Optimizing your strategy for a fantasy football draft is an interesting problem. Should you should go RB early? Wait on RB's? Should you do something productive with your free time instead of fantasy football? (probably). Optimizing your draft picks can be viewed as an optimization where you try to maximize the projected points of your selected players. In this post I will go through my optimization methodology. To start, I have a dataframe of players and their projected points and their ADPs (Average draft positions).
head(adp[, c("Player", "Pos", "ADP_est", "ADPSD_est", "ADP_Rank", "HALF", "STD", "PPR")], 25)## Player Pos ADP_est ADPSD_est ADP_Rank HALF STD PPR
## 120 Todd Gurley RB 1.85 0.90 1 286.9787 278.7288 295.3511
## 119 Leveon Bell RB 2.25 1.00 2 285.5994 276.2004 294.9930
## 118 Ezekiel Elliott RB 3.40 1.35 3 245.7330 240.7392 250.8822
## 117 David Johnson RB 3.90 1.10 4 237.7158 232.9482 242.4851
## 123 Antonio Brown WR 5.10 1.40 5 244.1744 220.2120 268.1369
## 122 Alvin Kamara RB 6.00 1.25 6 245.4832 235.7970 255.2076
## 82 Saquon Barkley RB 6.80 1.80 7 221.9244 216.4002 227.4485
## 87 Deandre Hopkins WR 8.80 1.90 8 217.1364 196.1761 238.0967
## 121 Kareem Hunt RB 9.30 1.75 9 229.6042 222.5463 236.7176
## 78 Leonard Fournette RB 10.00 1.80 10 213.3087 207.6375 219.0514
## 79 Melvin Gordon RB 10.45 2.05 11 212.0997 205.3586 218.8665
## 89 Odell Beckham WR 11.50 2.05 12 196.8351 178.9319 214.7382
## 76 Dalvin Cook RB 12.90 2.00 13 204.0279 199.3044 208.7746
## 93 Julio Jones WR 14.10 2.15 14 224.4879 202.2329 246.7428
## 85 Michael Thomas WR 15.90 2.30 15 208.1782 188.1379 228.2185
## 81 Devonta Freeman RB 17.55 2.50 16 202.7999 196.5961 209.0049
## 94 Davante Adams WR 18.10 2.40 17 176.9410 161.1901 192.6918
## 95 Keenan Allen WR 18.40 2.50 18 193.9841 176.8953 211.0729
## 80 Lesean Mccoy RB 18.85 2.90 19 195.3838 189.0302 201.7331
## 83 Christian Mccaffrey RB 20.15 3.10 20 213.4223 203.1830 223.5142
## 96 Aj Green WR 20.55 2.25 21 185.0449 168.3994 201.6903
## 77 Jerick Mckinnon RB 20.60 3.50 22 194.1646 187.8265 200.4310
## 26 Jordan Howard RB 22.10 3.05 23 170.0072 166.0453 174.0318
## 86 Michael Evans WR 23.55 2.75 24 182.9814 164.8576 201.1052
## 84 Robert Gronkowski TE 23.70 3.65 25 176.8560 160.0528 193.6592
For league settings, I am using Yahoo's defaults[1]. I can then easily set up an optimization where I say to maximize the sum of the projected points of the 15 players taken. Given the slot I am picking at, which for this example I will say is slot 4, I just constrain it to take 15 players with ADP>=4, 14 players with ADP>=21, etc. The end result is a function which takes different parameters for the optimization and returns the optimal draft picks.
