# How to Project Receiving Yards

A method to come up with a starting point for your wide receiver projections

The number of receiving yards a player produces is the result of a large number of variables. Some of them, like the receiver's ability, are pretty consistent from year to year. But other factors are less reliable, or less "sticky" from year to year.  I thought it would be informative to look at three key variables that impact the number of yards a wide receiver gains and measure how "sticky" they are from year to year. These three variables are:

• The number of pass attempts by his team;
• The percentage of his team's passes that go to him; and
• The receiver's average gain on passes that go to him.

We can redefine receiving yards to equal the following equation:

Receiving yards = Receiving Yards/Target x Targets/Team_Pass_Att  x  Team_Pass_Att.

You'll notice that Targets and Team Pass Attempts are in both the numerator and denominator of one of the fractions, and they will cancel each other out: that's why this formula is equivalent to receiving yards.

Last year, Calvin Johnson's team led the NFL in pass attempts and Brandon Marshall was number one in percentage of team targets. Depending on your cut-offs, either Danario Alexander (on 62 targets) or Demaryius Thomas (on 141 targets) finished first in yards per target. Picking among Johnson, Marshall, or Thomas in many ways involves deciding which variable is most likely to repeat itself in 2013.

Alternatively, regression to the mean principles could have you high on a receiver who had an unusually low number in one of these three metrics. The Seahawks were last in pass attempts last year; an increase could be good news for Sidney Rice (ignoring the Percy Harvin acquisition). Among receivers to play in 14+ games, Josh Gordon and Malcom Floyd were the two WR1s who received the fewest percentage of their team targets. And Larry Fitzgerald finished last among receivers in yards per target. Knowing which of those three statistics - pass attempts, percentage of the pie, and yards per target - is most likely to regress to the mean is very helpful when it comes to making fantasy projections.

## Team Pass Attempts

How sticky are team pass attempts from year to year? I'm actually going to further break down "Pass Attempts" into two variables: Offensive Plays and Pass Attempts per Offensive Play (excluding sacks from the numerator but including them in the denominator). We can use those two variables to predict future pass attempts. Based on data from the last 10 years, the best fit formula is:

Future Pass Attempts = 36 + (450 x Pass_Attempts/Play) + (0.255 x Offensive Plays)

What does that mean for 2013? I took last year's stats and applied that formula, which gives us a best-guess projection for 2013 in terms of number of pass attempts. The Lions rank 1st in projected pass attempts but they are still projected to throw significantly less often in 2013.  Last year, Detroit passed on 63.8% of all pass plays and ran 1,160 plays. The Lions finished the season with an insane 740 passes, but project to lead the league with "only" 619 passes this year, for a difference of 121 fewer passes.

RankTeam2012 PA/P2012 Off Plays2012 Passes2013 Proj PassDifference
1 DET 63.8 1160 740 619 -121
2 NOR 62.9 1067 671 591 -80
3 DAL 62.7 1049 658 586 -72
4 NWE 53.8 1191 641 582 -59
5 IND 56.6 1109 628 574 -54
6 OAK 60.9 1032 629 573 -56
7 PHI 57.3 1079 618 569 -49
8 ATL 60.2 1021 615 567 -48
9 ARI 59.7 1018 608 564 -44
10 DEN 53.9 1090 588 557 -31
11 JAX 59 994 586 555 -31
12 PIT 56.1 1023 574 549 -25
13 TAM 56.2 1008 566 546 -20
14 CLE 56.7 998 566 546 -20
15 BAL 53.7 1042 560 544 -16
16 GNB 53.6 1042 558 543 -15
17 HOU 50.8 1090 554 543 -11
18 STL 55.6 1002 557 542 -15
19 CIN 53.1 1016 540 534 -6
20 TEN 56.4 957 540 534 -6
21 NYG 55.7 968 539 533 -6
22 SDG 53.4 988 528 528 0
23 BUF 52 983 511 521 10
24 MIA 51.4 981 504 517 13
25 NYJ 47.7 1034 493 514 21
26 CAR 49.6 988 490 511 21
27 CHI 48.5 999 485 509 24
28 MIN 48.3 1001 483 508 25
29 KAN 46.8 1015 475 505 30
30 WAS 44.5 994 442 490 48
31 SFO 45 969 436 486 50
32 SEA 41.6 974 405 471 66

These number should never be taken as gospel. If you think the Lions are likely to pass 700+ times again this year, that's fine. This simply says that on average, teams like the Lions tend to see a significant dip in pass attempts. It doesn't mean Detroit will throw "only" 621 times, just that projecting a big dropoff makes some sense. If you have reasons that make you think the Lions will again pass 700+ times, then by all means, you should project just that.

