Turning Projections to Dynasty Auction Values

| 2012/08/06

It is finally time to put my summer full of research to good use. Previously, I developed a table of discount rates for player position-categories. Those provide the basis for the present value formula, which can produce a current auction price for players for any roster and rule set. In particular, they are useful for dynasty and keeper leagues.

The table of discount rates is the only reference material you need to price players with my model. However, there are several steps you will need to take to get there. With practice, it will become easier, but I wanted to give detailed instructions because not every step is intuitive.

Here are the steps:

 

1. Determine roster compositions

I like to use all the information I have at my disposal. At a minimum, you should know the number of teams in your league, the number of players that start at each position, and the number of players on the bench. If that is all that you have, then you will need to estimate the composition of bench players.

I always assume that only 1 defense and 1 kicker will be drafted per team. That leaves some quarterbacks, running backs, wide receivers, and tight ends on the benches. A nice place to start is with the ratio of starters. If there are 40 total bench spots in the league and each team starts just 1 QB, 1 RB, 1 WR, and 1 TE, you can estimate that the combined benches will hold 10 QBs, 10 RBs, 10 WRs, and 10 TEs.

From there, use common sense. If there is a clear tier drop at a position after which there are a lot of similar options, that might be the logical place to assume the position will stop being drafted. In addition, be mindful of handcuff and sleeper tendencies. Sometimes, owners will look at players with an expected baseline of production below the replacement level because they prefer the small chance of an elite upside.

For this exercise, I will work from a 10-team league where I assume the following rosters:

 

Position  Starters/Team  Total Starters  VBD Total
QB 1 10 16
RB 2 20 36
WR 3 30 60
TE 1 10 12
DST 1 10 10
K 1 10 10
BE 7 70 16
160 160

 

The VBD Total column shows the number of players at each position I expect drafted. If you have ADP results for leagues with similar scoring, that can help. If you have played in similar leagues with the same owners, use previous draft results to make your estimations.

 

2. Make or choose player projections

You can be as detailed as you want to be. Frequently, I build draft lists from previous seasons’ VBD analyses with price adjustments based on my opinion of players. Here is an example of a VBD analysis. Make sure your VBD prices are representative of your league scoring rules and rosters.

For this article, I am going to use our PFF player projections to create auction prices.

 

3. Identify the expected players above the replacement level

The bulk of this work was done in step 1. Once you know how many players should be drafted at each position, you can simply pull that many of the top players by their projections. As an example, I will use the fantasy points listed in the PFF projections. They use standard scoring with PPR. If the projections you use do not list fantasy points that match your scoring rules, calculate them in a spreadsheet.

 

4. Solve for Value-Based Draft points

The VBD points of a player are the expected fantasy points minus the expected fantasy points of the baseline player at his position. The baseline players are simply the last players drafted at each position, which you identified in step 3. You will know that you correctly calculated VBD when the baseline player has a VBD of 0. He has no value because he is the definition of a replaceable player in your format.

 

5. Calculate prices based on VBD estimates

You need two pieces of information before you can turn your VBD estimates into auction prices. First, you need the total expected fantasy points scored by all players above the replacement level. In a spreadsheet, you can calculate that by the sum of the VBD column. Second, you need to know the total available dollars in your league. Here is a generalized formula:

 

#TeamsInYourLeague * ($TotalBudgetOfAllTeams – #RosterSpotsOfAllTeams)

 

You will need to subtract $1 for every roster spot in the league, as shown in the formula, because it is a typical requirement of auction leagues that you field a complete roster. In other words, you have to spend at least $1 for every player on your roster, and so that money is not available for you to spend on a maximum bid.

To create a price factor, divide the total budget of all teams by the total expected fantasy points scored by all players above the replacement level. Then, multiply the price factor by the VBD points of every player. The result is his 2012 auction price.

In my example, the 124 players above replacement project to have 7,399 VBD points. The budget of a 10-team league with 16 roster spots and $200 caps is $1,840. The price factor, then, is $0.25.

 

6. Categorize players to determine discount rates

Feel free to use the categories I listed for the players. They should apply for most scoring systems. You can refer back to this article for a detailed explanation. Some players will require a judgment call, and the differences in their projections can be fairly substantial based solely on different categories. Try them both ways to see if one result makes better intuitive sense.