getPicks(slot="Slot4", numRB=4, numWR = 6,numTE=1,numK=1,numQB=2, numDST=1,numFLEX = 0,shift=0, out=c(), fix=c(), scoring='HALF')## Pos Player ADP_est ADP_Rank HALF Slot
## 122 RB Alvin Kamara 6.00 6.0 245.4832 4
## 77 RB Jerick Mckinnon 20.60 22.0 194.1646 21
## 88 WR Tyreek Hill 29.65 29.0 184.3552 28
## 90 WR Juju Smith Schuster 42.35 45.0 179.3604 45
## 106 QB Russell Wilson 57.10 57.5 291.4859 52
## 109 QB Cam Newton 74.05 76.0 274.0508 69
## 32 TE Delanie Walker 79.15 80.0 132.7886 76
## 61 WR Cooper Kupp 100.70 100.0 149.4343 93
## 42 WR Robby Anderson 104.65 107.0 145.7251 100
## 62 WR Sterling Shepard 119.10 125.0 139.7021 117
## 387 RB Devontae Booker 119.40 126.0 122.6159 124
## 40 WR Rishard Matthews 142.75 146.0 133.4577 141
## 30 RB James White 149.30 155.0 137.4044 148
## 315 DST Pit 163.35 186.0 122.0000 165
## 5 K Harrison Butker NA 500.0 145.3158 172
The parameters of getPicks() specify number of players at each position to take. I also added the shift parameter which can shift everyone's ADP by a given fraction i.e. shift=.1 would subtract 10% from everyone's ADP. I can also make adjustments like constraining to only select 1QB in the first 10 rounds.
getPicks(slot="Slot4", numRB=4, numWR = 6,numTE=1,numK=1,numQB=2, numDST=1,numFLEX = 0,shift=0, out=c(), fix=c(), scoring='HALF', onePos=rep("QB", 10))## Pos Player ADP_est ADP_Rank HALF Slot
## 122 RB Alvin Kamara 6.00 6.0 245.4832 4
## 77 RB Jerick Mckinnon 20.60 22.0 194.1646 21
## 88 WR Tyreek Hill 29.65 29.0 184.3552 28
## 90 WR Juju Smith Schuster 42.35 45.0 179.3604 45
## 106 QB Russell Wilson 57.10 57.5 291.4859 52
## 15 RB Tarik Cohen 75.80 78.0 132.4949 69
## 32 TE Delanie Walker 79.15 80.0 132.7886 76
## 61 WR Cooper Kupp 100.70 100.0 149.4343 93
## 42 WR Robby Anderson 104.65 107.0 145.7251 100
## 39 WR Kelvin Benjamin 112.70 117.0 137.0975 117
## 62 WR Sterling Shepard 119.10 125.0 139.7021 124
## 107 QB Alexander Smith 148.65 152.0 259.3228 141
## 30 RB James White 149.30 155.0 137.4044 148
## 315 DST Pit 163.35 186.0 122.0000 165
## 5 K Harrison Butker NA 500.0 145.3158 172
Rotoviz already has an app which does a similar optimization. The results do seem to suggest certain things like how you should often take RB's early. Looking at the optimal first two picks for each draft slot, you can see how RB's are usually suggested for the early picks:
sapply(paste0("Slot", 1:12), function(x) getPicks(slot=x, numRB=4, numWR = 6,numTE=1,numK=1,numQB=2, numDST=1,numFLEX = 0,shift=0, out=c(), fix=c(), scoring='HALF')[1:2,],simplify = FALSE,USE.NAMES = TRUE)## $Slot1
## Pos Player ADP_est ADP_Rank HALF Slot
## 120 RB Todd Gurley 1.85 1 286.9787 1
## 84 TE Robert Gronkowski 23.70 25 176.8560 24
##
## $Slot2
## Pos Player ADP_est ADP_Rank HALF Slot
## 119 RB Leveon Bell 2.25 2 285.5994 2
## 84 TE Robert Gronkowski 23.70 25 176.8560 23
##
## $Slot3
## Pos Player ADP_est ADP_Rank HALF Slot
## 118 RB Ezekiel Elliott 3.4 3 245.7330 3
## 77 RB Jerick Mckinnon 20.6 22 194.1646 22
##
## $Slot4
## Pos Player ADP_est ADP_Rank HALF Slot
## 122 RB Alvin Kamara 6.0 6 245.4832 4
## 77 RB Jerick Mckinnon 20.6 22 194.1646 21
##
## $Slot5
## Pos Player ADP_est ADP_Rank HALF Slot
## 122 RB Alvin Kamara 6.00 6 245.4832 5
## 83 RB Christian Mccaffrey 20.15 20 213.4223 20
##
## $Slot6
## Pos Player ADP_est ADP_Rank HALF Slot
## 122 RB Alvin Kamara 6.00 6 245.4832 6
## 83 RB Christian Mccaffrey 20.15 20 213.4223 19
##
## $Slot7
## Pos Player ADP_est ADP_Rank HALF Slot
## 121 RB Kareem Hunt 9.30 9 229.6042 7
## 83 RB Christian Mccaffrey 20.15 20 213.4223 18
##
## $Slot8
## Pos Player ADP_est ADP_Rank HALF Slot
## 121 RB Kareem Hunt 9.30 9 229.6042 8
## 83 RB Christian Mccaffrey 20.15 20 213.4223 17
##
## $Slot9
## Pos Player ADP_est ADP_Rank HALF Slot
## 121 RB Kareem Hunt 9.30 9 229.6042 9
## 83 RB Christian Mccaffrey 20.15 20 213.4223 16
##
## $Slot10
## Pos Player ADP_est ADP_Rank HALF Slot
## 78 RB