000102141314220364.7%566591222161319
57Isaac CurtisCIN1973458439124865.5%373356159141318
58Eric MouldsBUF19986713689188365.1%557502221161318
59Sterling SharpeGNB1993112127411205464.9%552558215161315
60Henry EllardRAM198886141410204466.4%542550218161315
61Randy VatahaNWE1971518729130766.6%392366174141314
62Michael IrvinDAL19947912416175664.8%571468227161310
64Hines WardPIT20056997511154064.4%551411218161308
65Cliff BranchOAK1975518939132865.7%418376183141301
66Joe HornNOR20009413408197064.7%566536222161300
67Derrick MasonTEN20039513038193864%550527214161298
69Charley TaylorWAS1972496737105866.2%376295169141296
70Andre ReedBUF19898813129193266.5%552513229161296
71James ScottCHI1977508093111965.9%384331162141292
72Cris CarterMIN20009612749193464.7%566530222161291
73Andre JohnsonHOU201211215984223864.5%592582246161282
74Terrell OwensSFO200097145113219664.7%566608222161278
75Lynn SwannPIT19786188011140566.1%459405178161272
77Hines WardPIT2002112132912212964%577585227161270
78Hines WardPIT20048010044148464.5%548394225161269
79Jerry RiceSFO1990100150213226265.7%521620211161268
80Mike QuickPHI198369140913201465.8%545543225161267
81Robert BrooksGNB1995102149713226764.6%593626236161263
82Herman MooreDET199472117311175364.8%571485227161262
83Jerry RiceSFO199284120110182165.3%520512205161261
84Terrell OwensDAL200781135515206063.7%567556228161258
85Randy MossMIN199869131317199865.1%557558221161258
86Marvin HarrisonIND200695136612208164.4%549572219161258
87Randy MossMIN199980141311203364.9%581573228161258
88Joey GallowayTAM200583128710190264.4%551528218161257
89Tim BrownRAI19948913099193464.8%571538227161255
90Drew PearsonDAL19746210872143765.6%401432171141252
91Isaac BruceSTL19968413387189864.6%569538222161252
92Harold CarmichaelPHI19785510728150766.1%459442178161250
93Mark ClaytonMIA198473138918211466%559586228161250
94Charlie BrownWAS1982326908101065.9%30728322191249
95Dwight ClarkSFO1982609135131365.9%30736822191248
96Roy GreenSTL198378122714189765.8%545519225161248
97Charlie JoinerSDG19765010567144665.8%403434173141248
98Gene A. WashingtonSFO19724691812138866.2%376402169141248
99Lynn SwannPIT19754978111124665.7%418368183141247
100Anquan BoldinARI200310113778204264%550578214161247
101Tim BrownOAK199710414085202865.1%566587219161244
102John GilliamMIN19724710357141066.2%376411169141240
103Antonio FreemanGNB199781124312188865.1%566549219161239
104Terance MathisATL199864113611167665.1%557477221161235
105Willie GaultRAI1990509853129565.7%521365211161233
106Roy GreenSTL198478155512218566%559615228161231
107Ken BurroughHOU1977438168119165.9%384370162141230
108Jimmy SmithJAX200111213738209364.5%561597221161230
109Stanley MorganNWE198684149110211166.1%560604226161229
110Paul WarfieldMIA1973295141187965.5%373269159141229
111Andre JohnsonHOU200910115699225464.3%567618232161227
112Steve SmithCAR20038811107169064%550486214161227
113Keyshawn JohnsonNYJ19998911708177564.9%581513228161227
114Brandon MarshallDEN200710213257197563.7%567547228161226
115Lynn SwannPIT1977507897117965.9%384368162141225
116Herman MooreDET199710412938197365.1%566581219161223
117Laveranues ColesNYJ20028912645180964%577517227161221
118Rich CasterNYJ19723983310122866.2%376364169141219
119Jerry RiceSFO198765107822184365.6%521530224151218
120Charlie BrownWAS19837812258177565.8%545498225161217
121Antonio FreemanGNB199884142414212465.1%557614221161216
122Tim BrownOAK200076112811172864.7%566503222161216
123Gary GarrisonSDG197044100612146666.2%410444181141215
124Wes WelkerNWE201112215699235965.1%581644245161214
125Harold JacksonPHI19726210484143866.2%376428169141214
126Torry HoltSTL20008216356216564.7%566631222161214
127Wes ChandlerNOR19796510696151466%501445199161214
128Jimmy SmithJAX19987811828173265.1%557502221161213
