Depth-Adjusted Efficiency — 2016’s Best and Worst

Yesterday I showed which players were 2016’s most- and least- efficient pass catchers from the perspective of yards per target over expectation (YPTOE). YPTOE situationally adjusted a player’s efficiency based on down, distance, and yard line. Today, I will depth-adjust those numbers, because not all passing depths are created equal.


The methodology behind this was quite basic. I simply regressed each player’s average air yards per target (aYPT) against YPTOE, to find how far players were above or below the regression line. I call this depth-adjusted YPTOE (da.YPTOE).

A more accurate, and better version of this would be to do this on a pass-by-pass basis for each player, rather than with each player’s average depth, but that will have to come in some future research. That will allow us to account for the distribution of target depths along with the down, distance, and field position at which that target depth occurred. For example, a pass 12 yards into the air from the opponents 12 yard line is far different than a pass 12 yards into the air on 1st and 10 from a player’s own 20 yard line.

However, today we’ll just work with averages, which still gives us a very strong picture of which players stood out in 2016.

YPTOE and aYPT express a near-linear relationship, with YPTOE decreasing as target depth increases. That makes sense, because not only does catch rate decrease, but yards after the catch also tends to decrease with increased target depth.


It’s interesting to see how the shorter depths were more tightly grouped around the trend line than longer depths. A simple explanation is that shorter passes have a more consistent catch rate across players, whereas deeper targets have a much higher variance in catch rate.

However, simply taking each player’s da.YPTOE1 doesn’t do us justice. That’s because it’s far easier to put up a big number above expectation at a higher depth, since at the shorter depths things are so much more consistent.

While raw da.YPTOE is great for finding actual depth-adjusted efficiency I also looked at something else. Suppose we wanted to ask the question “is Jarvis Landry better at catching his distribution of passes than DeSean Jackson is at catching his distriubiton of passes,” then da.YPTOE wouldn’t get us there. That’s because Jackson has a YPTOE of 1.82, while Landry had a 1.74 value, but it’s far easier to put up a 1.82 da.YPTOE on deeper passes, because the spread is larger.

As it turns out, that 1.82 da.YPTOE value is only in the 80th percentile of players with an average target depth of about 13.8 yards. However, Landry’s 1.74 is actually in the 90th percentile of players that have a target depth of approximately 6.5 yards. We can translate those percentiles to z-scores, which I call Z.da.YPTOE in the table below.

Both metrics are useful. I think da.YPTOE is better for fantasy purposes, because it answers the question which players provided the most raw yardage value over depth expectations. Z.da.YPTOE tells us who the most efficient players were in their roles. In other words, the latter might be useful for scouting collegiate prospects2 or for evaluating NFL talent in free-agency.3

So, with our depth-adjusted values in hand, let’s see which players topped 2016’s depth-adjusted efficiency, and which ones wound up in the cellar.