Leonard Fournette 10.00 10 213.3087 10
## 83 RB Christian Mccaffrey 20.15 20 213.4223 15
##
## $Slot11
## Pos Player ADP_est ADP_Rank HALF Slot
## 79 RB Melvin Gordon 10.45 11 212.0997 11
## 83 RB Christian Mccaffrey 20.15 20 213.4223 14
##
## $Slot12
## Pos Player ADP_est ADP_Rank HALF Slot
## 93 WR Julio Jones 14.10 14 224.4879 12
## 83 RB Christian Mccaffrey 20.15 20 213.4223 13
There are some shortcomings with using this basic optimization to inform your strategy. First of all, the thing you want to optimize is not all of your picks' points--a more appropriate objective would be to draft in a way that will give you the eventual best starting lineup. This would ideally take into account the uncertainty of the projections, the fact that you can only start a limited number of each position, and the possibility of getting waiver wire adds. I'll show how I account for this below.
For the more complicated case, my methodology will be to get an optimal lineup, but I will evaluate its performance not by the sum of the projected points, but rather by how strong it's mean-simulated top starting lineup is. I will explain this in depth later. To do this method though, I will first need estimates of the errors of the projections. It is widely assumed that RBs have errors with high variance while something like a TE has low variance, and so this should be accounted for when simulating the actual values from the projections.
I summarize below the projection error (actual-projected) for 2009-2017, grouped by projection range and position. A negative mean-value means players have underperformed for that subgroup. A high SD value means players; performance has been more volatile in that subgroup:
## fantPts_bin Pos meanError medianError sdError n
## 4 (25,75] DST 7.666667 -3.500000 33.10992 6
## 13 (75,125] DST 17.542373 12.000000 29.61336 118
## 5 (25,75] K 13.788522 15.425605 42.57718 11
## 14 (75,125] K 14.556467 16.501889 28.48010 198
## 22 (125,175] K -8.139669 -8.531961 28.08898 50
## 7 (25,75] QB 7.924877 -9.800000 51.62458 125
## 16 (75,125] QB 8.771959 -9.153795 84.60471 34
## 24 (125,175] QB -20.094962 -49.006279 83.69827 52
## 28 (175,225] QB 1.696868 16.909655 77.97935 83
## 32 (225,400] QB 4.746088 17.668665 68.98852 142
## 8 (25,75] RB 2.842122 -8.079204 42.24322 360
## 17 (75,125] RB -3.965397 -13.923055 59.31428 218
## 25 (125,175] RB -24.732960 -23.050371 64.53592 184
## 29 (175,225] RB -20.815804 -22.195431 80.09488 103
## 33 (225,400] RB -52.632221 -40.454483 91.39643 37
## 9 (25,75] TE -2.415085 -10.941867 33.11226 343
## 18 (75,125] TE -4.810404 -3.372042 42.56975 164
## 26 (125,175] TE -18.583065 -8.739259 52.57490 65
## 30 (175,225] TE -18.295723 -22.789903 61.48846 8
## 10 (25,75] WR 3.406541 -7.491818 42.56455 593
## 19 (75,125] WR -6.952610 -11.369156 51.59724 330
## 27 (125,175] WR -11.229153 -10.060463 55.86669 233
## 31 (175,225] WR -12.854190 -8.263119 57.03709 115
## 34 (225,400] WR -21.528408 -10.719617 64.93034 23
Plotting the above standard deviations of the errors by position:
I can also look at the plots of the actual data by subgroup:
Looking at the above data and plots, I see how different positions have different error distributions. I initially was going to assume all errors are normally distributed, but looking at all plots I see that many of the subgroups are skewed right (ex: RBs 75-125) and some are normally distributed (WRs 125-175). In addition, there appears to be some bias as top RBs have seem to underperformed their projections and DSTs have overperformed my projections. For the bias, I can ignore it and chalk it up to sample size or I can un-bias my projections. This is definitely an important question because it would determine whether I take off points from the projections of the top RBs. I will first assume the projections are not biased and so shift all errors to be centered at 0. I outline the assumptions below.
