The two inputs of fantasy value are opportunity and efficiency. Much of opportunity is controlled. The Giants chose to pass the ball on a greater percentage of their snaps in 2011 than in 2010. However, some opportunity seems to be random. The Giants did not choose to have 1,013 offensive snaps in 2011. They did not choose to have 1,034 offensive snaps in 2010. It is a small difference, but one that could have a real effect on fantasy production.
Before I made a blanket assumption, I wanted to be sure. There are some teams that show consistency on either side of the mean. For example, the Bills never exceeded 1,000 offensive snaps from 2008-2011 while the Ravens never failed to exceed 1,000 offensive snaps. I wondered if there was some characteristic of a team that could influence expectations for snaps in future seasons, and so I ran a regression analysis on each pair of year y to year y + 1 over those four seasons.
The r-squared of the model was 0.10, which represents a very weak correlation. One cannot use the offensive snaps of a team in one year to predict them in the next. Snaps are random, and as such, represent a risk for expected future production.
On average, teams have experienced a 35-snap* annual deviation from 2008-2011, which when scaled to total snaps makes for a coefficient of variation of 0.035. However, to apply the risk of a decrease in offensive snaps to my pricing model, I cannot use the variation scaled to snaps. I have to scale them to fantasy points.
To do so, I selected the players I previously identified as stars in their prime in each of 2009, 2010, and 2011. I added up their fantasy points and snaps played from that window and divided them to create a points per snap estimation for their position. In effect, the players I selected could overestimate the effect of snap variation for the position because the elite star players would be expected to produce more fantasy production per snap. However, I chose stars in their prime over the entire population of players above replacement in order to isolate the effect of snap variation. So deep into the study, I am afraid I will accidently double-count a risk by overlapping factors, and the star players lend me confidence that the year-to-year fluctuation in their numbers is mostly noise.
The five quarterbacks combined to score 4126.4 fantasy points in 15,750 snaps, a ratio of 0.262 points per snap.
The eight running backs combined to score 4909.8 fantasy points in 17,041 snaps, a ratio of 0.288 points per snap.
Finally, the wide receivers and tight ends—which I combined because there are only 2 tight ends that were stars in their prime in all three seasons—combined to score 4349.1 fantasy points in 25,000 snaps, a ratio of 0.174 points per snap.
To solve for an estimated change in fantasy points due to offensive snap variance, I simply multiplied those points per snap figures by the 35 snaps standard deviation. The results are 9 points for quarterbacks, 10 points for running backs, and 6 points for receivers and tight ends.
|PPS||PP 35 Snaps||CV|
The final step in creating a discount rate for offensive snap variance is to scale those results by the average fantasy points scored by all players above the replacement level over the same three-year window, which is the value pool that informs our auction prices. For quarterbacks, wide receivers, and tight ends, there is a coefficient of variation of 0.001. For running backs, there is a coefficient of variation of 0.002.
Here is the updated table of all of the discount factors so far:
|Position||Category||Risk-free rate||Positional risk||Attrition rate||Snaps risk||Discount rate|
|QB||Star in prime||0.009||0.029||0.224||0.001||0.263|
|QB||Star in decline||0.009||0.029||0.652||0.001||0.692|
|QB||Star with reservations||0.009||0.029||0.001|
|RB||Star in prime||0.009||0.028||0.256||0.002||0.295|
|RB||Star in decline||0.009||0.028||0.652||0.002||0.691|
|RB||Star with reservations||0.009||0.028||0.002|
|WR||Star in prime||0.009||0.020||0.242||0.001||0.272|
|WR||Star in decline||0.009||0.020||0.652||0.001||0.682|
|WR||Star with reservations||0.009||0.020||0.001|
|TE||Star in prime||0.009||0.016||0.263||0.001||0.289|
|TE||Star in decline||0.009||0.016||0.652||0.001||0.678|
|TE||Star with reservations||0.009||0.016||0.001|
*At original publication, this read as a 68-snap deviation, but that was based on an incorrect snap report. I have corrected all of the results that were based on that report. Thank you to thebenny for realizing my mistake.
Questions and comments are always welcome via Twitter – @PFF_ScottSpratt
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