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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.

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:

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.

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.

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.