Assumption 1. I will assume the error of a player is randomly sampled from their corresponding error-bin, and I will add a constant to each error bin so that the errors of each bin have mean 0.
Assumption 2. I also assume that you will be able to pick up undrafted players. I assume you will be able to get the third highest performing undrafted player at each position. This may be aggressive but it's likely that if you only need DST and TE mid-season, you will be able to get a strong one at both.
Finally, I am ready to simulate a season from my optimal lineup.
First I get the optimal picks at Slot=4/12, same as in base case:
## Pos Player ADP_est ADP_Rank HALF Slot
## 122 RB Alvin Kamara 6.00 6.0 245.4832 4
## 77 RB Jerick Mckinnon 20.60 22.0 194.1646 21
## 88 WR Tyreek Hill 29.65 29.0 184.3552 28
## 90 WR Juju Smith Schuster 42.35 45.0 179.3604 45
## 106 QB Russell Wilson 57.10 57.5 291.4859 52
## 109 QB Cam Newton 74.05 76.0 274.0508 69
## 32 TE Delanie Walker 79.15 80.0 132.7886 76
## 61 WR Cooper Kupp 100.70 100.0 149.4343 93
## 42 WR Robby Anderson 104.65 107.0 145.7251 100
## 62 WR Sterling Shepard 119.10 125.0 139.7021 117
## 387 RB Devontae Booker 119.40 126.0 122.6159 124
## 40 WR Rishard Matthews 142.75 146.0 133.4577 141
## 30 RB James White 149.30 155.0 137.4044 148
## 315 DST Pit 163.35 186.0 122.0000 165
## 5 K Harrison Butker NA 500.0 145.3158 172
Then I can get the top starting lineup from 1 simulation, determining simulated points by sampling from players' error bin. Projected Points=HALF. Simulated Points=Sim:
## Pos Player ADP_est ADP_Rank HALF Slot fantPts_bin error Sim
## 5 QB Russell Wilson 57.10 57.5 291.48588 52 (225,400] 41.478576 332.9645
## 1 RB Alvin Kamara 6.00 6.0 245.48323 4 (225,400] 37.900172 283.3834
## 2 RB Jerick Mckinnon 20.60 22.0 194.16459 21 (175,225] 3.721077 197.8857
## 4 WR Juju Smith Schuster 42.35 45.0 179.36045 45 (175,225] 4.591072 183.9515
## 14 DST Pit 163.35 186.0 122.00000 165 (75,125] 57.457627 179.4576
## 7 TE Delanie Walker 79.15 80.0 132.78858 76 (125,175] 46.257469 179.0460
## 18 WR Jermaine Kearse NA 500.0 90.74932 NA (75,125] 76.459712 167.2090
## 10 WR Sterling Shepard 119.10 125.0 139.70207 117 (125,175] 19.095437 158.7975
## 15 K Harrison Butker NA 500.0 145.31579 172 (125,175] -12.334207 132.9816
Undrafted players can end up in the top lineup for a given simulation if their HALF+error is better than the players I drafted. Finally, I repeat the simulation a large number of times to get the mean-simulated optimal lineup from a set of picks. The sum of the top lineup will stabilize to a given value as I repeat the top-lineup simulation a large number of times.
The last step of the system is to test different parameters. I can specify things like number of players to take at each position or whether I should lock in a certain player. I repeat the above simulation many times and I want to find the parameters that result in the best mean-simulated optimal lineup. Below I plot the simulation results for different parameter combinations.