The one hard-and-fast rule of the categories is that they must match up with their player projections. For example, I think of Demaryius Thomas as a potential star, but if I listed him as such and used the PFF projections, which see him as the No. 19 receiver in 2012, then his value will cascade upward from there. That effect is most pronounced with potential stars. If you have doubts, you can substitute star in prime or P&Q, or simply manually adjust the prices when you finish.

 

7. Estimate the years players have until retirement

I went over this in some detail, previously. I am using 39 as the retirement age for quarterbacks, 33 for running backs, and 37 for wide receivers and tight ends. Do not adjust the retirement ages for anticipated production loss. That is covered in the discount rates under attrition. If you are convinced a specific player has an imminent decline, account for that by his category. Star in decline has a much steeper value loss than star in prime.

For the players in the table, the age is listed as of September 1, 2012. The Years Left is simply the difference between the two.

 

8. Calculate the present value of the future production of players

This will vary based upon the keeper rules in your league. For example, a player that can be kept for 2 years will have a value calculated by –PV(Discount rate, 2, 2012 auction price), assuming that the player has at least 2 years before retirement. For a dynasty player, substitute the Years Left for the 2 in the formula.

Here is the full table of values based on the outlined rosters, scoring, and PFF projections. I included 2-year and 3-year keeper prices as well as Dynasty prices, but, with the 2012 price and the discount rate, you can calculate the present value of a player for any period.

 

