Fantasy: Variance of Efficiency

| 2012/08/01

Small-seeming changes in efficiency can lead to dramatic changes in fantasy production. Dwayne Bowe increased his total yards from scrimmage from 1,166 yards in 2010 to 1,171 yards in 2011, but he dropped from 15 touchdowns to only 5. Those 10 touchdowns he lost were 60 fantasy points, enough to drop him from the No. 2 fantasy receiver in 2010 to the No. 17 fantasy receiver in 2011 in typical scoring. Was Bowe a worse player? Probably not, but he provided less than half of his fantasy value from the previous season.

Bowe is a perfect illustration of the nature of the NFL. There were 19 wide receivers that caught 70 or more balls in 2010. In 2011, there were 18. And Bowe was one of just 10 wide receivers that had 70 receptions in both seasons. He is one of the safest plays at the position, and in 2012 where, contract issues aside, he will be in a similar situation with a similar team around him as in the two years before, he seems as likely to be the No. 5 receiver in fantasy as the No. 15 receiver, or anywhere in between.

With so profound an effect, one would think it would be simple to capture in a risk estimate. However, more so with efficiency than with opportunity, the trouble is in its isolation. LeSean McCoy went from 4 touchdowns in 2009 to 9 in 2010 before he jumped to 20 in 2011. The latter move was one similar to but opposite of Bowe, but there was more to the former. In 2009, McCoy was below the replacement level in value. He was a part-time player that rookie season. He needed more than variance to vault him to fantasy stardom.

And so, as I did with my offensive snap study, I will limit my research of variance of efficiency to players I identified as stars in their prime in each of 2009, 2010, and 2011. They are the players with the volume of work to minimize the impact of outlier plays. From my previous article, I already have the cumulative fantasy production of those stars. However, because I will look at several metrics of efficiency for the positions with different fantasy values, I need to break down their production by more than fantasy points.

To do so, I will adhere to a concept of measurement I will label opportunities (Opp). For a quarterback, opportunities will equal pass attempts. For receivers, opportunities will equal targets. For backs, opportunities will be either rushes or targets, or both. All of the rate metrics will be of opportunities, as opposed to completions or receptions, so that variance of completion percentage and reception percentage could be included in the study without expanding the number of variables.

Based on opportunities, I will measure quarterback efficiency by yards per pass attempt (Y/A), touchdown percentage (TD%), and turnover percentage (TO%), which combines interceptions and fumbles lost. I will measure running back efficiency by yards per rush attempt (Y/Rush), yards per pass target (Y/TA), TD%, and TO%. And I will measure wide receiver and tight end efficiency by Y/TA, TD%, and TO%.

First, I recorded those statistics for each star player in 2009, 2010, and 2011. From that, I calculated the combined standard deviation of each metric for each position. That deviation represents the random changes of efficiency from year to year, or efficiency risk. That is the starting place for the following table:

 

Metric Std. Dev. Opp Var Scoring PPM FanPts CV
QB Y/A 0.55 8261 4560.8 0.04 182.4301 4126.4 0.044
TD% 1.03% 8261 84.8 4 339.2385 4126.4 0.082
TO% 0.83% 8261 68.8 2 137.5706 4126.4 0.033
0.160
RB Y/Rush 0.41 6380 2646.5 0.1 264.6541 4909.8 0.054
Y/TA 1.21 1293 1570.1 0.1 157.0146 4909.8 0.032
TD% 0.98% 7673 74.8 6 449.0883 4909.8 0.091
TO% 0.37% 7673 28.3 2 56.51852 4909.8 0.012
0.135
WR and TE Y/TA 0.96 3542 3390.7 0.1 339.066 4349.1 0.078
TD% 2.44% 3542 86.3 6 517.6464 4349.1 0.119
TO% 0.79% 3542 28.0 2 56.01009 4349.1 0.013
0.210

 

The Std. Dev. column shows those standard deviations for each metric by position. I multiplied those standard deviations by the total opportunities of all players at each position to get the total variance of each metric (Var). You’ll notice that, for the running backs, Y/Rush uses combined rush attempts, Y/TA uses combined targets, and TD% and TO% use combined touches, which are rush attempts plus targets.

