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Wednesday 26th Apr 2017

I’m about to do something a little odd in that I’m not sure that the data presented below is of any major significance. That is, it may look cool and everything, but I’m not sure it is actionable in a practical sense. I suspect at the end of the day, the numbers are pretty and everything, but winning a league still comes down to picking good players. However, in leagues where the competition is skilled and balanced, any edge is a good one.  Besides, I have spent the bulk of my time typing into word documents lately and my Excel program is feeling neglected.

Here’s the principle. By definition, a draft consists of successive picks, dropping in potential value as you serpentine through the snake. The reversal of the order for each round is done to equalize the potential each owner can amass.  If this is the case, the expected difference between consecutive picks should be the same.

A few weeks back, I presented some data showing that in practical terms, this is not the case. There is what I term a value slope that is steepest early and flattens out as the draft proceeds. The difference in expected value between the first pick and last pick in each round is greatest in round one and lessens from there. I compared this to the National Football League draft. You may be familiar with a trading grid that is provided to the clubs to help them deal equal value in a trade. For example, switching picks in the first round and switching picks in the third round is not a fair trade, as the difference in quality of the players in the first round exceeds that of the players in the third, even though they are the separated by the same number of picks.

Today, I am going to present that data again, but this time in conjunction with how the potential value in a snake draft “should” be, where the slope is constant from the first pick to the last.  The hypothesis is perhaps something can be learned about the expected return on investment of each pick. Maybe we can glean where we should play it safe and when we should start taking chances, I suspect there is an analogy to poker betting here, but to be honest, I am not a poker player. I just have seen enough and can deduce enough that there may be a way to quantify how much risk one should take at each draft spot the same way you can quantify your bets most efficiently with respect to the pot and your chances of winning. Actually, I like that approach – perhaps this is a means to be more efficient with your picks.

We will base the values on the standard $260 for an auction and I will use 15 teams, the principle is the same regardless. I used the values from our most recent update. There will be 345 picks with a total value of $3900 (15 x $260). Please realize these values are derived from the site projections. The exact values will be different from year to year, but the range is pretty close. That is, the top player will usually be worth about $45. Conventionally, the last player drafted is worth $1, in my system, it is actually $.501 which rounds up to $1.

To compare, I set the 345th player at $.501 and added the same amount to each player, so at the end, the sum total of all 345 players is $3900 and the difference between consecutive players is the same throughout.

Before I go on, I want to present some data I first discussed about ten years ago, just because I have seen this exact exercise repeated since and I selfishly want everyone to know I have been doing it for ten years. Below is a table adding up the potential value per team. You can readily see what I was talking about with the value slope and how in a practical sense, the snake does not even out the potential value.

 

TEAM PROJ SNAKE
1 267.57 260.44
2 262.77 260.38
3 262.34 260.31
4 260.14 260.25
5 259.98 260.19
6 260.03 260.13
7 258.11 260.06
8 257.87 260.00
9 257.71 259.94
10 259.63 259.87
11 259.23 259.81
12 258.31 259.75
13 258.46 259.69
14 258.55 259.62
15 259.32 259.56

 

Note how TEAM 1 at least has the potential to accrue more value if the draft goes “chalk”.  I also included the values for the snake, which should be the same per team except an active roster has an odd number of players so the team picking first gets just a little more than the rest because the even round is not there to balance the snake.

OK, here is the data for a 15-team, 23 round snake draft. The final column is the expected return on investment (projected value – expected value)/expected value.  The expected value is that which is determined from the snake.

 

