# HSAC’s Fantasy Value Handbook, Part III

Part III: Projecting Draft Pick Value

by Sam Waters

This is the third section of our guide to calculating player value in fantasy football. Each part will lay out a different aspect of the process. Part I and Part II are already up, and Parts IV and V will be published on our blog throughout the week.

Last week, in Part II, we finished calculating the past value of every player from the last five years. Now, we can use these historical results to project the value of each player at each positional ranking for this year in a standard league. By positional ranking I mean the first-ranked player, second-ranked player, third-ranked player, and so on at each position. So we are not projecting specific player performances, but rather the value of whatever player falls at each ranking at every position. That way, we will be able to say that if C.J. Spiller is your projected third-best running back, he should have approximately *this much* value.

In order to find these projected values for each position, we take the last five years of data, and find a line of best fit for the relationship between preseason ESPN consensus ranking and actual seasonal value. This gives us an equation that predicts seasonal value, and we can plug in each ranking to find its expected value based on player performances from 2008 to 2012. This expected value is our projection for this year.

The same general forces are at work for every positional model so first let’s just take a look at the data, and then we can examine the results and conclusions:

First off, we see that better-ranked players tend to accrue more value (in terms of PAR) than players with worse rankings. Not exactly groundbreaking, I know. It also looks clear that running backs have more spread between the players with high and low rankings, while defenses and kickers have almost none. This will be critical in our value calculation later.

As for the shape of these relationships, a logarithmic or quadratic regression was the best fit for every position, meaning that there is a larger difference between the higher-ranked players than between the lower-ranked players for each group (except defense, which could just be a sample-size fluke). Some of these fits, whether logarithmic or quadratic, are better than others. Let’s take a look at the regression equations and r-squared values for each position:

 Position Regression Type Regression Equation R-Squared Value QB Logarithmic Predicted PAR = -20.63*ln(ranking) + 60.186 0.269 RB Logarithmic Predicted PAR = -27.02*ln(ranking) + 108.94 0.308 WR Quadratic Predicted PAR = 0.0203*(ranking^2) – 1.7463*ranking + 37.961 0.198 TE Logarithmic Predicted PAR = -12.8*ln(ranking) + 36.761 0.164 DEF Quadratic Predicted PAR = -0.0058*(ranking^2) – 1.1057*ranking + 16.29 0.068 K Quadratic Predicted PAR = 0.0229*(ranking^2) – 0.9375*ranking + 8.4516 0.038

The r-squared values tell us what percent of the variation in expected value is due to variation in preseason ranking, so the higher the r-squared value the more predictable a position is for the season. From most to least predictable, we have RB, QB, WR, TE, DEF, and K. The lines of best fit for QB, RB, and TE are logarithmic, which indicates that we can expect a faster rate of increase in value for the elite players at these positions than at WR, DEF, and K. It’s telling to see wide receivers grouped in with kickers and defenses in this comparison. Wide out performances for the whole season are much less differentiated than at the other skill positions, just as they were for weekly performance. At least they are more predictable than defenses or kickers, who are close to totally random.

After looking at the shape and spread of the data, the next thing you might have noticed is that the regressions predict more players to hold positive seasonal value than there are available starting spots in a standard league. For example, eighteen quarterbacks have a predicted full-season PAR above zero, with room for only ten starting quarterbacks. This result backs up my Manning-Roethlisberger example from Part I. While there is only room for ten QB’s in the seasonal top ten, the guys that occupy that starter territory from week to week can and do change. So while only ten guys can be the ten best guys for the season (by definition), more players (in this case eight more) should also achieve a positive cumulative contribution by gaining relevance for just a week or two. There are actually more projected players than available starting spots for every position, so this concept applies across the board. So when you see this trend, now you know that having so many guys with projected positive value is not a mistake- it reflects how the value distribution actually looks.

Now that we have a picture of this distribution at each position and the projected value at each positional rank, you probably also want to know the value of the player at a certain overall rank or draft pick. To get there, I took all of the positional rankings and their projected values, sorted them to get an overall ranking that includes positions, and regressed those values again to smooth out any kinks in the data. After doing this, we get the following expected PAR values for each overall ranking:

 Overall Position Exp. PAR 1 RB1 109 2 RB2 90 3 RB3 79 4 RB4 71 5 RB5 65 6 RB6 61 7 QB1 60 8 RB7 56 9 RB8 53 10 RB9 50 11 RB10 47 12 QB2 46 13 RB11 44 14 RB12 42 15 RB13 40 16 RB14 38 17 QB3 38 18 TE1 37 19 WR1 36 20 RB15 36 21 WR2 35 22 RB16 34 23 WR3 33 24 RB17 32 25 QB4 32 26 WR4 31 27 RB18 31 28 WR5 30 29 RB19 29 30 WR6 28 31 RB20 28 32 TE2 28 33 QB5 27 34 WR7 27 35 RB21 27 36 RB22 25 37 WR8 25 38 RB23 24 39 WR9 24 40 QB6 23 41 RB24 23 42 TE3 23 43 WR10 23 44 RB25 22 45 WR11 21 46 RB26 21 47 QB7 20 48 WR12 20 49 RB27 20 50 TE4 19 51 RB28 19 52 WR13 19 53 RB29 18 54 WR14 17 55 QB8 17 56 RB30 17 57 WR15 16 58 TE5 16 59 RB31 16 60 RB32 15 61 WR16 15 62 DEF1 15 63 QB9 15 64 RB33 14 65 WR17 14 66 DEF2 14 67 TE6 14 68 RB34 14 69 WR18 13 70 DEF3 13 71 RB35 13 72 QB10 13 73 RB36 12 74 WR19 12 75 TE7 12 76 DEF4 12 77 RB37 11 78 WR20 11 79 QB11 11 80 RB38 11 81 DEF5 11 82 WR21 10 83 TE8 10 84 RB39 10 85 DEF6 9 86 WR22 9 87 RB40 9 88 QB12 9 89 TE9 9 90 RB41 9 91 WR23 9 92 DEF7 8 93 RB42 8 94 WR24 8 95 K1 8 96 RB43 7 97 TE10 7 98 QB13 7 99 DEF8 7 100 WR25 7 101 RB44 7 102 K2 7 103 WR26 6 104 RB45 6 105 TE11 6 106 DEF9 6 107 K3 6 108 QB14 6 109 WR27 6 110 RB46 5 111 K4 5 112 WR28 5 113 TE12 5 114 RB47 5 115 DEF10 5 116 WR29 4 117 RB48 4 118 K5 4 119 QB15 4 120 TE13 4 121 WR30 4 122 RB49 4 123 K6 4 124 WR31 3 125 RB50 3 126 K7 3 127 QB16 3 128 TE14 3 129 WR32 3 130 WR33 2 131 K8 2 132 TE15 2 133 WR34 2 134 K9 2 135 QB17 2 136 WR35 2 137 WR36 1 138 K10 1 139 TE16 1 140 WR37 1 141 WR38 1 142 WR39 1 143 WR40 1 144 QB18 1 145 WR41 0 146 WR42 0 147 WR43 0 148 QB19 0 149 QB20 0 150 WR44 0

It looks like we finally have our final projected values for each player at each ranking, but, unfortunately, our work is still not done. We have to make adjustments for the structure of the draft and the presence of in-season free agency to actually calculate draft, auction, and trade prices/values. Our journey will continue tomorrow as we make these corrections and get our final values at last. I know that drafts have already happened, but all of this still applies to in-season valuation for making trades, so stay tuned for Part IV this week.