Fantasy: Variance of Opportunity

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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.

Player	Snaps	FanPts
Aaron Rodgers	2947	859.96
Drew Brees	3259	911.36
Tom Brady	3220	877.32
Eli Manning	3179	710.24
Philip Rivers	3145	767.52
	15750	4126.4

The five quarterbacks combined to score 4126.4 fantasy points in 15,750 snaps, a ratio of 0.262 points per snap.

Player	Snaps	FanPts
Ray Rice	2488	754.5
Maurice Jones-Drew	2357	738.6
Michael Turner	1558	569
Frank Gore	2076	555.6
Adrian Peterson	1913	700.7
Steven Jackson	2507	578
Fred Jackson	1980	477.1
Matt Forte	2162	536.3
	17041	4909.8

The eight running backs combined to score 4909.8 fantasy points in 17,041 snaps, a ratio of 0.288 points per snap.

Player	Snaps	FanPts
Calvin Johnson	2963	578.1
Wes Welker	2497	499.1
Larry Fitzgerald	2985	518
Roddy White	2987	556.3
Marques Colston	2350	460.7
Brandon Marshall	2602	450.3
Greg Jennings	2409	478.6
Jason Witten	3239	391.4
Vernon Davis	2968	416.6
	25000	4349.1

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
QB	0.262	9	0.001
RB	0.288	10	0.002
WR/TE	0.174	6	0.001

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	Rookie prospect	0.009	0.029		0.001
QB	Potential star	0.009	0.029	-0.009	0.001	0.031
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
QB	RORA	0.009	0.029	0.633	0.001	0.672
QB	P&Q	0.009	0.029	0.029	0.001	0.068
QB	Non-star	0.009	0.029	0.236	0.001	0.276
RB	Rookie prospect	0.009	0.028		0.002
RB	Potential star	0.009	0.028	-0.041	0.002	-0.003
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
RB	RORA	0.009	0.028	0.647	0.002	0.685
RB	P&Q	0.009	0.028	0.282	0.002	0.321
RB	Non-star	0.009	0.028	0.443	0.002	0.482
WR	Rookie prospect	0.009	0.020		0.001
WR	Potential star	0.009	0.020	0.104	0.001	0.134
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
WR	RORA	0.009	0.020	0.694	0.001	0.724
WR	P&Q	0.009	0.020	0.152	0.001	0.182
WR	Non-star	0.009	0.020	0.441	0.001	0.471
TE	Rookie prospect	0.009	0.016		0.001
TE	Potential star	0.009	0.016	0.162	0.001	0.188
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
TE	RORA	0.009	0.016	0.656	0.001	0.682
TE	P&Q	0.009	0.016		0.001
TE	Non-star	0.009	0.016	0.508	0.001	0.534

 

*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.

 

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