129Herman MooreDET199610612969200664.6%569587222161212
130Terrell OwensSFO2002100130013206064%577593227161212
131Jerry RiceSFO199180120614188665.7%534546215161211
132Braylon EdwardsCLE200780128916200963.7%567564228161210
133Brett PerrimanDET199510814889220864.6%593637236161209
134Roddy WhiteATL2010115138910216464.2%575600236161209
135Steve LargentSEA19787111688168366.1%459511178161208
136Joe HornNOR200494139911208964.5%548583225161207
137Cris CarterMIN199990124113195164.9%581573228161207
138Rod SmithDEN19988612226177265.1%557516221161207
139Dwayne BoweKAN201072116215182264.2%575507236161204
141Art MonkWAS19917110498156465.7%534456215161202
142Tony MartinATL19986611816163165.1%557477221161202
143Nat MooreMIA197540705498565.7%418302183141201
144Jimmy SmithJAX19978213244181465.1%566544219161201
145Troy BrownNWE200110111995180464.5%561528221161198
146Marlin BriscoeBUF19705710368148166.2%410455181141198
147Tim BrownOAK199589134210198764.6%593579236161197
148Bob ChandlerBUF19766182410132965.8%403416173141197
149Harold CarmichaelPHI19736711169163165.5%373513159141196
150Michael CrabtreeSFO20128511059171064.5%592477246161195
151Ken BurrowATL1971337416102666.6%392316174141195
152Tim BrownOAK19999013446191464.9%581569228161192
153Eric MartinNOR19926810415148165.3%520441205161191
154Todd ChristensenRAI198392124712194765.8%545559225161190
155John StallworthPIT1977447847114465.9%384368162141188
156Terrell OwensDAL200685118013186564.4%549543219161188
157Cris CarterMIN1995122137117232164.6%593682236161187
159Calvin JohnsonDET200878133112196164.4%549561224161183
160Ed McCaffreyDEN200010113179200264.7%566599222161183
161Carl PickensCIN199599123417206964.6%593611236161181
162Rob MooreARI19979715848222965.1%566680219161181
163Rod SmithDEN20058511056165064.4%551488218161180
164Ron ShanklinPIT19733071110106165.5%373339159141177
165Henry EllardRAM19897013828189266.5%552555229161173
166Calvin JohnsonDET201196168116248165.1%581702245161172
167Marvin HarrisonIND200582114612179664.4%551535218161172
168Jerry RiceSFO199610812548195464.6%569592222161171
169Isaac BruceSTL20008714719208664.7%566631222161170
170A.J. GreenCIN201297135011205564.5%592586246161169
171Larry FitzgeraldARI2007100140910210963.7%567614228161167
172Marvin HarrisonIND200394127210194264%550588214161166
173Amani ToomerNYG20028213438191364%577573227161165
174Antonio GatesSDG20048196413162964.5%548471225161165
175Jerry RiceSFO19886413069180666.4%542549218161164
176John StallworthPIT19797011838169366%501519199161164
177Rod SmithDEN199770118012177065.1%566548219161163
178Andre JohnsonHOU200610311475176264.4%549524219161163
179Henry EllardWAS19947413976188764.8%571567227161162
180Jeff GrahamCHI19958213014179164.6%593538236161161
181Reggie WayneIND20068613109192064.4%549572219161161
182Randy MossMIN200210613477201764%577607227161160
183Calvin JohnsonDET201212219645267464.5%592769246161159
184Kevin HouseTAM19815611769163666.4%543492223161155
185Steve SmithCAR20117913947192965.1%581554245161154
186Harold JacksonRAM1975437867114165.7%418364183141154
187Ron JessieRAM1976347796106965.8%403347173141154
188Warren WellsOAK19704393511137066.2%410437181141154
189Charley TaylorWAS1973598017123665.5%373403159141153
190Mervyn FernandezRAI19895710699153466.5%552458229161152
191Demaryius ThomasDEN201294143410210464.5%592609246161151
192Kevin JohnsonCLE20018410979169764.5%561517221161151
193Andre RisonATL199386124215197264.9%552613215161150
194Joe HornNOR20028813127189264%577575227161148
195Marvin HarrisonIND200486111315184364.5%548541225161148
196Steve WatsonDEN198160124413180466.4%543546223161147
198Andre ReedBUF19949013038191364.8%571583227161146
199James LoftonGNB19846213617181166%559548228161145
200Steve LargentSEA19867010709160066.1%560492226161144

