Daily Fantasy Sports team optimizing - NFL Football Mathematics Part 1

Daily Fantasy Sports just seems to get hotter every week.   prokopyshen.com agrees with the 40+ State Attorney Generals that it is a game of skill.  To win you need to identify lopsided matchups, pick players who are hot, read and evaluate team injury reports, grasp how your fantasy site weights the stats and in general be a fan of the game.   There are lots of sites and twitter feeds that follow each sport in detail to help you with all of these.
But there is one more critical factor in daily fantasy sports that this article addresses: Daily Fantasy Mathematical Strategy.  You really need to understand the value of any player in the context of the salary that the daily fantasy site has assigned that player.  You will have to pick a team that meets a salary cap which means picking a team that generates the most scoring points per dollar  you have control over.
This article will look at one site and sport - FanDuel.com NFL - and outline some of the mathematics of selecting the optimal team of players within a salary cap.  It is more complex than it appears.
We will use FanDuel.com $60K NFL games as our example as it is very popular.  Most fantasy sites and sports are similar.  FanDuel assigns every player on every NFL team a salary, and you have to pick a team of 9 players staying under a salary cap of $60K.  As of this writing, the rules require that you pick a team with 1 QB (Quarterback), 2 RB (Running Back),  3 WR (Wide Receiver), 1 TE (Tight End), 1 K (Kicker) and pick a D (defense team) for a total of 9 selections.  This means you have to visit 6 markets and pick a total of 9 players while spending no more then $60K.
The first constraint to be aware of is that there is a floor salary for every position.  In the FanDuel NFL example, the "minimum wage" for a QB is $5000.  You must name a QB, so this means that $5000 is required just to play the game with a QB.  The floor salary for K and D is also $5000 while RB, WR and TE can be available for just $4500.  Lets add that up: (3 * $5000) + (6 * $4500) = $42,000.  We must spend $42000 just to enter the game.  This is a really important point - your fantasy team picking skills only have control over the remainder :  $60K - $42K = $18K .
As of this writing, FanDuel prices players at the $100 dollar increment.    So, you really have only 180 $100 bills to spend, and to play this game means selecting 9 items from 6 markets with those 180 benjamins.   Sounds easy, right?
Fantasy Sports player value is the concept that you will get scoring points in exchange for the 180 $100 bills you can control.  Lets define value as Fantasy points per $100 bill.  Example:  You pick a QB with a salary of $8000 and he generated 15 fantasy points.   You really just made a decision to spend 30 of your $100 bills  ( $8000 - base  salary = $8000 - $5000 = $3000 / $100 = 30).  Your Fantasy Sport value is 0.50 points per $100 ( 15 points / 30  = 0.50).   
Let's compare your purchase to your buddy who picked a different QB who cost a lot less but didnt generate quite as many points:  say $7000 and 12 points.  Your buddy may have done better by getting 0.60 points per $100, as the value calculation is ( 12 points / (7000 - 5000) = 12 /20 = 0.60 points per $100).
Why is it that  your buddy may have done better by getting 0.60 points per $100 versus your choice that returned only 0.50 points per $100?  Because he spent less - effectively only $2000  and you spent $3000 .  Your buddy has $1000 more then you to spend in markets other then quarterbacks then you do.  Your buddy had a higher  return (0.60 verus 0.50) then you did.  If he can spend the extra $1000 to advantage on other positions, he will be in a better position.  This is why it is called value based drafting.
Key point : When you have a choice, always pick players with the highest potential fantasy points per effective salary that you can afford.  Be aware of the salary floor and divide out what you think the points per salary return will be. 
In part 2, we will look a real example.
If you have comments or suggestions on this, please ContactMe .   Good picking !