*Fat Eddie Lacy would be our dream girl if he were a receiver. I mean not really, but anytime you can start a post with Fat Eddie Lacy and dream girl, you have to.
Not long ago Chase Stuart posted some analysis on Matt Waldman’s blog that came to the conclusion that while NFL teams seem to favor taller receivers when drafting them, in the regressions that he ran he couldn’t find evidence that teams undervalue tall receivers. A quote from Stuart’s analysis:
First, I ran a regression using Draft Pick Value as my sole input and True Receiving Yards as my output. The best-fit formula was:
TRY through five years = 348 + 131.3 * Draft Pick Value
That doesn’t mean much in the abstract, so let’s use an example. Keyshawn Johnson was the first pick in the draft, which gives him a draft value of 34.6. This formula projected Johnson to have 4,890 TRY through five years. In reality, he had 4,838. The R^2 in the regression was 0.60, which is pretty strong: It means draft pick is pretty strongly tied to wide receiver production, a sign that the market is pretty efficient.
Then I re-ran the formula using draft pick value *and* height as my inputs. As it turns out, the height variable was completely meaningless. The R^2 remained at 0.60, and the coefficient on the height variable was not close to significant (p=0.53) despite a large sample of 543 players.
Good Things Come in Small Packages.. Wait…Nevermind.
So that the analysis that I post here doesn’t seem like I’m trying to move the goalposts, let me say that in the work that I do I almost always refer to receiver size in terms of weight rather than height. Also, when I say “almost always” I really mean “always”. I have a few reasons.
First, there are just a small number of unique measurements for height, whereas weight is essentially a continuous scale for WRs from 170 to 240 pounds. Second, I came to my weight emphasis while creating my prospect models. I could never get height to stay in as a significant variable when weight was included so I always dropped height. This is reflected in any number of my posts where I show prospect attributes by weight and don’t even list height in the table. Having said that, the two are likely to be correlated so I don’t really make a point of correcting the various mentions of player height by popping in every time to say that the people talking height should actually be talking weight. Also, I’ve created red zone TD rate models in the past and the significant variables I found then were QB quality, WR height, and field position. So height definitely matters in some sense.
But when trying to compare what we do here with Stuart’s work it’s important to remember that we’re looking at different numbers. We tend to predict fantasy points, which has 3X the emphasis1 for TDs compared to Stuart’s model.
But we also do a good amount of popping off about how NFL teams undervalue big receivers, so if that’s not actually true we should probably shut up.
For what it’s worth, I’m still pretty sure we’re right.
I ran a series of regressions using data from the 2000-2013 seasons available from Armchair Analysis. This data comes preloaded with height, weight and draft pick numbers for players. That’s nice because it cuts down on the data munging often required when doing this sort of work. It also contains target information for plays, which I think is important for reasons that I’ll explain.
Wide Receiver Stats: Heads I Win, Tails You Lose
In Stuart’s work he used a number that he calls True Receiving Yards which is an era and team adjusted way to describe a player’s receptions, yards and touchdowns in one number. I thought a straightforward way for me to look at the problem would be to simply use Adjusted Yards from the Adjusted Yards per Attempt formula. I think it’s a pretty defensible way to look at the issue. We know that AYA is pretty highly correlated with winning. Our concept of a receiver’s value should be tied to whether or not they can help win football games. The main place I’ll be deviating from commonly accepted notions of receiver value is that this means that I’m giving WRs some credit for INTs as well.
Some might argue that it’s not fair to award a receiver credit for INTs. INTs are thrown by QBs. Well touchdowns are thrown by QBs too, but we give receivers credit for touchdowns. Adding INTs to a receiver’s side of the ledger also corrects for another issue that plagues receiver evaluation, and that’s the fact that there’s no penalty for volume when most people discuss receivers.
Let me explain why this is. Every pass attempt that an offense makes has the potential to be intercepted, which is going to reduce the team’s chances of winning. Interceptions are probably the reason that lots of football people still prefer ground and pound. So pass attempts aren’t costless. And yet we’ve historically treated receivers as if their contributions can only be positive. Giving receivers credit for INTs just forces them to produce yards and touchdowns at a rate that exceeds the INTs that they account for. And if they can’t produce yards and touchdowns at a rate that exceeds the INTs they account for, how valuable are they anyway? It’s a lot more likely that they’re just beneficiaries of a team outlook that tends not to care about turnovers, which is to say that the apparent value of the yards and touchdowns they produce is probably illusory.
Here are the steps I used when I performed this analysis:
- Calculate Adjusted Yards (AY) for every play from 2000-2013
- Total up AY for each receiver for each of his first three years in the league. Greg Little just got cut after his third year in the league so I feel like that’s probably a pretty safe window to use. Just to be clear, because I don’t want this to be missed, the number we’re using is cumulative. It’s not a per target number. That rewards players that can compile volume.
- Delete receivers that didn’t start their careers during the 2000 season or after. Bye bye Randy Moss.
- Delete receivers that hadn’t played their third year by 2012. Bye bye Josh Gordon.
- Adjust each player’s AY so that it’s inflated making each season equal to 2013 in terms of total AY. I did this to account for changes over time in league passing.
- Assign all undrafted players the very highest pick in any draft over that time, which was pick 255.
- The resulting data set had 559 players (if you cut it down to just drafted players it’s 350).
- Run the regression once with Total AY in First Three Years as the dependent variable and Draft Position as the independent variable.
- Run the regression again but add in Weight as an independent variable.
Here are the results of each regression:
Draft Position Only Model
You can see that the Adjusted R-Squared is about .33. The p-value for Draft Position is such that it would pass commonly accepted tests of significance. The formula for estimating AY for a receiver in their first three years is 1376 + DraftPosition * –4.7917.
Draft Position + Weight Model
The r-squared doesn’t improve a lot (it does improve slightly) but weight would pass most tests of significance. Perhaps the most important point is that from an economic significance standpoint, weight certainly seems to be important. The coefficient for draft position is –4.7 while the coefficient for WT is 3.88. Each pound is worth about 82% of one draft spot. Or, in case a very simple hypothetical helps, a 200 pound player selected with the 1st overall pick could be expected to have compiled the same number of Adjusted Yards as a (roughly) 230 pound player at the 26th overall selection.
Also, it may be worth noting that the draft position side of the equation really benefited from throwing out the 2012 and 2013 draft classes. Even though it’s cumulative, Josh Gordon and Alshon Jeffery have produced enough in two years to move the numbers a little (with a little help from AJ Jenkins).
I think it would be really tough to argue that the method I’ve used to do perform this analysis isn’t related to real world receiver value. I also think it would be tough to argue that it’s biased in favor of larger receivers in a way that would deviate from football’s natural bias towards larger receivers. And yet there it is, evidence that NFL teams do undervalue receiver size in the draft. And for those that say there is no Moneyball in football, we’ve just found that a pound on a receiver is worth about 4/5ths of a draft spot. That’s probably actionable information.
- a TD is worth 60 yards in most fantasy leagues and only 20 yards in Stuart’s work (back)