Pos Age YLeft Player  Category Pts Est. VBD Est. Price DRate 2-Year 3-Year Dynasty
QB 28 11 Aaron Rodgers Star in prime 371 133 $33 0.423 $40 $51 $77
QB 33 6 Drew Brees Star in prime 325 87 $22 0.423 $26 $33 $45
QB 35 4 Tom Brady Star in prime 315 77 $19 0.423 $23 $30 $34
QB 23 16 Cam Newton Star in prime 314 76 $19 0.423 $23 $29 $45
QB 32 7 Michael Vick Star with reservations 309 71 $18 0.464 $20 $26 $35
QB 24 15 Matthew Stafford Star with reservations 299 61 $15 0.464 $17 $22 $33
QB 22 17 Robert Griffin III Rookie prospect 285 47 $12
QB 32 7 Tony Romo Star in prime 278 40 $10 0.423 $12 $15 $22
QB 36 3 Peyton Manning Star in decline 275 37 $9 0.851 $8 $9 $9
QB 31 8 Eli Manning Star in prime 274 36 $9 0.423 $11 $14 $20
QB 27 12 Matt Ryan Star in prime 272 34 $8 0.423 $10 $13 $20
QB 30 9 Philip Rivers Star in prime 269 31 $8 0.423 $9 $12 $17
QB 24 15 Josh Freeman P&Q 249 11 $3 0.228 $4 $6 $11
QB 29 10 Ryan Fitzpatrick Non-star 243 5 $1 0.435 $1 $2 $3
QB 30 9 Ben Roethlisberger Star in prime 243 5 $1 0.423 $1 $2 $3
QB 22 17 Andrew Luck Rookie prospect 238 0 $0
RB 26 7 Arian Foster Star in prime 305 170 $42 0.430 $50 $65 $90
RB 24 9 Ryan Mathews Star in prime 281 146 $36 0.430 $43 $56 $81
RB 24 9 LeSean McCoy Star in prime 275 140 $35 0.430 $41 $53 $78
RB 25 8 Ray Rice Star in prime 272 137 $34 0.430 $41 $52 $75
RB 26 7 Chris D. Johnson Star in prime 249 114 $28 0.430 $34 $43 $61
RB 26 7 Matt Forte Star in prime 242 107 $27 0.430 $32 $41 $57
RB 27 6 Maurice Jones-Drew Star in prime 241 106 $26 0.430 $31 $40 $54
RB 25 8 Darren McFadden Star with reservations 240 105 $26 0.430 $31 $40 $57
RB 24 9 Demarco Murray Star in prime 239 104 $26 0.430 $31 $40 $58
RB 29 4 Steven Jackson Star in prime 234 99 $25 0.430 $29 $38 $44
RB 22 11 Trent Richardson Rookie prospect 234 99 $25
RB 25 8 Jamaal Charles Star in prime 233 98 $24 0.430 $29 $37 $53
RB 26 7 Ahmad Bradshaw Star in prime 224 89 $22 0.430 $26 $34 $47
RB 27 6 Adrian L. Peterson Star in prime 219 84 $21 0.430 $25 $32 $43
RB 29 4 Darren Sproles RORA 214 79 $20 0.820 $17 $20 $22
RB 27 6 Reggie Bush RORA 210 75 $19 0.820 $16 $19 $22
RB 31 2 Fred Jackson Star in prime 204 69 $17 0.430 $20 $20 $20
RB 26 7 Marshawn Lynch RORA 200 65 $16 0.820 $14 $16 $19
RB 23 10 Doug Martin Rookie prospect 200 65 $16
RB 23 10 Jahvid Best P&Q 187 52 $13 0.456 $15 $19 $28
RB 27 6 Shonn Greene P&Q 184 49 $12 0.456 $14 $18 $24
RB 25 8 C.J. Spiller Potential star 178 43 $11 0.132 $18 $25 $51
RB 30 3 Willis McGahee Star in decline 176 41 $10 0.826 $9 $10 $10
RB 26 7 James Starks P&Q 173 38 $9 0.456 $11 $14 $19
RB 25 8 Donald Brown P&Q 173 38 $9 0.456 $11 $14 $20
RB 29 4 Frank Gore Star in prime 168 33 $8 0.430 $10 $13 $15
RB 25 8 Jonathan Stewart Potential star 168 33 $8 0.132 $14 $19 $39
RB 23 10 Roy Helu Potential star 164 29 $7 0.132 $12 $17 $39
RB 22 11 Mark Ingram Potential star 161 26 $6 0.132 $11 $15 $36
RB 24 9 Beanie Wells P&Q 154 19 $5 0.456 $5 $7 $10
RB 26 7 Peyton Hillis Non-star 146 11 $3 0.617 $3 $3 $4
RB 20 13 Ronnie Hillman Rookie prospect 144 9 $2
RB 30 3 Michael Turner Star in prime 143 8 $2 0.430 $2 $3 $3
RB 27 6 Pierre Thomas Non-star 142 7 $2 0.617 $2 $2 $3
RB 21 12 David Wilson Rookie prospect 136 1 $0
RB 25 8 LeGarrette Blount P&Q 135 0 $0 0.456 $0 $0 $0
WR 26 11 Calvin Johnson Star in prime 291 169 $42 0.482 $48 $60 $86
WR 28 9 Larry Fitzgerald Star in prime 246 124 $31 0.482 $35 $44 $62
WR 28 9 Greg Jennings Star in prime 244 122 $30 0.482 $34 $44 $61
WR 23 14 Julio Jones Star in prime 242 120 $30 0.482 $34 $43 $62
WR 30 7 Roddy White Star in prime 238 116 $29 0.482 $33 $41 $56
WR 24 13 Hakeem Nicks Star in prime 238 116 $29 0.482 $33 $41 $60
WR 31 6 Andre Johnson Star with reservations 236 114 $28 0.482 $32 $41 $53
WR 29 8 Marques Colston Star in prime 230 108 $27 0.482 $30 $39 $53
WR 25 12 Victor Cruz RORA 227 105 $26 0.934 $20 $24 $28