In the plot you can see the effect of different actions. For example, it suggests you should definitely take 2 QBs, as the 1 QB test (case 6) performs very poorly. Taking Antonio Brown instead of Kamara in round 1 slightly decreases the median-simulated starting lineup, despite Antonio Brown's raw projection actually being higher than Kamara's. The planned draft from the optimal parameter combo (case 3) is shown below.
getPicks(slot="Slot4", numRB=4, numWR = 6,numTE=1,numK=1,numQB=2, numDST=1,numFLEX = 0,shift=0, out=c(), fix=c(), scoring='HALF')## Pos Player ADP_est ADP_Rank HALF Slot
## 122 RB Alvin Kamara 6.00 6.0 245.4832 4
## 77 RB Jerick Mckinnon 20.60 22.0 194.1646 21
## 88 WR Tyreek Hill 29.65 29.0 184.3552 28
## 90 WR Juju Smith Schuster 42.35 45.0 179.3604 45
## 106 QB Russell Wilson 57.10 57.5 291.4859 52
## 109 QB Cam Newton 74.05 76.0 274.0508 69
## 32 TE Delanie Walker 79.15 80.0 132.7886 76
## 61 WR Cooper Kupp 100.70 100.0 149.4343 93
## 42 WR Robby Anderson 104.65 107.0 145.7251 100
## 62 WR Sterling Shepard 119.10 125.0 139.7021 117
## 387 RB Devontae Booker 119.40 126.0 122.6159 124
## 40 WR Rishard Matthews 142.75 146.0 133.4577 141
## 30 RB James White 149.30 155.0 137.4044 148
## 315 DST Pit 163.35 186.0 122.0000 165
## 5 K Harrison Butker NA 500.0 145.3158 172
Before I mentioned that the projections I am using have been biased for certain positions. For the last part of my analysis I'd like to see how the bias might affect my results. Looking at the errors, I'm going to create a shifted projection "HALF2" below that accounts for bias. Another term for this is sensitivity analysis--I want to see how my parameter optimization changes if I change the projections.
head(adp[, !grepl("STD|PPR", colnames(adp))], 10)## fantPts_bin Pos Player ADP_est ADPSD_est ADP_Rank HALF meanError HALF2
## 120 (225,400] RB Todd Gurley 1.85 0.90 1 286.9787 -52.63222 234.3465
## 119 (225,400] RB Leveon Bell 2.25 1.00 2 285.5994 -52.63222 232.9672
## 118 (225,400] RB Ezekiel Elliott 3.40 1.35 3 245.7330 -52.63222 193.1008
## 117 (225,400] RB David Johnson 3.90 1.10 4 237.7158 -52.63222 185.0835
## 123 (225,400] WR Antonio Brown 5.10 1.40 5 244.1744 -21.52841 222.6460
## 122 (225,400] RB Alvin Kamara 6.00 1.25 6 245.4832 -52.63222 192.8510
## 82 (175,225] RB Saquon Barkley 6.80 1.80 7 221.9244 -20.81580 201.1086
## 87 (175,225] WR Deandre Hopkins 8.80 1.90 8 217.1364 -12.85419 204.2822
## 121 (225,400] RB Kareem Hunt 9.30 1.75 9 229.6042 -52.63222 176.9720
## 78 (175,225] RB Leonard Fournette 10.00 1.80 10 213.3087 -20.81580 192.4929
From the error analysis, top-rated RB's have underperformed greatly, based on a sample size of around 40. With the bias-adjusted projections, I am now projecting Antonio Brown to do much better than some of the top RBs. I'll now redo the initial optimization, using these new projections:
#getPicks() with "HALF2" scoring
getPicks(slot="Slot4", numRB=4, numWR = 6,numTE=1,numK=1,numQB=2, numDST=1,numFLEX = 0,shift=0, out=c(), fix=c(), scoring='HALF2')## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 123 WR Antonio Brown 5.10 5.0 244.1744 222.6460 4
## 77 RB Jerick Mckinnon 20.60 22.0 194.1646 173.3488 21
## 88 WR Tyreek Hill 29.65 29.0 184.3552 171.5010 28
## 90 WR Juju Smith Schuster 42.35 45.0 179.3604 166.5063 45
## 106 QB Russell Wilson 57.10 57.5 291.4859 296.2320 52
## 109 QB Cam Newton 74.05 76.0 274.0508 278.7969 69
## 61 WR Cooper Kupp 100.70 100.0 149.4343 138.2051 76
## 42 WR Robby Anderson 104.65 107.0 145.7251 134.4959 93
## 384 RB Duke Johnson 106.70 109.0 121.1553 117.1899 100
## 387 RB Devontae Booker 119.40 126.0 122.6159 118.6505 117
## 396 TE Jack Doyle 127.25 131.5 117.6762 112.8658 124
## 40 WR Rishard Matthews 142.75 146.0 133.4577 122.2286 141
## 30 RB James White 149.30 155.0 137.4044 112.6714 148
## 315 DST Pit 163.35 186.0 122.0000 139.5424 165
## 356 K Matthew Prater 169.30 196.0 124.8721 139.4285 172
The optimal solution for the base case changes in favor of picking Antonio Brown in Round 1. Next I repeat the parameter optimization to see the effect of my projections' bias on that:
The results now are less clear on whether to pick an WR in Round 1, although some conclusions remain the same such as to take a backup QB, and don't go zero-RB. Looking at the top 2 picks by round for the bias-adjusted projections, you can see how the suggested picks changed from before, and the first two rounds suggest more of a mix of picks:
sapply(paste0("Slot", 1:12), function(x) getPicks(slot=x, numRB=6, numWR = 4,numTE=1,numK=1,numQB=2, numDST=1,numFLEX = 0,shift=0, out=c(), fix=c(), scoring='HALF2')[1:2,],simplify = FALSE,USE.NAMES = TRUE)## $Slot1
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 120 RB Todd Gurley 1.85 1 286.9787 234.3465 1
## 84 TE Robert Gronkowski 23.70 25 176.8560 158.5603 24
##
## $Slot2
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 119 RB Leveon Bell 2.25 2 285.5994 232.9672 2
## 84 TE Robert Gronkowski 23.70 25 176.8560 158.5603 23
##
## $Slot3
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 123 WR Antonio Brown 5.1 5 244.1744 222.6460 3
## 77 RB Jerick Mckinnon 20.6 22 194.1646 173.3488 22
##
## $Slot4
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 123 WR Antonio Brown 5.1 5 244.1744 222.6460 4
## 77 RB Jerick Mckinnon 20.6 22 194.1646 173.3488 21
##
## $Slot5
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 82 RB Saquon Barkley 6.80 7 221.9244 201.1086 5
## 83 RB Christian Mccaffrey 20.15 20 213.4223 192.6065 20
##
## $Slot6
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 82 RB Saquon Barkley 6.80 7 221.9244 201.1086 6
## 83 RB Christian Mccaffrey 20.15 20 213.4223 192.6065 19
##
## $Slot7
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 82 RB Saquon Barkley 6.80 7 221.9244 201.1086 7
## 83 RB Christian Mccaffrey 20.15 20 213.4223 192.6065 18
##
## $Slot8
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 78 RB Leonard Fournette 10.00 10 213.3087 192.4929 8
## 83 RB Christian Mccaffrey 20.15 20 213.4223 192.6065 17
##
## $Slot9
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 78 RB Leonard Fournette 10.00 10 213.3087 192.4929 9
## 83 RB Christian Mccaffrey 20.15 20 213.4223 192.6065 16
##
## $Slot10
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 78 RB Leonard Fournette 10.00 10 213.3087 192.4929 10
## 83 RB Christian Mccaffrey 20.15 20 213.4223 192.6065 15
##
## $Slot11
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 79 RB Melvin Gordon 10.45 11 212.0997 191.2839 11
## 83 RB Christian Mccaffrey 20.15 20 213.4223 192.6065 14
##
## $Slot12
## Pos Player ADP_est ADP_Rank HALF HALF2 Slot
## 93 WR Julio Jones 14.10 14 224.4879 211.6337 12
## 83 RB Christian Mccaffrey 20.15 20 213.4223 192.6065 13
In conclusion, I created a system that optimizes to get the best eventual starting lineup for fantasy football. In testing different strategies, it seems you should definitely draft 2 QBs, you should not do zero-RB, and it is unclear if you should draft RB first. I found these conclusions through parameter optimization and sensitivity analysis. The main flaw still remaining in all of this is the uncertainty in opponent picks. If an optimal strategy depends on getting a high value QB in round 10 for example, it should factor in what happens if someone else takes the QB. I will talk about that in a future post.
[1] Yahoo default is 12-team league with 15 picks per team. Positions=1 QB, 2 WR, 2 RB, 1 TE, 1 FLEX, 1 DST, 1 K. Scoring = .5 PPR