abbottjamesr
Footballguy
A linear equation does work and does account for a non-linear curve in calculating $ values for players. A teams total score for a week is the sum of the players scores, so value of one player is directly proportional to the difference to another player of the same position. This is the definition of VBD. In the past it has just been that the distribution of scores among the positions has been exponential, but the beauty of VBD is that it maps the 1 to 1 to that distribution so no fudge factor is needed. This is easy to see if we model a simple league. I used the three year average of the top players at each position in non-ppr(but it doesn't change anything in principle to be ppr) and modeled a 12 team, 6 roster spot league that starts 1 QB, 2 Rb, 2 WR, 1 TE with a $100 budget per team. Below are the auction values based on VBD. This is easy to model because we assume no injuries, no bench, and that the points given are how many they are going to score each week. It does not matter which 6 players you pick, if you stay in $100 you can not do better than 15.4 VBD (there may be a slight variation as the dollars are rounded as shown, in the sheet there are cents as well). There is no arbitrage available. You can stick Superman in as RB1 for 35 PPG and the calculation still works.
QB
VBD
$ Value
RB
VBD
$ Value
WR
VBD
$ Value
TE
VBD
$ Value
$ 1,200
Total Auction $
28.3
7.3
$46
18.9
9.2
$57
16.3
7.2
$45
12.7
6.0
$38
$ 72
Roster Spots
25.7
4.7
$30
17.5
7.8
$48
15.6
6.5
$41
11.0
4.3
$28
$ 1,128
$ to distribute
23.5
2.5
$16
16.5
6.7
$42
14.5
5.4
$34
10.3
3.6
$23
184.6
Total VBD
23.4
2.4
$16
15.5
5.8
$36
14.3
5.3
$33
10.0
3.3
$21
$ 6.110
$/VBD
23.2
2.2
$14
14.9
5.2
$33
13.8
4.7
$30
9.1
2.4
$16
15.39
Total VBD if $100 spent
22.7
1.7
$11
14.6
4.9
$31
13.1
4.0
$25
8.7
2.0
$13
22.2
1.2
$8
14.1
4.4
$28
12.7
3.6
$23
8.2
1.5
$10
21.8
0.8
$6
13.3
3.5
$23
12.4
3.3
$21
8.1
1.4
$10
21.4
0.5
$4
13.1
3.3
$21
12.2
3.1
$20
7.6
1.0
$7
21.3
0.3
$3
12.6
2.9
$19
12.1
3.0
$19
7.3
0.6
$5
21.1
0.1
$2
12.3
2.6
$17
12.0
2.9
$19
6.8
0.1
$2
21.0
0.0
$1
11.9
2.1
$14
11.8
2.7
$18
6.7
0.0
$1
11.7
2.0
$13
11.3
2.2
$15
11.5
1.8
$12
11.0
2.0
$13
11.4
1.7
$11
10.7
1.6
$11
11.2
1.4
$10
10.5
1.5
$10
11.0
1.3
$9
10.4
1.3
$9
10.8
1.0
$7
10.3
1.2
$8
10.5
0.8
$6
10.1
1.0
$7
10.3
0.6
$5
10.0
0.9
$6
10.3
0.5
$4
9.6
0.5
$4
10.1
0.4
$3
9.4
0.4
$3
9.8
0.1
$1
9.3
0.2
$2
9.7
0.0
$1
9.1
0.0
$1
There are three main questions in my mind to solve for real leagues.
1. What do you use for the baseline when taking injuries and bye weeks into consideration. I have not found an mathematical optimal solution for this yet. My gut tells me that since byes don't start till week 5 that optimal strategy is to use best starter as the baseline and to spend all your money on your starting line up. I've had pretty good luck with this over the last 5 years, but I haven't been able to prove why its better than any other strategy. This year I have been looking at how many games the average player plays at every position in a given year through week 13 (FF reg season). I looked at only the top 36 of RB's and WR's and 24 of QB's and TE's in terms of PPG over the last three years. When you factor in the bye weeks. You get QB's average 10.28 games, TE average 10.34 games, RB average 9.55 games, WR average 10.92 games. I then divide the number of games to cover for each position(for QB is 13 games x 12 Teams X 1 roster spot = 156 games) and get 15.2 QB's are in play for the regular season. In my start 2 RB, 2 WR, 1 Flex league this is the top 77 total RB's and WR's are in play (minimum 33 Rb's or 29 WR's). I like this approach but it over values QB and TE in my mind.
2. It is hard to predict who will be the top 1 or 2 guys at each position and by how much. Most every year the top player(s) at each position are outliers. Most people don't go into the season projecting a RB to score 18 ppg in standard, or for a QB to get 30 ppg but most years it happens. We tend to under project the top guys and over project the middle guys. One of the top 5 drafted RB's will likely be the outlier, but it is bad business to pay the value of the outlier for any of them. CalBear is on to something in finding a way to do projections as a probability curve. The top 5 RB's may have a 15% chance each of being an outlier and a 15% chance of being a total bust and that is worth much more than the RB ranked 12 who has maybe a 1% chance of being an outlier and 25% chance of bust. This is my project for this season and next off season, to find a decent way to do projections like this. I think we all kind of intuitively do this any way. Its why Zeke and David Johnson are ranked so high right, they both have the potential to be outliers. This outweighs much of the risk of them busting. But how do we price this??
3. Baseline for QB and TE. I think this is different than for RB and WR. In 12 man leagues where maybe only 16-18 Qb's and TE's will be roster'd the value seems to be much less than best starter. I don't have any imperical data to back any of this up at this time, but here is my conjecture. 1. The delta from QB/TE 8 to 20 is relatively small and it has no price to acquire and you don't even have to waste a roster spot on the back up as a replacement is free. 2. QB/TE is lower variance week to week. I would guess that the 1 standard deviation for QB and TE is around 50% of the average where for RB and WR its closer to 80%. The higher variance over 5 or 6 positions is worth much more than a low variance on one position. 3. TE's just don't score enough to matter. The average TE score in my non-ppr league in 2014 was 7.35 points in 78 contests. The average margin of victory in the 78 contests was 20 points. I did this analysis that year cause I had Jimmy Graham and he finished TE2 that year. If I would have taken a 0 at TE each week it would not have affected a single outcome for the entire season. That was $40 wasted on a player that had 0 impact on my team. Over the whole season that year if the winner of each game would have taken a 0 in their TE spot it would have only changed 10 games results. TE scores less than K or D. I don't know what the answer is to use as baseline but I currently use the first guy in my rankings that I can get for $1. This year its Fitzpatrick (QB 7) and Gates (TE6).