ROUND TEAM PICK SNAKE PROJ ROI
1.01 1 1 22.11 43.91 98.6%
1.02 2 2 22.04 38.97 76.8%
1.03 3 3 21.98 38.63 75.7%
1.04 4 4 21.92 35.81 63.4%
1.05 5 5 21.86 35.52 62.5%
1.06 6 6 21.79 35.27 61.9%
1.07 7 7 21.73 33.69 55.0%
1.08 8 8 21.67 32.80 51.4%
1.09 9 9 21.61 32.72 51.5%
1.10 10 10 21.54 32.29 49.9%
1.11 11 11 21.48 31.43 46.3%
1.12 12 12 21.42 30.89 44.2%
1.13 13 13 21.35 30.62 43.4%
1.14 14 14 21.29 29.96 40.7%
1.15 15 15 21.23 29.96 41.1%
2.01 15 16 21.17 29.58 39.8%
2.02 14 17 21.10 29.29 38.8%
2.03 13 18 21.04 28.84 37.1%
2.04 12 19 20.98 28.82 37.4%
2.05 11 20 20.91 28.71 37.3%
2.06 10 21 20.85 28.67 37.5%
2.07 9 22 20.79 25.94 24.8%
2.08 8 23 20.73 25.79 24.4%
2.09 7 24 20.66 24.96 20.8%
2.10 6 25 20.60 24.91 20.9%
2.11 5 26 20.54 24.53 19.4%
2.12 4 27 20.47 24.37 19.0%
2.13 3 28 20.41 24.24 18.8%
2.14 2 29 20.35 24.01 18.0%
2.15 1 30 20.29 23.60 16.3%
3.01 1 31 20.22 23.43 15.9%
3.02 2 32 20.16 23.31 15.6%
3.03 3 33 20.10 22.95 14.2%
3.04 4 34 20.03 22.85 14.0%
3.05 5 35 19.97 22.79 14.1%
3.06 6 36 19.91 22.76 14.3%
3.07 7 37 19.85 22.32 12.5%
3.08 8 38 19.78 22.25 12.5%
3.09 9 39 19.72 22.25 12.8%
3.10 10 40 19.66 21.76 10.7%
3.11 11 41 19.60 21.75 11.0%
3.12 12 42 19.53 21.68 11.0%
3.13 13 43 19.47 21.34 9.6%
3.14 14 44 19.41 21.28 9.6%
3.15 15 45 19.34 21.04 8.8%
4.01 15 46 19.28 20.84 8.1%
4.02 14 47 19.22 20.68 7.6%
4.03 13 48 19.16 20.55 7.3%
4.04 12 49 19.09 20.10 5.3%
4.05 11 50 19.03 20.08 5.5%
4.06 10 51 18.97 19.65 3.6%
4.07 9 52 18.90 19.47 3.0%
4.08 8 53 18.84 19.45 3.2%
4.09 7 54 18.78 19.31 2.8%
4.10 6 55 18.72 19.16 2.3%
4.11 5 56 18.65 19.01 1.9%
4.12 4 57 18.59 18.86 1.5%
4.13 3 58 18.53 18.47 -0.3%
4.14 2 59 18.46 18.19 -1.5%
4.15 1 60 18.40 18.17 -1.2%
5.01 1 61 18.34 18.15 -1.0%
5.02 2 62 18.28 18.15 -0.7%
5.03 3 63 18.21 17.99 -1.2%
5.04 4 64 18.15 17.85 -1.7%
5.05 5 65 18.09 17.61 -2.6%
5.06 6 66 18.03 17.42 -3.4%
5.07 7 67 17.96 17.38 -3.2%
5.08 8 68 17.90 17.36 -3.0%
5.09 9 69 17.84 17.31 -2.9%
5.10 10 70 17.77 17.28 -2.8%
5.11 11 71 17.71 17.11 -3.4%
5.12 12 72 17.65 16.91 -4.2%
5.13 13 73 17.59 16.72 -4.9%
5.14 14 74 17.52 16.64 -5.0%
5.15 15 75 17.46 16.58 -5.1%
6.01 15 76 17.40 16.50 -5.2%
6.02 14 77 17.33 16.43 -5.2%
6.03 13 78 17.27 16.33 -5.5%
6.04 12 79 17.21 16.26 -5.5%
6.05 11 80 17.15 16.22 -5.4%
6.06 10 81 17.08 15.93 -6.7%
6.07 9 82 17.02 15.89 -6.6%
6.08 8 83 16.96 15.81 -6.8%
6.09 7 84 16.89 15.76 -6.7%
6.10 6 85 16.83 15.70 -6.8%
6.11 5 86 16.77 15.67 -6.6%
6.12 4 87 16.71 15.57 -6.8%
6.13 3 88 16.64 15.45 -7.1%
6.14 2 89 16.58 15.32 -7.6%