The Scoring column outlines the value of each metric to fantasy. Because 25 yards passing is worth 1 fantasy point in typical scoring, the weight of variance in Y/A is 1/25, or 0.04. I used 4 points for passing touchdowns, 6 points for rushing and receiving touchdowns, -2 points for interceptions or fumbles lost, and 10 yards rushing or receiving per point, or 0.10.

The Points per Metric (PPM) column shows the total variance of each statistic weighted by fantasy points. For every position, TD% is the major driving force of efficiency risk, which makes sense. There are few enough touchdowns scored by individual players in a season that small changes from year to year create big changes by percentage, and touchdowns are worth more in fantasy than other plays.

Finally, I needed to standardize the PPM values to create efficiency risk rates. I divided the PPM of each statistic by the total fantasy points scored by the stars of each position. The result is a coefficient of variation (CV), which is shown in the final column. You can see them broken down by individual metric, and then I combined then by position, which are shown in bold.

Now, I can plug the efficiency risk rates into my table of discount rates:

 

Position Category Risk-free rate Positional risk Attrition rate Snaps risk Efficiency risk Discount rate
QB Rookie prospect 0.009 0.029 0.001 0.160
QB Potential star 0.009 0.029 -0.009 0.001 0.160 0.190
QB Star in prime 0.009 0.029 0.224 0.001 0.160 0.423
QB Star in decline 0.009 0.029 0.652 0.001 0.160 0.851
QB Star with reservations 0.009 0.029 0.001 0.160
QB RORA 0.009 0.029 0.633 0.001 0.160 0.832
QB P&Q 0.009 0.029 0.029 0.001 0.160 0.228
QB Non-star 0.009 0.029 0.236 0.001 0.160 0.435
RB Rookie prospect 0.009 0.028 0.002 0.135
RB Potential star 0.009 0.028 -0.041 0.002 0.135 0.132
RB Star in prime 0.009 0.028 0.256 0.002 0.135 0.430
RB Star in decline 0.009 0.028 0.652 0.002 0.135 0.826
RB Star with reservations 0.009 0.028 0.002 0.135
RB RORA 0.009 0.028 0.647 0.002 0.135 0.820
RB P&Q 0.009 0.028 0.282 0.002 0.135 0.456
RB Non-star 0.009 0.028 0.443 0.002 0.135 0.617
WR Rookie prospect 0.009 0.020 0.001 0.210
WR Potential star 0.009 0.020 0.104 0.001 0.210 0.344
WR Star in prime 0.009 0.020 0.242 0.001 0.210 0.482
WR Star in decline 0.009 0.020 0.652 0.001 0.210 0.892
WR Star with reservations 0.009 0.020 0.001 0.210
WR RORA 0.009 0.020 0.694 0.001 0.210 0.934
WR P&Q 0.009 0.020 0.152 0.001 0.210 0.392
WR Non-star 0.009 0.020 0.441 0.001 0.210 0.681
TE Rookie prospect 0.009 0.016 0.001 0.210
TE Potential star 0.009 0.016 0.162 0.001 0.210 0.398
TE Star in prime 0.009 0.016 0.263 0.001 0.210 0.498
TE Star in decline 0.009 0.016 0.652 0.001 0.210 0.888
TE Star with reservations 0.009 0.016 0.001 0.210
TE RORA 0.009 0.016 0.656 0.001 0.210 0.892
TE P&Q 0.009 0.016 0.001 0.210
TE Non-star 0.009 0.016 0.508 0.001 0.210 0.744

 

My risk table is finally complete. The discount rates are based on a risk-free rate adjusted for positional risk, attrition, and variation of snaps, yards per opportunity, touchdown percentage, and turnover percentage. That covers pretty much all of the things that can go wrong for your fantasy players.

The goal of this research is to create a model to value dynasty and keeper players in an auction. If you remember from my previous articles, I am using the present value formula, which captures anticipated future returns in one current price, based on expected risk. Well, with the discount rate table complete, that risk is established. The next step will be to estimate the value streams of players.

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Questions and comments are always welcome via Twitter – @PFF_ScottSpratt

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