## Targets per Team Attempt

Next, let's look at targets per team attempt. There were 256 wide receivers from 2000 to 2011 who met the following three criteria:

• Played in at least 14 games in one year;
• Were targeted at least 100 times in that season; and
• Played in at least 14 games in the next season for the same team.

In Year N, on average, the receivers in this group saw 132 targets, played on teams that threw 538 passes, and therefore saw 25.0% of their team's targets.  In Year N+1, they saw 129 targets, played on teams that threw 540 passes, and saw 23.9% of their team's targets.

But we don't care too much about the average: what we really want to look at is each wide receiver's percentage of the pie when it comes to team targets. How "sticky" is the percent of targets each receiver sees from year to year? For this group of 256 wideouts, the best-fit formula is:

Future Percentage of Targets = 6.2% + 71.3% x Past Percentage of Targets

What does that mean? There is some regression to the mean, but not too much: for the most part, the piece of the pie that a receiver sees is pretty consistent from year to year. There were 28 wide receivers who played in at least 14 games and saw 100+ targets in 2012, and are back with the same team in 2013. The table below shows the percentage of team targets this formula would tell us to project for those players for 2013:

RankWide ReceiverTeam2012 Targets2012 Team Pass Att2012 Tar/TPA2013 ProjectionDiff
1 Brandon Marshall CHI 192 485 39.6 34.4 -5.2
2 Reggie Wayne IND 195 628 31.1 28.3 -2.7
3 A.J. Green CIN 165 540 30.6 28 -2.6
4 Andre Johnson HOU 162 554 29.2 27 -2.2
5 Steve Johnson BUF 148 511 29 26.9 -2.1
6 Steve Smith CAR 138 490 28.2 26.3 -1.9
7 Calvin Johnson DET 204 740 27.6 25.9 -1.7
8 Victor Cruz NYG 143 539 26.5 25.1 -1.4
9 Brian Hartline MIA 131 504 26 24.7 -1.3
10 Vincent Jackson TB 147 566 26 24.7 -1.3
11 Larry Fitzgerald ARI 156 608 25.7 24.5 -1.2
12 Demaryius Thomas DEN 141 588 24 23.3 -0.7
13 Roddy White ATL 143 615 23.3 22.8 -0.5
14 Justin Blackmon JAX 131 586 22.4 22.1 -0.2
15 Mike Williams TB 126 566 22.3 22.1 -0.2
16 Dez Bryant DAL 138 658 21 21.2 0.2
17 Julio Jones ATL 128 615 20.8 21 0.2
18 Eric Decker DEN 122 588 20.7 21 0.2
19 Torrey Smith BAL 110 560 19.6 20.2 0.6
20 Jeremy Maclin PHI 121 618 19.6 20.2 0.6
21 Marques Colston NO 130 671 19.4 20 0.6
22 Kendall Wright TEN 104 540 19.3 19.9 0.7
23 Andre Roberts ARI 114 608 18.8 19.6 0.8
24 Randall Cobb GB 104 558 18.6 19.5 0.9
25 Denarius Moore OAK 114 629 18.1 19.1 1
26 Miles Austin DAL 119 658 18.1 19.1 1
27 Cecil Shorts JAX 105 586 17.9 19 1.1
28 Lance Moore NO 104 671 15.5 17.3 1.8

With the exception of Brandon Marshall, who had a ridiculous 40% target rate last year, every other receiver is projected to come in with a very similar rate in 2013. And, of course, Marshall is still projected to be #1 by a significant amount in target percentage.

That sort of consistency would render this article useless if it applied to all of these statistics. But as we're about to see, that's not the case.

