It is obviously impossible to separate the receiver from the quarterback when it comes to offensive production. Either party could have a bad day and influence the output. A quarterback could drop the ball in the receiver's hands and deserve most of the credit, or the receiver could force a would-be-tackler to miss and rack up yards after the catch.
We go into this exercise knowing that this is for fun, but also to show how certain players and positions within the Patriots offense are able to withstand the offensive currents, whether by schematic advantage, or just transcendent player ability.
Beta is a term used in finance to essentially explain how a company will react to a change in the market. A beta of 1 means that if the market increases in value, the company will increase in kind- and if the market declines, the company will also decline in value. A beta of less than 1 means that the company will react with less volatility and might not reap the full benefits of an upswing, but they're also slightly more impervious to downswings. A beta of more than 1 means the company will be more volatile.
In order to apply this concept to the Patriots passing offense, know that there are five overly simplified, yet separate, roles in the offense. There's the X, or traditional outside receiver; there's the Y, or the traditional in-line tight end; there's the Z, or the flanker receiver who moves around the formation; there's the slot receiver, we'll call them S; and there's the receiving backs, which we'll call B.
It's extremely important to note that five separate entities cannot be combined to create a "market" that would hold legitimacy in any financial calculations. But we can also say that these five entities combine to create a market that, in other words, is equal to the quarterback's output.
Beta is calculated by comparing the industry's volatility against that of the individual company's fluctuations. In our exercise, we can compare how each position's output changes with spikes in Tom Brady's production. Here's our results:
X Receivers: beta of 0.12; not statistically significant
Y Receivers: beta of 0.37; statistically significant
Z Receivers: beta of 0.09; not statistically significant- but the Y intercept, or the baseline production, for the Z receiver is significant
S Receivers: beta of 0.27; statistically significant
B Receivers: beta of 0.15; statistically significant
Essentially what we find is that the tight ends, slot receivers, and running backs all have their production change depending on which Tom Brady shows up to play. The fact that the Y has the highest beta lends some credence to the notion that Brady's best days are when he has his tight end and that he'll struggle without one.
The standard outside receiver's production doesn't hinge upon Brady on a given day- instead, the X receiver's output seems to stand alone. This is likely due to the lack of a consistent X presence over the past couple of seasons, where Aaron Dobson would have a tremendous game against the Steelers, and then there would be no X receivers for the 2013 playoffs due to injuries.
We find that the Z receiver, or Julian Edelman, is the most interesting of all the categories. Like the X receiver, Edelman's output wasn't overly impacted by Brady's performance. Unlike the X, Edelman's baseline for production was significant, which means that he would be expected to put up a consistent amount of yards, regardless of whether Apex Brady plays, or the version against Kansas City takes the field.
One of the limitations of only have five variables is that it really prevents the opportunity for negative betas. I was hoping there would be an example of a position that receives too much focus in games where the offensive output is lacking. For example, I was thinking that the more receiving yards the running backs had, the more Brady would be checking down, and possibly the more limited the offensive output.
Instead, all five were positive to various degrees, which means that all offensive positions are adding to the offense (which is a good thing!).
I did find some curious results in the correlation of all the data sets. The quarterback's output is best correlated with production of the tight end and out of the slot. It turns out that when the X receiver produces, the tight end position sees an increase in output, but the slot, flanker, and running back positions see a sharp decline in production.
The only position with a negative correlation with the slot receiver's output is the X receiver. A reason could be that when the X is having a tough time producing, Brady will default to using his slot receivers and clogging the middle of the field- which is the Rex Ryan special.
From a fantasy football perspective, you should feel comfortable taking a player like Edelman and know that he's a safe play regardless of the defense or how Brady produces. If you want to take a more aggressive boom-bust approach, taking the Patriots tight end will yield more points when Brady is on fire.
Next season will be an interesting approach since the offense will feature consistency at all points- with the X, Y, Z, and S all returning, along with the ever-fungible running back. The Patriots invested in their tight end position with Scott Chandler due to the importance of the tight end in the offense, while New England has to hope that Edelman isn't hurt- or that Danny Amendola is able to step in without missing a beat.