Cliff Branch teamed with Ken Stabler for two top-ten seasons in three years in the mid-’70s. Steve Smith checks in with the third best season since 1970 and three other top-200 seasons, but that’s not too surprising to regular readers. Jimmy Smith also has four top-200 seasons, but that’s also not too surprising. Paul Warfield, another frequently-profiled wideout at Football Perspective, has a top-five season. Jerry Rice has eleven top-200 seasons, which is pretty freakin’ ridiculous. Marvin Harrison (8), Randy Moss (6), Michael Irvin (5),Terrell Owens (5), Rod Smith (5), Tim Brown (5), and Chad Johnson (5) are the only other receivers with five top-200 seasons since the merger. As for Harold Jackson, he had just two other top-200 seasons, although impressively he pulled off that trick in back-to-back seasons for different teams. On an unrelated note, Jackson is one of several great players to wear #29 for the Rams (along with Eric Dickerson, Tommy McDonald, and Del Shofner).

Finally, let’s close with a look at the single-season leaders in True Receiving Yards back to 1970.

2012Brandon MarshallCHI118150811231864.5%592529246161460
2011Wes WelkerNWE12215699235965.1%581644245161214
2010Roddy WhiteATL115138910216464.2%575600236161209
2009Andre JohnsonHOU10115699225464.3%567618232161227
2008Steve SmithCAR7814216193164.4%549434224161506
2007Randy MossNWE98149323244363.7%567607228161367
2006Lee EvansBUF8212928186264.4%549478219161347
2005Steve SmithCAR103156312231864.4%551477218161696
2003Randy MossMIN111163217252764%550562214161587
2002Marvin HarrisonIND143172211265764%577614227161510
2001Terrell OwensSFO93141216219764.5%561532221161449
2000Randy MossMIN77143715212264.7%566530222161417
1999Marvin HarrisonIND115166312247864.9%581560228161569
1998Eric MouldsBUF6713689188365.1%557502221161318
1997Yancey ThigpenPIT7913987193365.1%566486219161432
1996Isaac BruceSTL8413387189864.6%569538222161252
1995Michael IrvinDAL111160310235864.6%593512236161607
1994Jerry RiceSFO112149913231964.8%571546227161483
1993Jerry RiceSFO98150315229364.9%552559215161466
1992Sterling SharpeGNB108146113226165.3%520570205161406
1991Gary ClarkWAS70134010189065.7%534456215161453
1990Jerry RiceSFO100150213226265.7%521620211161268
1989Jerry RiceSFO82148317223366.5%552528229161455
1988Eddie BrownCIN5312739171866.4%542422218161441
1987Jerry RiceSFO65107822184365.6%521530224151218
1986Jerry RiceSFO86157015230066.1%560608226161330
1985Louis LippsPIT59113412166966.3%562545227161080
1984John StallworthPIT80139511201566%559478228161461
1983Mike QuickPHI69140913201465.8%545543225161267
1982Wes ChandlerSDG4910329145765.9%30735022191457
1981Kevin HouseTAM5611769163666.4%543492223161155
1980John JeffersonSDG82134013201065.5%526626214161108
1979Wes ChandlerNOR6510696151466%501445199161214
1978Wesley WalkerNYJ4811698156966.1%459431178161335
1977Nat MooreMIA5276512126565.9%384347162141393
1976Cliff BranchOAK46111112158165.8%403389173141523
1975Ken BurroughHOU5310638148865.7%418374183141465
1974Cliff BranchOAK60109213165265.6%401359171141732
1973Harold JacksonRAM4087413133465.5%373288159141742
1972Charley TaylorWAS496737105866.2%376295169141296
1971Paul WarfieldMIA4399611143166.6%392318174141656
1970Gene A. WashingtonSFO53110012160566.2%410391181141511
• Malcolm