## Yards per Target

As it turns out, yards per target -- even when only looking at the best receivers -- isn't a very "sticky" metric. This makes sense. Targets are a good thing and are indicators of talent and ability. Punishing a player for a "failed" target doesn't make a lot of sense, and it doesn't help you predict the future. By dividing by targets, you're implying that a target that yields no yards is a bad thing, but in fact, the opposite is often the case. On a given incomplete pass, the targeted receiver may have done the best job of the players on the field, and that makes him more likely to see targets in the future.

Of course, that's just theory. What do the numbers say? Looking at that same group of 256 wide receivers, here is the best-fit formula to project future Yards/Target from past Yards/Target:

Future Yards/Target = 5.5 + 0.29 x Past Yards/Targets

This formula tells us that receivers retain very little of their Yards/Target value, whether positive or negative. Essentially, this means that even though Demaryius Thomas averaged a high number of Yards/Target, we're not going to bet on that happening again. It also means that Larry Fitzgerald's poor Yards/Target average last year may not be as big of a deal as you might think. The table below shows the 2013 projections for the same 28 wide receivers as before in Yards/Target.

RankWide ReceiverTeam2012 Yards2012 Targets2012 Yards/Target2013 Yards/TargetDifference
1 Demaryius Thomas DEN 1434 141 10.2 8.5 -1.7
2 Dez Bryant DAL 1382 138 10 8.4 -1.6
3 Lance Moore NO 1041 104 10 8.4 -1.6
4 Andre Johnson HOU 1598 162 9.9 8.4 -1.5
5 Calvin Johnson DET 1964 204 9.6 8.3 -1.3
6 Roddy White ATL 1351 143 9.4 8.2 -1.2
7 Vincent Jackson TB 1384 147 9.4 8.2 -1.2
8 Julio Jones ATL 1198 128 9.4 8.2 -1.1
9 Cecil Shorts JAX 979 105 9.3 8.2 -1.1
10 Randall Cobb GB 954 104 9.2 8.2 -1
11 Marques Colston NO 1154 130 8.9 8.1 -0.8
12 Eric Decker DEN 1064 122 8.7 8 -0.7
13 Steve Smith CAR 1174 138 8.5 8 -0.5
14 Brian Hartline MIA 1083 131 8.3 7.9 -0.4
15 A.J. Green CIN 1350 165 8.2 7.9 -0.3
16 Miles Austin DAL 943 119 7.9 7.8 -0.1
17 Mike Williams TB 996 126 7.9 7.8 -0.1
18 Brandon Marshall CHI 1508 192 7.9 7.8 -0.1
19 Torrey Smith BAL 855 110 7.8 7.8 0
20 Victor Cruz NYG 1092 143 7.6 7.7 0.1
21 Jeremy Maclin PHI 857 121 7.1 7.6 0.5
22 Steve Johnson BUF 1046 148 7.1 7.6 0.5
23 Reggie Wayne IND 1355 195 6.9 7.5 0.6
24 Andre Roberts ARI 759 114 6.7 7.4 0.8
25 Justin Blackmon JAX 865 131 6.6 7.4 0.8
26 Denarius Moore OAK 741 114 6.5 7.4 0.9
27 Kendall Wright TEN 626 104 6 7.3 1.2
28 Larry Fitzgerald ARI 798 156 5.1 7 1.9

Now, what if we put it all together? Remember, we can define Receiving Yards as Team Pass Attempts multiplied by (Targets/Team Pass Attempt) multiplied by (Receiving Yards/Target). Since we now have projections for each of these 28 receivers in each of these three categories, we can come up with a baseline projection of 2013 receiving yards.