WR 23 14 Kenny Britt Star with reservations 226 104 $26 0.482 $29 $37 $53
WR 24 13 Percy Harvin Star with reservations 226 104 $26 0.482 $29 $37 $53
WR 31 6 Wes Welker Star in prime 225 103 $26 0.482 $29 $37 $48
WR 23 14 Dez Bryant Star in prime 217 95 $24 0.482 $27 $34 $49
WR 26 11 Mike Wallace Star in prime 217 95 $24 0.482 $27 $34 $48
WR 24 13 Jeremy Maclin Star in prime 216 94 $23 0.482 $26 $34 $48
WR 24 13 A.J. Green Star in prime 215 93 $23 0.482 $26 $33 $48
WR 27 10 Jordy Nelson RORA 215 93 $23 0.934 $18 $21 $25
WR 28 9 Brandon Marshall Star in prime 215 93 $23 0.482 $26 $33 $47
WR 24 13 Demaryius Thomas Star in prime 214 92 $23 0.482 $26 $33 $47
WR 28 9 Miles Austin Star in prime 213 91 $23 0.482 $26 $33 $46
WR 33 4 Steve L. Smith Star in prime 211 89 $22 0.482 $25 $32 $36
WR 29 8 Vincent Jackson Star in prime 210 88 $22 0.482 $25 $31 $43
WR 31 6 Brandon Lloyd Star with reservations 203 81 $20 0.482 $23 $29 $38
WR 27 10 Robert Meachem P&Q 201 79 $20 0.392 $24 $32 $48
WR 25 12 Eric Decker Star in prime 201 79 $20 0.482 $22 $28 $40
WR 26 11 Steve Johnson Star with reservations 198 76 $19 0.482 $21 $27 $39
WR 33 4 Reggie Wayne Star in decline 194 72 $18 0.892 $14 $17 $19
WR 27 10 Dwayne Bowe Star in prime 187 65 $16 0.482 $18 $23 $33
WR 24 13 Antonio Brown Potential star 187 65 $16 0.344 $21 $28 $46
WR 23 14 Torrey Smith Potential star 184 62 $15 0.344 $20 $26 $44
WR 27 10 Pierre Garcon P&Q 180 58 $14 0.392 $18 $23 $35
WR 26 11 Sidney Rice P&Q 179 57 $14 0.392 $18 $23 $35
WR 25 12 DeSean Jackson Star with reservations 174 52 $13 0.482 $15 $19 $27
WR 29 8 Lance Moore Non-star 173 51 $13 0.681 $12 $15 $18
WR 29 8 Nate Washington Non-star 169 47 $12 0.681 $11 $14 $17
WR 23 14 Titus Young Potential star 169 47 $12 0.344 $15 $20 $33
WR 23 14 Denarius Moore P&Q 168 46 $11 0.392 $14 $18 $29
WR 25 12 Darrius Heyward-Bey P&Q 167 45 $11 0.392 $14 $18 $28
WR 31 6 Anquan Boldin Star in decline 163 41 $10 0.892 $8 $10 $11
WR 26 11 Davone Bess Non-star 159 37 $9 0.681 $9 $11 $13
WR 26 11 Austin Collie Non-star 159 37 $9 0.681 $9 $11 $13
WR 23 14 Greg Little Potential star 155 33 $8 0.344 $11 $14 $23
WR 22 15 Michael Floyd Rookie prospect 153 31 $8
WR 25 12 Brandon LaFell Non-star 152 30 $7 0.681 $7 $9 $11
WR 30 7 Malcom Floyd P&Q 149 27 $7 0.392 $8 $11 $15
WR 25 12 Mike A. Williams P&Q 149 27 $7 0.392 $8 $11 $17
WR 27 10 Laurent Robinson RORA 147 25 $6 0.934 $5 $6 $7
WR 23 14 Brian Quick Rookie prospect 146 24 $6
WR 23 14 Doug Baldwin Non-star 146 24 $6 0.681 $6 $7 $9
WR 28 9 Santonio Holmes Star with reservations 146 24 $6 0.482 $7 $9 $12
WR 24 13 Michael Crabtree P&Q 145 23 $6 0.392 $7 $9 $14
WR 25 12 Jacoby Ford Non-star 143 21 $5 0.681 $5 $6 $8
WR 22 15 Justin Blackmon Rookie prospect 142 20 $5
WR 21 16 Rueben Randle Rookie prospect 140 18 $4
WR 22 15 Kendall Wright Rookie prospect 134 12 $3
WR 25 12 David Nelson Non-star 131 9 $2 0.681 $2 $3 $3
WR 29 8 Jason Avant Non-star 130 8 $2 0.681 $2 $2 $3
WR 34 3 Chad Ochocinco Star in decline 130 8 $2 0.892 $2 $2 $2
WR 24 13 Golden Tate Potential star 129 7 $2 0.344 $2 $3 $5
WR 22 15 Randall Cobb Potential star 122 0 $0 0.344 $0 $0 $0
TE 25 12 Jimmy Graham Star in prime 249 97 $24 0.498 $27 $34 $48
TE 23 14 Rob Gronkowski Star in prime 237 85 $21 0.498 $24 $30 $42
TE 30 7 Jason Witten Star in prime 206 54 $13 0.498 $15 $19 $25
TE 32 5 Antonio Gates Star in decline 204 52 $13 0.888 $10 $12 $14
TE 25 12 Jermichael Finley Star in prime 187 35 $9 0.498 $10 $12 $17
TE 22 15 Aaron Hernandez Star in prime 185 33 $8 0.498 $9 $12 $16
TE 36 1 Tony Gonzalez Star in decline 185 33 $8 0.888 $4 $4 $4
TE 28 9 Vernon Davis Star in prime 183 31 $8 0.498 $9 $11 $15
TE 27 10 Jacob Tamme Non-star 170 18 $4 0.744 $4 $5 $6
TE 27 10 Brandon Pettigrew Non-star 168 16 $4 0.744 $4 $4 $5
TE 26 11 Fred Davis Non-star 162 10 $2 0.744 $2 $3 $3
TE 27 10 Brent Celek Non-star 152 0 $0 0.744 $0 $0 $0

