Addendum to post on drafting inefficiencies

I detailed here a way to calculate the penalty involved in reaching for a player given the difference between his expected pick based on rankings (xPk) and where he's actually taken (aPk). I said in that post you want to draft the best player available in at least the first five rounds. Using that as a rule of thumb, it is possible to derive how far you should reach for a player.

Assuming you want to draft the best player available in the first five rounds, the smallest possible penalty is then taking a player who sits just outside that value in your league. In a ten team league, that means taking the #51 ranked player with pick #50 (the last pick in the fifth round). Using the formula (10*(aPk-xPk))/(10+aPk), that gives you a value of negative one-sixth (-.16666). That is a good starting point for the maximum penalty you would want to accrue; anything larger than that has similar negative value to reaching in the first five rounds. So by setting the formula in question equal to -0.16666, you end up with the following two equations:

Equation 1: aPk= (60*xPk-10)/61

Equation 2: xPk = (10+61*aPk)/60

Equation 1 is how early you can take the player ranked at xPk without accruing a significant penalty, while Equation 2 is how far you can reach with your current pick without getting more than that same penalty.

If you have the fifth pick in the tenth round (pick 95), then the farthest you want to reach is only down to pick (10+(61*95))/60= 96.75, or roughly pick 97. Similarly, if you really want the 95th ranked player, then you should only take him as early as ((60*95)-10)/61= 93.27, or pick 93. This is obviously quite stringent, and you can set the value more liberally. It does jive with the notion that you should draft best overall as much as possible in the first ten rounds, though.

The most I would set the value to is -1. That is approximately the average cost of reaching for the #51 player with any given pick in the fifth round. That yields

Equation 1: aPk= ((10*xPk)-10)/11

Equation 2: xPk= (10+(11*aPk))/10

Using these standards, the farthest you want to reach with the 95th pick is (10+(11*95))/10= 105.5, or player #106 (about one round). If you want the 95th ranked player, then the earliest you should take him is ((10*95)-10)/11= 85.45, or about pick 85 (again, one round).

**Update**

Using the -1 scalar value standard (detailed immediately above), here's a good rule of thumb for number of picks to reach: take the round, and add 0.55 (that is, in round 1 do not reach more than 1.55 picks, 7.55 picks in round 7, etc). The calculations assume a 10-team league and a median pick (pick 5.5 in each round). The number should be higher for a lower pick in the round, and smaller for a higher pick.