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:

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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.

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