Great stuff! What about receiving 1st downs? Some of your calculations in the past account for 1st downs into the ACY.

• The 5-yard bonus for catches is a proxy for the value of 1st downs, as explained by Chase here:

The trouble with directly using 1st downs, of course, is that we wouldn’t have that data for but a fraction of the historical seasons we’re trying to look at here (and this dataset only goes back to the merger). But no doubt somebody like Bobby Engram — long a Football Outsiders darling b/c of his remarkable ability to get 1st downs — is getting underrated here because we’re not measuring 1st downs directly. Engram never had more than 942 True Rec Yds in a season, and only cracked 800 3 times, but probably would be a lot higher if we factored in actual 1st downs instead of using catches as a proxy.

• Kibbles

In addition to Engram, using a flat proxy would also be expected to hurt deep threats like Warfield. For instance, Vincent Jackson (17.8 career ypr) has gotten a first down on 84% of his receptions. Calvin (16.1 ypr) is at 76%. Steve Smith (14.7 ypr) has converted 63% of his catches into a new set of downs. Percy Harvin (11.8 ypr) has done it just 59% of the time. Welker (11.2 ypr) is at 57%. Danny Amendola and his paltry 8.9 ypr has converted just 49% of receptions into a first down. I’d imagine there’s a relatively linear relationship between average yards per receptions and average first downs per reception, and the flat proxy could be replaced by a scaled one.

Of course, that’s easy for me to say, since I wouldn’t be the guy calculating the relationship or updating the formulas…

• ryan

Great work neil and chase…will yoou be posting a career list tomorrow or sometime later?

• I believe that’s the plan.

• Btw, I can tell you right away that Hines Ward fans will be pleased.

• Also, here’s my pre-emptive disclaimer: I don’t think this is in any way the be-all or end-all of receiving stats, and I realize it’s controversial to have a season like Calvin Johnson’s rank 183rd since 1970. The league passing attempts/team passing attempts adjustment will be a particularly upsetting factor to some readers. However, this metric is a simple way to codify all of the adjustments we can currently make to a receiver’s basic boxscore stats.

Think about it: we’ve adjusted raw yardage for pretty much everything we can — catches (a proxy for 1st downs), TDs, schedule length, league passing environment, and yes, even the general number of opportunities a receiver had to catch the ball relative to his peers. Perhaps the latter adjustment is too strong; I certainly can’t prove it isn’t. However, I also think it’s more important to make that adjustment in some way than to ignore it completely. Perhaps further research will help us know exactly how much we should take into account the differences in team passing attempts between 2 receivers, but for now I don’t think it’s that unreasonable of an assumption to say that Calvin Johnson had 60% more opportunities to rack up receiving stats than somebody like Michael Crabtree did in 2012.

• Tom Gower

I’m pretty skeptical there’s the sort of strictly linear relationship between team passing attempts and receiver catches the methodology seems to assume, especially when I see 25 of the top 30 receivers played for below-average passing volume teams, 14 of them for teams that passed at least 10% less than the average team.

• Chase Stuart

Thanks, Tom. Neil and I have are doubts on that, too, but we’re trying to look into that.