6.15 1 90 16.52 15.32 -7.3%
7.01 1 91 16.45 15.29 -7.1%
7.02 2 92 16.39 15.15 -7.5%
7.03 3 93 16.33 15.14 -7.3%
7.04 4 94 16.27 15.14 -6.9%
7.05 5 95 16.20 14.79 -8.7%
7.06 6 96 16.14 14.72 -8.8%
7.07 7 97 16.08 14.67 -8.7%
7.08 8 98 16.02 14.61 -8.8%
7.09 9 99 15.95 14.48 -9.2%
7.10 10 100 15.89 14.46 -9.0%
7.11 11 101 15.83 14.41 -8.9%
7.12 12 102 15.76 14.35 -8.9%
7.13 13 103 15.70 14.34 -8.7%
7.14 14 104 15.64 14.26 -8.8%
7.15 15 105 15.58 14.17 -9.0%
8.01 15 106 15.51 14.12 -9.0%
8.02 14 107 15.45 14.03 -9.2%
8.03 13 108 15.39 14.03 -8.8%
8.04 12 109 15.32 13.98 -8.8%
8.05 11 110 15.26 13.97 -8.5%
8.06 10 111 15.20 13.94 -8.3%
8.07 9 112 15.14 13.91 -8.1%
8.08 8 113 15.07 13.88 -7.9%
8.09 7 114 15.01 13.76 -8.3%
8.10 6 115 14.95 13.68 -8.5%
8.11 5 116 14.88 13.56 -8.9%
8.12 4 117 14.82 13.52 -8.8%
8.13 3 118 14.76 13.46 -8.8%
8.14 2 119 14.70 13.42 -8.7%
8.15 1 120 14.63 13.27 -9.3%
9.01 1 121 14.57 13.24 -9.1%
9.02 2 122 14.51 13.23 -8.8%
9.03 3 123 14.44 13.20 -8.6%
9.04 4 124 14.38 13.17 -8.4%
9.05 5 125 14.32 13.15 -8.2%
9.06 6 126 14.26 13.14 -7.8%
9.07 7 127 14.19 13.12 -7.6%
9.08 8 128 14.13 13.02 -7.8%
9.09 9 129 14.07 13.01 -7.5%
9.10 10 130 14.01 12.73 -9.1%
9.11 11 131 13.94 12.68 -9.1%
9.12 12 132 13.88 12.59 -9.3%
9.13 13 133 13.82 12.56 -9.1%
9.14 14 134 13.75 12.56 -8.7%
9.15 15 135 13.69 12.54 -8.4%
10.01 15 136 13.63 12.52 -8.1%
10.02 14 137 13.57 12.52 -7.7%
10.03 13 138 13.50 12.41 -8.1%
10.04 12 139 13.44 12.24 -8.9%
10.05 11 140 13.38 12.22 -8.7%
10.06 10 141 13.31 12.16 -8.6%
10.07 9 142 13.25 12.09 -8.8%
10.08 8 143 13.19 12.04 -8.7%
10.09 7 144 13.13 11.98 -8.7%
10.10 6 145 13.06 11.98 -8.3%
10.11 5 146 13.00 11.97 -7.9%
10.12 4 147 12.94 11.87 -8.3%
10.13 3 148 12.87 11.86 -7.9%
10.14 2 149 12.81 11.71 -8.6%
10.15 1 150 12.75 11.68 -8.4%
11.01 1 151 12.69 11.67 -8.0%
11.02 2 152 12.62 11.51 -8.8%
11.03 3 153 12.56 11.33 -9.8%
11.04 4 154 12.50 11.24 -10.1%
11.05 5 155 12.43 11.24 -9.6%
11.06 6 156 12.37 11.21 -9.4%
11.07 7 157 12.31 11.16 -9.3%
11.08 8 158 12.25 11.04 -9.9%
11.09 9 159 12.18 10.97 -10.0%
11.10 10 160 12.12 10.95 -9.6%
11.11 11 161 12.06 10.84 -10.1%
11.12 12 162 12.00 10.83 -9.7%
11.13 13 163 11.93 10.82 -9.3%
11.14 14 164 11.87 10.75 -9.4%
11.15 15 165 11.81 10.72 -9.2%
12.01 15 166 11.74 10.70 -8.9%
12.02 14 167 11.68 10.17 -13.0%
12.03 13 168 11.62 10.03 -13.7%
12.04 12 169 11.56 9.91 -14.3%
12.05 11 170 11.49 9.86 -14.2%
12.06 10 171 11.43 9.78 -14.5%
12.07 9 172 11.37 9.74 -14.3%
12.08 8 173 11.30 9.73 -13.9%
12.09 7 174 11.24 9.69 -13.8%