Depth-Adjusted Efficiency Results

Chris HoganNE5813.84.945.072.82
Devonta FreemanATL651.14.252.542.52
Adam ThielenMIN9210.83.973.892.41
Taylor GabrielATL5110.43.513.392.14
Julio JonesATL12914.13.63.752.06
Travis KelceKC1176.73.252.681.98
Terrance WilliamsDAL6111.
Vernon DavisWAS598.
Martellus BennettNE735.33.222.431.92
Melvin GordonSD570.53.621.751.81
Doug BaldwinSEA1258.92.972.691.80
Eli RogersPIT669.42.882.661.74
Pierre GarconWAS11410.32.642.511.59
Michael ThomasNO1218.72.632.331.57
Jimmy GrahamSEA959.42.342.121.39
Jarvis LandryMIA1316.52.341.741.29
Stefon DiggsMIN1128.52.131.811.23
Cameron MeredithCHI97102.071.911.22
Greg OlsenCAR12910.92.041.971.22
A.J. GreenCIN10012.
Willie SneadNO1047.52.131.681.19
Brandin CooksNO117131.891.981.13
Mohamed SanuATL8181.971.581.10
Phillip DorsettIND59131.721.811.03
Robert WoodsBUF76111.741.671.03
Duke JohnsonCLE743.12.391.161.03
Cole BeasleyDAL986.31.941.310.98
Tyler LockettSEA6610.61.661.560.98
DeSean JacksonWAS10014.91.631.820.97
Mike WallaceBAL11712.21.591.620.95
DeMarco MurrayTEN671.22.590.910.90
David JohnsonARI1204.71.991.090.89
Eric EbronDET858.31.561.210.83
T.Y. HiltonIND15512.21.351.380.81
Travis BenjaminSD7513.81.331.460.81
Zach MillerCHI646.71.641.070.79
Marvin JonesDET10314.11.281.430.79
Gary BarnidgeCLE8171.561.040.76
Amari CooperOAK1319.81.311.130.73
Giovani BernardCIN512.22.170.740.69
Jack DoyleIND756.41.520.910.68
Kenny BrittLA11111.
Malcolm MitchellNE4810.
Mark IngramNO580.42.530.630.65
Jamison CrowderWAS998.11.280.910.63
Demaryius ThomasDEN14410.31.10.970.61
Steve SmithBAL1028.71.140.840.57
DeVante ParkerMIA8811.90.860.870.52
Golden TateDET1358.11.090.720.50
Chris ConleyKC699.50.970.760.50
Tyrell WilliamsSD11911.60.830.810.49
Chris ThompsonWAS621.
Marqise LeeJAC10512.10.740.760.45
Coby FleenerNO829.30.890.660.43
Dontrelle InmanSD97110.760.690.42
Alshon JefferyCHI9413.40.570.680.38
Tyler BoydCIN818.30.90.550.38
Ty MontgomeryGB561.22.050.370.37
Zach ErtzPHI1068.20.820.460.32
Isaiah CrowellCLE530.72.130.310.32
Rishard MatthewsTEN10813.20.440.540.31
Sammie CoatesPIT4920.80.280.680.30
Dennis PittaBAL1216.210.360.27
Quincy EnunwaNYJ1058.90.640.360.24
Jason WittenDAL956.40.920.310.23
Victor CruzNYG72120.370.390.23
Brandon LaFellCIN10710.20.490.350.22
Cameron BrateTB829.70.430.240.16
Jordan ReedWAS897.
Sammy WatkinsBUF5214.
Delanie WalkerTEN1029.50.430.220.14
Emmanuel SandersDEN13712.
Robby AndersonNYJ7816.9-
Jerick McKinnonMIN530.51.890.020.02
Larry FitzgeraldARI1517.70.440.010.01
Jordy NelsonGB15212.3-0.06-0.02-0.01
Dwayne AllenIND5290.25-0.02-0.01
Randall CobbGB846.40.58-0.03-0.02
Hunter HenrySD538.70.24-0.06-0.04
Julian EdelmanNE1608.80.19-0.1-0.07
Darren SprolesPHI710.81.67-0.12-0.12
Kelvin BenjaminCAR11711.8-0.24-0.24-0.14
Adam HumphriesTB835.60.53-0.21-0.16
Kyle JuszczykBAL491.41.45-0.18-0.18
Odell BeckhamNYG16910.9-0.28-0.35-0.22
Ted GinnCAR9512.3-0.48-0.44-0.26
Dez BryantDAL9614.5-0.67-0.5-0.27
Davante AdamsGB12111.9-0.48-0.47-0.28
John BrownARI7214.1-0.67-0.52-0.29
Antonio BrownPIT15410.3-0.36-0.49-0.31
Charles ClayBUF878-0.07-0.46-0.32
Jordan MatthewsPHI1169.6-0.32-0.52-0.34
Cordarrelle PattersonMIN704.90.4-0.46-0.37
Andrew HawkinsCLE537.8-0.14-0.55-0.39
Brian QuickLA7711.1-0.58-0.64-0.39
Tyreek HillKC838-0.32-0.71-0.49
Michael CrabtreeOAK14510.4-0.72-0.84-0.53
Kamar AikenBAL5011.4-0.86-0.89-0.54
Jermaine GreshamARI617.6-0.37-0.81-0.57
Will FullerHOU9215.5-1.37-1.15-0.60
Terrelle PryorCLE14114.4-1.31-1.14-0.62
Kyle RudolphMIN1326.8-0.34-0.89-0.65
Will TyeNYG706.4-0.32-0.93-0.70
Jeremy MaclinKC7610.8-1.07-1.15-0.71
J.J. NelsonARI7416.9-1.72-1.44-0.72
Mike EvansTB17114.6-1.58-1.4-0.76
Todd GurleyLA581.20.82-0.86-0.85
Jared CookGB519.9-1.16-1.33-0.85
Garrett CelekSF519.3-1.1-1.33-0.88
Kenny StillsMIA8114.3-1.79-1.63-0.89
Anquan BoldinDET955.7-0.48-1.2-0.93
Travaris CadetNO543.8-0.04-1.12-0.95
Clive WalfordOAK528.1-1.05-1.42-0.98
Breshad PerrimanBAL6613.6-2-1.88-1.05
Sterling ShepardNYG1059.3-1.42-1.65-1.09
Brandon MarshallNYJ12912.5-1.97-1.92-1.12
Quinton PattonSF639-1.42-1.69-1.13
C.J. FiedorowiczHOU896.8-0.99-1.54-1.13
Allen HurnsJAC769.9-1.61-1.78-1.14
Jermaine KearseSEA8911.7-1.96-1.97-1.18
Ryan GriffinHOU746.9-1.17-1.71-1.25
Tajae SharpeTEN8313.1-2.34-2.25-1.28
DeAndre HopkinsHOU15111.9-2.2-2.19-1.30
Allen RobinsonJAC15013.2-2.41-2.31-1.31
Jordan HowardCHI502.6-0.12-1.46-1.33
Theo RiddickDET670.30.64-1.29-1.35
Michael FloydNE7614.6-2.79-2.61-1.41
James WhiteNE861.20.21-1.47-1.45
Trey BurtonPHI607.9-1.82-2.22-1.55
Marquise GoodwinBUF6814.8-3.09-2.9-1.56
T.J. YeldonJAC680.20.34-1.62-1.71
Jeremy KerleySF1158.6-2.27-2.58-1.75
Lance KendricksLA875-1.43-2.28-1.82
Jesse JamesPIT606.9-1.96-2.5-1.83
Albert WilsonKC517.1-2.07-2.58-1.87
Corey ColemanCLE7314.1-3.58-3.43-1.89
Devin FunchessCAR5813.2-3.51-3.41-1.93
Antonio GatesSD938.3-2.57-2.92-2.01
Seth RobertsOAK778.4-2.6-2.94-2.01
Julius ThomasJAC517.1-2.36-2.87-2.08
Torrey SmithSF4913.5-3.9-3.78-2.12
Dorial Green-BeckhamPHI7410.3-3.23-3.36-2.12
Nelson AgholorPHI6910.6-3.44-3.54-2.21
Corey BrownCAR5310.2-3.35-3.49-2.22
Donte MoncriefIND5610.3-3.55-3.68-2.33
Tavon AustinLA1066.9-2.95-3.49-2.55