One thing to keep in mind: in general, good teams pass less (especially for most of the 43-year period in question). So to the extent the best wide receivers are on the best teams, we would expect them to play for below-average pass volume teams. The ’73 Rams were 1st in socring, 1st in points differential, and 4th in points allowed. As a result, they ended up leading the league in rushing attempts. They had a very good running game, too.

• Chase Stuart

I’ll also note the following. I’m quite confident that to the extent this system is friendly to low-pass volume teams, the magnitude of the bias is significantly smaller than the extent normal metrics are biased towards high-pass volume teams.

• Tom Gower

Yeah, conceptually I have no problem with some sort of adjustment for volume-related adjustment.

To the extent pass attempts are a function of game situation, I’d want to attempt to isolate receivers from defense. That the Rams ranked fourth in points allowed is more or less orthogonal to how good Jackson was, in my point of view. It’s a tricky adjustment to make, especially if you want to conceptually tease out the concepts of best receiving seasons and passing seasons most dependent on a single receiver. The list works well for the latter; I’m much less convinced it does for the former.

• Bowl Game Anomaly

I don’t necessarily think the system should be friendly to low-pass volume teams at all. While the WRs on high-pass volume teams got a lot more opportunities, they were also a much more critical part of their teams’ offenses. I’ve seen people argue that we shouldn’t downgrade RBs from the 70’s for having low YPC and looking to modern eyes like compilers because the offensive style at the time was run-heavy, but you can’t have it both ways. If RBs were more important in the 70’s than now, then WR’s were less important. I guess what I’m arguing is that if you replaced Harold Jackson, Cliff Branch, or Paul Warfield with JAG, their teams wouldn’t suffer all that much compared to how the Lions would suffer if Calvin Johnson was replaced with with JAG.

• Chase Stuart

From a value standpoint, I might be inclined to agree with you. The ’74 Raiders led the NFL in points and points differential; unfortunately, they ranked only 23rd in attempts out of 26 teams (but 1st in Net Yards per Attempt).

Is the argument that if Branch was better, Oakland would have passed more? I find that hard to believe. How do you compare Branch’s 60-1092-13 on a team with 359 pass attempts to Calvin Johnson’s season on a Lions teams with 769 passes? Do you think Johnson’s season was better?

• Bowl Game Anomaly

No, I’m not arguing that the Raiders would have passed more, but I don’t know what “better” means. Who was more valuable? Johnson. Who contributed more relative to the opportunities he was given? Probably Branch. So if you’re measuring actual contribution, then the adjustment makes no sense, but if you’re trying to measure talent in a vacuum, I can see why you would make the adjustment. So as long as we’re clear that the purpose of True Receiving Yards is estimate how good guys like Jackson and Branch might look if they got the chance to play in more favorable circumstances, and not an estimate of how valuable their contributions actually were, then I’m OK with it.

Basically I’m saying that this is a list of the best hypothetical WR seasons, not a list of the best actual WR seasons.

• That’s the right idea. It’s not trying to measure actual value, because like you said, receivers from the 1970s were literally less valuable than they would have been in any other era due to the run-oriented nature of the game. So on the spectrum laid out by this post, True Receiving Yards would fall on the “ability” end.

Now, in light of Dave’s comments, I’m definitely going to refine the team passing attempts adjustment, but the basic goal of even the version above was to project what a receiver “would have” produced in a neutral league.

• Steven

The list does not include Tight Ends?

• I think the version of the data Chase was working off didn’t have TEs included, but we can easily compute it for WRs, TEs, RBs, you name it.

• Dave

For one I think it’s best not to even try to compare across eras even thought we often try. Also we have at least what 20 + years of WR target data right? Well maybe not that much in the pfr database. It seems like a waste to not use that. I’d rather see a pre-target list and post.