12.10 6 175 11.18 9.69 -13.3%
12.11 5 176 11.12 9.67 -13.0%
12.12 4 177 11.05 9.64 -12.8%
12.13 3 178 10.99 9.64 -12.3%
12.14 2 179 10.93 9.63 -11.9%
12.15 1 180 10.86 9.63 -11.4%
13.01 1 181 10.80 9.60 -11.1%
13.02 2 182 10.74 9.46 -11.9%
13.03 3 183 10.68 9.36 -12.3%
13.04 4 184 10.61 9.31 -12.3%
13.05 5 185 10.55 9.14 -13.4%
13.06 6 186 10.49 9.13 -13.0%
13.07 7 187 10.43 9.10 -12.7%
13.08 8 188 10.36 9.02 -13.0%
13.09 9 189 10.30 8.92 -13.3%
13.10 10 190 10.24 8.86 -13.4%
13.11 11 191 10.17 8.82 -13.3%
13.12 12 192 10.11 8.67 -14.2%
13.13 13 193 10.05 8.60 -14.4%
13.14 14 194 9.99 8.60 -13.9%
13.15 15 195 9.92 8.59 -13.4%
14.01 15 196 9.86 8.51 -13.7%
14.02 14 197 9.80 8.50 -13.2%
14.03 13 198 9.73 8.42 -13.5%
14.04 12 199 9.67 8.38 -13.3%
14.05 11 200 9.61 8.37 -12.9%
14.06 10 201 9.55 8.19 -14.2%
14.07 9 202 9.48 8.14 -14.2%
14.08 8 203 9.42 8.12 -13.9%
14.09 7 204 9.36 8.10 -13.4%
14.10 6 205 9.29 8.08 -13.0%
14.11 5 206 9.23 8.07 -12.6%
14.12 4 207 9.17 7.98 -13.0%
14.13 3 208 9.11 7.75 -14.9%
14.14 2 209 9.04 7.72 -14.6%
14.15 1 210 8.98 7.68 -14.5%
15.01 1 211 8.92 7.64 -14.4%
15.02 2 212 8.85 7.61 -14.1%
15.03 3 213 8.79 7.56 -14.0%
15.04 4 214 8.73 7.55 -13.5%
15.05 5 215 8.67 7.41 -14.5%
15.06 6 216 8.60 7.36 -14.4%
15.07 7 217 8.54 7.24 -15.3%
15.08 8 218 8.48 7.20 -15.0%
15.09 9 219 8.42 7.05 -16.2%
15.10 10 220 8.35 7.04 -15.7%
15.11 11 221 8.29 7.04 -15.1%
15.12 12 222 8.23 7.03 -14.5%
15.13 13 223 8.16 6.99 -14.4%
15.14 14 224 8.10 6.88 -15.1%
15.15 15 225 8.04 6.82 -15.2%
16.01 15 226 7.98 6.73 -15.6%
16.02 14 227 7.91 6.73 -15.0%
16.03 13 228 7.85 6.60 -15.9%
16.04 12 229 7.79 6.44 -17.3%
16.05 11 230 7.72 6.40 -17.2%
16.06 10 231 7.66 6.36 -17.0%
16.07 9 232 7.60 6.32 -16.8%
16.08 8 233 7.54 6.13 -18.7%
16.09 7 234 7.47 6.11 -18.2%
16.10 6 235 7.41 6.02 -18.7%
16.11 5 236 7.35 6.00 -18.3%
16.12 4 237 7.28 5.81 -20.2%
16.13 3 238 7.22 5.77 -20.0%
16.14 2 239 7.16 5.76 -19.6%
16.15 1 240 7.10 5.71 -19.5%
17.01 1 241 7.03 5.69 -19.1%
17.02 2 242 6.97 5.65 -18.9%
17.03 3 243 6.91 5.47 -20.8%
17.04 4 244 6.84 5.45 -20.4%
17.05 5 245 6.78 5.43 -19.9%
17.06 6 246 6.72 5.36 -20.3%
17.07 7 247 6.66 5.31 -20.3%
17.08 8 248 6.59 5.30 -19.7%
17.09 9 249 6.53 5.19 -20.6%
17.10 10 250 6.47 5.18 -19.9%
17.11 11 251 6.41 5.14 -19.7%
17.12 12 252 6.34 5.11 -19.5%
17.13 13 253 6.28 5.07 -19.2%
17.14 14 254 6.22 5.06 -18.6%
17.15 15 255 6.15 4.97 -19.3%
18.01 15 256 6.09 4.96 -18.6%
18.02 14 257 6.03 4.76 -21.1%
18.03 13 258 5.97 4.66 -21.8%
18.04 12 259 5.90 4.56 -22.7%