Chris Hogan leads the table, just like he did in raw YPTOE and Sum.Z from yesterday’s article. This time he led not only in raw YPTOE, but also in depth-adjusted and Z.da.YPTOE. A couple things about Hogan here. First, I’m not saying he’s the best receiver in the NFL. I’m just saying he had a very good season, and of course we can’t discount the fact he had Tom Brady throwing him the ball. Also, the sample size isn’t huge, with only 58 targets to his name in 2016.

I’ll also once again harp on how good Kenny Britt is. He came in 41st overall, but 28th among WRs in Z.da.YPTOE, despite the terrible QB play around him in Los Angeles. If Cody Kessler starts from the get-go, and repeats his 7.2 AYA, Britt could be a huge sleeper at his WR54 ADP.4

At this point, it should be no surprise Devonta Freeman is elite in his role out of the backfield in the passing game. I bet it surprises you that Melvin Gordon checks in as second best out of the backfield, though. Compare Gordon to Jerick McKinnon who had the same aYPT of 0.5, but Gordon finished 1.75 yards above expected for that depth compared to McKinnon’s 0.02 above. And don’t blame QB play for McKinnon’s deficiency. Both Adam Thielen and Stefon Diggs came in with top-17 scores by the Z.da.YPTOE metric.

On Jacksonville, take note of Marqise Lee, who was 0.45 standard deviations above average for his depth. That may not sound great, but consider the next highest Jacksonville player was 1.14 standard deviations below, and now you see why Lee was 2016’s best Jaguar.

On the flip side, the player who performed worst relative to his role in 2016 is none other than Tavon Austin. Despite a 6.9 average depth, he came up 3.49 yards below his depth-adjusted expectation. When we compare that to Landry’s 6.5 depth and 1.74 yards above, Landry looks like God. Seriously. Landry is really freaking good at what he does, while Austin is really freaking bad at what he does.

Other interesting names of note that stunk up the joint: Donte Moncrief, Antonio Gates, and T.J. Yeldon, who comes in as the worst rated running back by the Z.da.YPTOE metric.

What else did you find interesting from the table? Let me know in the comments.

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  1. Which is calculated by taking the player’s actual YPTOE value minus the trend line YPTOE value for his average depth of target  (back)
  2. If we ever get air yards data for them.  (back)
  3. Even then, as I talked about in yesterday’s article, we’d have to make an adjustment for QB quality as well.  (back)
  4. ADP via the Best-Ball ADP App.  (back)
By RotoDoc | @RotoDoc | Archive

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  1. Really surprised to see the big 3 in GB all with 0 to slightly negative numbers, especially considering QB play might help those. Any thoughts on why that might be?

  2. Yes, it is. I have a much larger data set with multiple years. I just showed 2016.

    YPTOE also correlates strongly with @friscojosh's RACR metric, and when we depth adjust both (YPTOE linearly, RACR has a reciprocal relation with depth), they are basically the same thing (R^2 like 0.85)

  3. Yeah, Rodgers didn't have the most efficient year in terms of depth-adjusted efficiency. His super short passes were well above league average (which is why TyMo looks good), but the rest were medicore.

    @friscojosh showed me a graph of depth vs RACR against league average, and basically backs up what my findings found here.

  4. Sorry, this is Rodger's career YAC/catch rate and RACR.

    Picture is the same in 2016 tho, just larger error bands.

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