In we reality we know that Calvin Johnson had 203 targets to 150 for Steve Smith or a 35% difference. If we just use team passing attempts then we get 727/449 or the formula says that he had 62% more opportunities. Granted he had more plays on which to be a target but even the best WR isn’t going to be the main target on every pass play.So we might be skewing things in the opposite direction towards low volume passing teams. Let’s quickly dig a little deeper

So I did a quick and not very rigorous data collection and analysis but it will help illustrate my point. I pulled WR data from advancednflstats.com from 2005,2009,2012 regular season stats only.My X data column was team pass plays for those WR. Pass Attempts= passes+Sacks. My Y Collumn was targets per game played with a minimum of 12 games played.

The first data set had n=211 with team pass plays ranging from 769 to 411 and WR targets per game ranging from 3.4 to 13.2

So running a regression on the data set. You get and r-squared of 0.1 which means there is only a very loose correlation between the number of team passing attempts vs the number of targets a WR gets a game. Each additional passing attempt was on average worth 0.16 extra targets or an additional 16% of the team targets.

Then I restricted the data set further to guys getting a fair amount of targets I set the cutoff at 100 targets or 6.3 per game. This cut my data set down to an N of 120. Our min and max team passing attempts are still the same. But now our r-sqaured was down to 0.04. Very weak. And now each additional team passing attempt was on average only worth an additional 0.07 targets PER SEASON per team pass with a constant of 91 targets PER SEASON.

Let’s pretend that number is what we should use. Taking the Steve Smith / Calvin Johnson case pretending we don’t know how many targets they got. Just using team pass attempts we think Calvin had 769/477 =61% more opportunities. Using the formula above (91+0.07*769)/(91+0.0.07*477) = 145/124 = only an EXPECTED 16% more opportunities (targets)

So I think this idea definitely needs some more refinement as far as how to adjust for team passing attempts.

• Chase Stuart

Can you run those numbers but only using the top receivers on each team? Otherwise, I think it might jumble the results.

• Dave

Okay I did the following. Only took WR’s with 16 games played. Only selected the top WR on the team. And removed any WR’s with less than 100 targets. This gave me an N of 50. So small sample size theatre which could be improved with using more seasons but I got an r-squared of 0.096 with the following trendline:

0.11x+77.4

So repeating the Calvin Johnson/Steve Smith calculation: (77.4+0.11*769)/(77.4+0.11*477)= 162/130= an expected 25% more opportunities.

Using this same data set:
An average 100+target WR on a 450 pass attempt team can expect 28% of the team targets
An average 100+target WR on a 750 pass attempt team can expect 21% of the team targets

Theoretically his makes sense as a team that passes a lot on average has more good WR’s to throw to than one that throws very little. Or they have better QB that is better at spreading the ball around rather than force feeding one guy.

• Chase Stuart

Thanks Dave. Let me think on this.

• Ok, so I got a chance to look at this… I took all of the WRs in the dataset, who played in and started 16 games in back-to-back seasons (Y and Y+1). They had to be between age 23-30 in year Y. The sample was 245 pairs of player-seasons, after removing 2 extreme outliers: Drew Hill 1985 (went from 335 TRY w/o the team attempt adjustment in 16 gs in 1984 to 1048 in 1985), and our friend Roger Carr 1976 (went from 591 to 1438).

Anyway, the experiment was set up like this: for each player-season in the pair, I recorded how many True Receiving Yds they had *before* the team passing att adjustment (so only adjusting for schedule length and league passing environment). I also recorded their team’s ratio of dropbacks to the average team’s dropbacks. If there were a perfectly linear, 1-to-1 effect of team dropbacks on production (which we assumed in TRY v1.0), then I’d be able to predict the % change in TRY from year Y to Y+1 just by looking at the ratio of tm/lg dropbacks from Y to Y+1.

For instance, in 1979 Alfred Jenkins had 831 TRY before the team att adjustment, and his team’s ratio of dropbacks to the NFL avg was 1.063. In 1980, he started 16 games again for a team with a ratio of 0.954. That means we’d expect Jenkins’ production to decline by 10.3%, derived from (.954/1.063)-1. In reality, though, he improved it by 14% (948 TRY). So that’s one data point.