 

There are some limitations to the model, which you probably realized by some missing values. First, without a production baseline, it cannot price rookies. I have some opinions about how to handle that, which I outlined here. In summary, I recommend that you slot their values based on comparable veteran players. Here is where I have them in this format (and it includes my opinion of their relative value, by its nature, while for all other players, I relied only on the projections):

 

Pos Age YLeft Player  Category Pts Est. VBD Est. Price DRate 2-Year 3-Year Dynasty
QB 22 17 Robert Griffin III Rookie prospect 285 47 $12 $8 $10 $15
QB 22 17 Andrew Luck Rookie prospect 238 0 $0 $1 $3 $12
RB 22 11 Trent Richardson Rookie prospect 234 99 $25 $31 $45 $65
RB 23 10 Doug Martin Rookie prospect 200 65 $16 $21 $27 $48
RB 20 13 Ronnie Hillman Rookie prospect 144 9 $2 $4 $12 $30
RB 21 12 David Wilson Rookie prospect 136 1 $0 $4 $11 $28
WR 22 15 Michael Floyd Rookie prospect 153 31 $8 $8 $12 $20
WR 23 14 Brian Quick Rookie prospect 146 24 $6 $7 $11 $18
WR 22 15 Justin Blackmon Rookie prospect 142 20 $5 $9 $14 $20
WR 21 16 Rueben Randle Rookie prospect 140 18 $4 $4 $6 $12
WR 22 15 Kendall Wright Rookie prospect 134 12 $3 $10 $15 $24

 

Second, the model assumes that your 2012 projections are for a full season and representative of the skill of the player. For someone like Michael Vick, who is often projected to miss a couple of games because of his injury history, that is no problem. For someone like Adrian Peterson, who will miss time in 2012 because of an injury that should not affect his long-term value, that is a problem. Those players require an additional step.

The PFF projections estimate Peterson will receive 268 total touches, gain 1,314 yards, and score 11 touchdowns. That all amounts to 219 fantasy points in this scoring. To keep the numbers simple, I will say that, in a healthy season, Peterson would receive 350 total touches (300 carries plus 50 receptions), 1,500 yards, and 15 touchdowns. That would be 290 fantasy points. To discount future production, I need to use the 290-point season as the baseline, and then adjust for 2011, since his health next season should not have an impact in future seasons. In dynasty, I would calculate that this way:

 

–PV(0.430, 6, $39) – (–PV(0.430, 1, $39 – $21)) = $68

 

That formula is complex, so let me break it down. Essentially, there are two separate calculations. First, I am calculating the dynasty price Peterson would have if he were completely healthy entering 2012. The $39 is the auction price representation of a 290-point back in fantasy. From that, I am subtracting the loss of value that occurs only in 2012 because of his injury, which is shown as $39 – $21. The $68 is the $80 Peterson would be worth if he were healthy now minus the $12 of value he will lose this season. Based on that calculation, Peterson is still the fifth-most valuable back in dynasty.

Fortunately, the process is a bit easier for a player that will miss an entire season. Hypothetically, if we knew for certain that Rashard Mendenhall were out all of 2012, and we expected him to return to situation and form—which I’ll estimate as $20—in 2013 and beyond, you would price him this way:

 

–PV(0.430, 8, $20) – (–PV(0.430, 1, $20)) = $30

 

The formula shows the value of all 8 years until expected retirement minus the value of 2012, which is lost because of injury.

And that is all there is to it. Ok, that was sort of a joke, but with access to well-formatted projections (like ours here) and some experience in Excel, you should be able to create a custom draft price sheet for your keeper or dynasty league in less than an hour. To my mind, that is time well spent if it will transform your auction draft from an exercise in frustration to one of confidence.

Questions and comments are always welcome via Twitter – @PFF_ScottSpratt

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