18.05 11 260 5.84 4.50 -22.9%
18.06 10 261 5.78 4.49 -22.2%
18.07 9 262 5.71 4.49 -21.4%
18.08 8 263 5.65 4.44 -21.5%
18.09 7 264 5.59 4.33 -22.6%
18.10 6 265 5.53 4.32 -21.8%
18.11 5 266 5.46 4.26 -22.0%
18.12 4 267 5.40 4.16 -23.0%
18.13 3 268 5.34 3.94 -26.2%
18.14 2 269 5.27 3.92 -25.7%
18.15 1 270 5.21 3.85 -26.2%
19.01 1 271 5.15 3.77 -26.7%
19.02 2 272 5.09 3.74 -26.5%
19.03 3 273 5.02 3.69 -26.5%
19.04 4 274 4.96 3.59 -27.6%
19.05 5 275 4.90 3.53 -28.0%
19.06 6 276 4.83 3.51 -27.4%
19.07 7 277 4.77 3.49 -26.9%
19.08 8 278 4.71 3.31 -29.8%
19.09 9 279 4.65 3.27 -29.7%
19.10 10 280 4.58 3.22 -29.8%
19.11 11 281 4.52 3.15 -30.2%
19.12 12 282 4.46 3.11 -30.2%
19.13 13 283 4.40 3.08 -29.9%
19.14 14 284 4.33 3.04 -29.8%
19.15 15 285 4.27 2.94 -31.2%
20.01 15 286 4.21 2.93 -30.2%
20.02 14 287 4.14 2.92 -29.6%
20.03 13 288 4.08 2.91 -28.6%
20.04 12 289 4.02 2.89 -28.0%
20.05 11 290 3.96 2.89 -26.9%
20.06 10 291 3.89 2.88 -26.1%
20.07 9 292 3.83 2.74 -28.5%
20.08 8 293 3.77 2.74 -27.3%
20.09 7 294 3.70 2.71 -26.8%
20.10 6 295 3.64 2.70 -25.8%
20.11 5 296 3.58 2.68 -25.0%
20.12 4 297 3.52 2.47 -29.8%
20.13 3 298 3.45 2.45 -29.0%
20.14 2 299 3.39 2.41 -28.9%
20.15 1 300 3.33 2.40 -27.9%
21.01 1 301 3.26 2.35 -28.0%
21.02 2 302 3.20 2.33 -27.1%
21.03 3 303 3.14 2.33 -25.9%
21.04 4 304 3.08 2.28 -26.0%
21.05 5 305 3.01 2.26 -25.0%
21.06 6 306 2.95 2.22 -24.7%
21.07 7 307 2.89 2.15 -25.7%
21.08 8 308 2.82 2.08 -26.2%
21.09 9 309 2.76 2.03 -26.4%
21.10 10 310 2.70 2.01 -25.4%
21.11 11 311 2.64 1.85 -29.6%
21.12 12 312 2.57 1.71 -33.7%
21.13 13 313 2.51 1.68 -33.0%
21.14 14 314 2.45 1.61 -34.2%
21.15 15 315 2.39 1.59 -33.5%
22.01 15 316 2.32 1.53 -33.9%
22.02 14 317 2.26 1.37 -39.5%
22.03 13 318 2.20 1.35 -38.4%
22.04 12 319 2.13 1.35 -36.8%
22.05 11 320 2.07 1.27 -38.5%
22.06 10 321 2.01 1.27 -36.6%
22.07 9 322 1.95 1.26 -35.1%
22.08 8 323 1.88 1.25 -33.5%
22.09 7 324 1.82 1.22 -32.8%
22.10 6 325 1.76 1.09 -37.7%
22.11 5 326 1.69 1.06 -37.2%
22.12 4 327 1.63 1.06 -35.1%
22.13 3 328 1.57 0.96 -39.1%
22.14 2 329 1.51 0.83 -44.7%
22.15 1 330 1.44 0.81 -44.2%
23.01 1 331 1.38 0.72 -47.8%
23.02 2 332 1.32 0.72 -45.7%
23.03 3 333 1.25 0.69 -45.2%
23.04 4 334 1.19 0.61 -48.6%
23.05 5 335 1.13 0.61 -46.1%
23.06 6 336 1.07 0.60 -43.3%
23.07 7 337 1.00 0.55 -45.0%
23.08 8 338 0.94 0.50 -46.6%
23.09 9 339 0.88 0.50 -42.9%
23.10 10 340 0.82 0.50 -38.5%
23.11 11 341 0.75 0.50 -33.4%
23.12 12 342 0.69 0.50 -27.3%
23.13 13 343 0.63 0.50 -20.0%
23.14 14 344 0.56 0.50 -11.1%
23.15 15 345 0.50 0.50 0.0%