Do that for all 245 pairs of seasons, and by no means does the regression have a high R^2 (it’s about 0.03)… however, the coefficient on the expected difference, 0.403, is very significant. That basically means that if there’s a 30% increase in team dropbacks, we should predict a 12% increase (40% of the difference between zero and 30%) in productivity/opportunity. This is pretty consistent with what Dave found in his comments:

http://www.footballperspective.com/true-receiving-yards-part-i/#comment-36209

That means Hines Ward, for instance, should only be getting a 15.7% productivity boost in 2004 when PIT threw 39% less than the average team. And Calvin Johnson should only be dinged by 9.2% instead of 23%. Which, I think, is a lot more reasonable than the original version of the formula.

• Re-running things, here are the new top 25 seasons since 1970:

```1. Cliff Branch, 1974 - 1,623 TRY
2. Randy Moss, 2003 - 1,609 TRY
3. Wes Chandler, 1982 - 1,578 TRY
4. Marvin Harrison, 2002 - 1,568 TRY
5. Steve Smith, 2005 - 1,559 TRY
6. Jerry Rice, 1995 - 1,543 TRY
7. Marvin Harrison, 1999 - 1,535 TRY
8. Torry Holt, 2003 - 1,525 TRY
9. Harold Jackson, 1973 - 1,503 TRY
10. Cliff Branch, 1976 - 1,491 TRY
11. Sterling Sharpe, 1992 - 1,488 TRY
12. Herman Moore, 1995 - 1,477 TRY
13. Jerry Rice, 1993 - 1,476 TRY
14. Isaac Bruce, 1995 - 1,476 TRY
15. Michael Irvin, 1995 - 1,476 TRY
16. Otis Taylor, 1971 - 1,473 TRY
17. Paul Warfield, 1971 - 1,469 TRY
18. Gene A. Washington, 1970 - 1,468 TRY
19. Harold Carmichael, 1973 - 1,464 TRY
20. Roger Carr, 1976 - 1,456 TRY
21. Marvin Harrison, 2001 - 1,456 TRY
22. Jerry Rice, 1994 - 1,444 TRY
23. Jimmy Smith, 1999 - 1,435 TRY
24. Randy Moss, 2007 - 1,425 TRY
25. Jerry Rice, 1989 - 1,418 TRY
```

Calvin Johnson 2012 still checks in 37th with 1,366 TRY, but that’s as much a function of the heavy environment adjustment (12.8% more receiving YPG in 2012 than the 1970-2012 avg) as anything else. He’s now 2nd only to Brandon Marshall among 2012 receivers.

• Dave

Awesome! CJ at 37th seems much more reasonable.

• Chase Stuart

I looked at all receivers since 1970 to play in at least 12 games and to have at least 400 receiving yards.

I then separated the receivers, by game, into their three highest attempt games and their three lowest attempt games.

In the HIGH attempt games, the teams passed 45.7 times, and the receivers recorded 91.7 ACY; they averaged 2.03 ACY/Attempt if you take an average of the average ACY/Att, and 2.01 ACY/Att if you divide 91.7 by 45.7. [Note: I think the latter is the more appropriate method, but I’m open to a counter argument.]

In the LOW attempt games, the teams passed 24.6 times, and the receivers recorded 63.6 ACY; they averaged 2.63 ACY/Attempt taking an average of the averages, and 2.58 if you divide 63.6 by 24.6.

So yes, in low-attempt games, WRs average more ACY/Attempt. On one hand, though, this is probably because WRs are doing a better job in high-attempt games than low-attempt games. Putting that issue aside, what does that mean?

When you increase pass attempts by 85.5%, you increase ACY by 44.3%; that implies a 52% ratio, not the 40% Neil got.

• Chase Stuart

If you just take the highest attempt game and lowest attempt games, you get:

High: 49.8 Att, 98.0 ACY, 1.97 ACY/Att;
Low: 21.8 Att, 60.0 ACY, 2.75 ACY/Att.