RankPlayerTeam2012 Rec Yds2013 Team Pass2013 Targ/TPA%2013 Yd/Tar2013 Rec YdsDifference
1 Brandon Marshall CHI 1508 509 34.4 7.8 1365 -143
2 Calvin Johnson DET 1964 619 25.9 8.3 1328 -636
3 Andre Johnson HOU 1598 543 27 8.4 1229 -369
4 Reggie Wayne IND 1355 574 28.3 7.5 1223 -132
5 A.J. Green CIN 1350 534 28 7.9 1178 -172
6 Vincent Jackson TB 1384 546 24.7 8.2 1111 -273
7 Demaryius Thomas DEN 1434 557 23.3 8.5 1097 -337
8 Steve Smith CAR 1174 511 26.3 8 1071 -103
9 Roddy White ATL 1351 567 22.8 8.2 1066 -285
10 Steve Johnson BUF 1046 521 26.9 7.6 1056 10
11 Dez Bryant DAL 1382 586 21.2 8.4 1043 -339
12 Victor Cruz NYG 1092 533 25.1 7.7 1035 -57
13 Brian Hartline MIA 1083 517 24.7 7.9 1012 -71
14 Julio Jones ATL 1198 567 21 8.2 982 -216
15 Larry Fitzgerald ARI 798 564 24.5 7 966 168
16 Marques Colston NO 1154 591 20 8.1 956 -198
17 Mike Williams TB 996 546 22.1 7.8 940 -56
18 Eric Decker DEN 1064 557 21 8 939 -125
19 Justin Blackmon JAX 865 555 22.1 7.4 912 47
20 Miles Austin DAL 943 586 19.1 7.8 873 -70
21 Jeremy Maclin PHI 857 569 20.2 7.6 867 10
22 Cecil Shorts JAX 979 555 19 8.2 865 -114
23 Randall Cobb GB 954 543 19.5 8.2 864 -90
24 Lance Moore NO 1041 591 17.3 8.4 858 -183
25 Torrey Smith BAL 855 544 20.2 7.8 852 -3
26 Andre Roberts ARI 759 564 19.6 7.4 821 62
27 Denarius Moore OAK 741 573 19.1 7.4 811 70
28 Kendall Wright TEN 626 534 19.9 7.3 772 146

What can we takeaway from this?

• When it comes to Brandon Marshall, he might be undervalued because the Bears should throw more frequently this year. Marshall had a huge percentage of Chicago's targets, and that's likely to repeat itself, so this formula projects him as the most likely player to lead the league in receiving yards.
• Calvin Johnson drops to #2 because he should experience a lot of regression when it comes to both team pass attempts and his yards per target. The Lions set an NFL record for pass attempts last season: at some point, Matthew Stafford isn't going to keep throwing 650+ pass attempts every year. That's a risk imbedded in drafting Megatron.
• Andre Johnson averaged 9.9 yards per target last year. He's an outstanding receiver, but that sort of production isn't very sustainable. Demaryius Thomas should experience some regression, too. Of course, in Thomas' case, having Peyton Manning should help to offset that. I wouldn't argue with you if you thought Thomas will have another huge year when it comes to Yards/Target. Again, these are just supposed to be a baseline projection: if you have a good reason to move a player up or down, you should feel comfortable doing that.
• Nobody is expecting Larry Fitzgerald to have just 798 yards again, but at least now we can specify exactly why. His yards/target average was abysmal last year, and that is the type of thing that usually reverts pretty aggresively to the mean. It's informative to compare Fitzgerald to his Cardinals teammate. In 2012, Andre Roberts saw 18.8% of the Cardinals targets and averaged 6.7 yards per target, while Fitzgerald was at 25.7% and 5.1, respectively. This formula tells us if that's all we know about these two players, Fitzgerald is the better bet for 2013.
• A similar analysis would inform a Justin Blackmon/Cecil Shorts decision, had Blackmon not been suspended for the first four games of the year. Blackmon saw 22.4% of the Jaguars targets, Shorts 17.9%; however, Shorts averaged 9.3 Y/T compared to only 7.4 Y/T for Blackmon. Despite Shorts gaining over 100 more receiving yards than Blackmon, this method would project Blackmon with about 50 more yards than Shorts this year, absent the suspension. Of course, one could argue that as Shorts continues to prove himself -- he was a first-year starter in 2012 -- his share of the pie will naturally increase.
• Steve Smith and Steve Johnson are both projected to do well in 2013 because they produced in 2012 for teams that didn't pass very often.  Both players were huge parts of their team's passing games, which is likely to repeat itself, and if Buffalo and Carolina pass more this year, the fantasy values of Smith and Johnson will increase. For Johnson, he's potentially undervalued for yet another reason: he averaged only 7.1 yards/target last year.