Again, I’m not completely sure what this all means. I do think it is interesting that the return on investment flips at the end of round four. My initial reaction is this is all the more reason to not take chances early, but rather to try to realize as much of that expected ROI as possible, then take chances after round four since that is the point the expected return becomes negative.

In the name of full disclosure, the real impetus for doing this is due to an interesting discussion I am having with respect to playing it safe in the first round or taking more of a chance. I was sort of hoping this exercise would help me figure out the right answer.  And maybe it does. The actual discussion revolves around Robinson Cano and my contention that I would take him as early as 5th overall, even though I would be eschewing other players “projected higher.” My argument is I prefer the sure thing value in the first round while the counter is even if Cano performs as expected, there are still going to be several teams ahead of me when comparing the first round return.

Studies have shown that 30% of players drafted in the first round in recent seasons ended the year with first round value, which means in a 15 team league, there will only be 4 or 5 “non-busts” in the first round. To reiterate, my present position is I want better odds of being one of those 4 or 5 with Cano than hoping I picked one of the others that finished better, especially since I feel Albert Pujols and Miguel Cabrera are as equally reliable as they are productive and if I am taking Cano, they are obviously gone which means there are 1 or 2 more guys (by my odds) that have a chance at beating Cano.

What I am wondering is if there is a mathematical means of plugging his expected value into a specific draft spot and use the expected snake value and 30% factoid to quantify the proper move.

Part of me feels one of my shortcomings is I fail to take risks at the appropriate time and I am hoping this will help elucidate the appropriate time. But, like I said, it all sounds really cool, but at the end of the day, it still comes down to just picking lots of good players.

Comments   

0 #2 Dan Holak 2012-02-25 18:57
(part 2) My chief debate rival says that a pick has a set value based on players expected to be there & pick trades should be "even money" no matter whether moving up or down. Of course he typically self adjusts his pick values to his advantage based on the range of players likely available, inflating his picks to the top of the range and your picks to the bottom, for whatever that is worth. So I think he believes in the concept of the added option value even if he doesn't realize it.

At any rate, more from a strategic analysis I am curious your take on the concept given the analysis in your article. You mention in the post that you are not sure of the analytical value, for me, it seems to be to be at least somewhat applicable to our league specifically with respect to pick trade strategy and evaluation, and what added picks can add value relative to the risk. Apologize for the long comments, appreciate the response, and great site!
Quote
0 #1 Dan Holak 2012-02-25 18:56
Todd, I stumbled across this fascinating post last night following a long day of email debating with several other owners in one of my most active leagues.

Briefly its an well established, experienced 18 team non-keeper mix league the chief quirk of which is we allow trading of draft picks following the random drawing of the draft order in early Feb, which gives us an extra 2 months of fantasy action. My strategy has always been to add early picks (top 3 rounds) at the expense of rounds 5-12 (roughly speaking). This year i have pick 3, 14, 23, 29 & 43, then don't pick again until 178, and have a bevy of picks in the 250-350 range to make up the diff.

I concur with the non-linear curve of values the dollar values suggest, and believe that in trading up for a higher pick you add inherent value because you increase your choices of more available players to be picked ie better chance to get the guys you like if you trust your pre-draft research. (continued)
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