This implies that for a 128% increase in pass attempts, you only get a 63% increase in ACY, which implies a 50% ratio.

• Chase Stuart

Since we seem to be using the comments as a think tank….

I just ran a regression using these inputs on WR games, with the minimums of 12 games and 400 receiving yards (and 1970):

Team Pass Attempt in Game X
Avg ACY/G in All Games that season but Game X
Avg TPA in all Games that season but Game X

My output was ACY in Game X

The best-fit formula was

9.7 + 1.364*TPA_G_X + 0.725*ACY/G_Avg – 1.05*TPA_Avg

Say a WR averages 100 ACY/G. If his team averages 40 attempts per game, and has 40 attempts in Game X, he’s projected at 94.7 ACY. If his team averages 40 att/g, and he has 50 attempts in Game X, he’s projected at 108.3 ACY. If his team instead throws 30 passes, he’s projected at 81.1 ACY. [One interpretation of this: If his team throws 66.67% more passes, he gains 33.5% more receiving yards.]

Now, say his team averages 30 attempts/game normally, but he’s still a 100 ACY/G guy. In a 30-attempt game, he’s projected at 91.6; in a 40-attempt game, 105; in a 50-attempt game, 118.9.

That “works” but I don’t know what we do with it. [One interpretation of this: If his team throws 66.67% more passes, he gains 29.8% more receiving yards.]

• Dave

“That “works” but I don’t know what we do with it. [One interpretation of this: If his team throws 66.67% more passes, he gains 29.8% more receiving yards.]”

Going back to the Steve Smith/ Calvin Johnson example this very close to what actually happened. DET threw 61% more than CAR but CJ only gained 25% more receiving yards.

• Dave

Just intuitively the main reason we can’t just divide by team passing attempts is realistically a top WR only gets targeted on about 25-30% of pass plays.

• Tim Truemper

I think Tom Gower is on to something on the low passing volume bias (arithmetically). Not being a math whiz, still I can’t help to think about what I learned in the past about restricted ranges and how they affect data magnitude. I look at one specific case from the list above and how it shows a low volume output qualified with the relative passing volume adjustments,and as a result this one receiver’s actual performance makes the list:

1973 Paul Warfield 29 catches 514 yards 11 TD’s.

It is an amazing ratio of TD’s to catches but the absolute #’s are so low. It strikes me that the denominators used against the derived numerators would give a bias toward a higher derived adjusted receiving yards. If I get the time I may compute some other eras and see how they come out. i.e. 1950’s or 1960’s since the data from PFR should be available. I like the described derivation of Neil’s for WR performance as it stimulates discussion and provides a new way to consider player performance across areas and also with the within groups consideration of strength of schedule.

• Dave

Sorry my 2nd point didn’t make sense but this one will. There are also a strong trend between the percent of the team pass plays the WR will get targeted vs how many pass plays the team runs. My cuttoff for this was 100 prorated targets

The R-squared on this regression was about 0.2

The average 100+ target WR on a 450 pass attempt team will average 27% of the teams targets
The average 100+ target WR on a 750 pass atempt team will average 18% of the teams targets

Big difference

• One final experiment for me on the matter…

I took the same sample of players I used for my year-to-year study, and I re-ran the same experiment as before, except I used in-season splits instead of back-to-back seasons. Specifically, I used the ratio of team dropbacks in odd-numbered games to dropbacks in even-numbered games to try to predict the change in ACY from even to odd-numbered games.

The regression once again had a very low R^2 but a significant coefficient on expected change in ACY, and that coefficient was 0.779!

So it’s all over the place. I think Chase’s 50% number is probably the best bet, if not simply because it splits the difference between all of the different results we’ve seen, and it’s pretty convenient. I’d be willing to settle on that as the “official” discount rate on team dropbacks vs league dropbacks in the TRY formula.

• Paul

So what is the final calculations? Do we drop the team adjustments?

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