Daily Fantasy Sports team optimizing – NFL Football Mathematics Part 3 - The Ladder Line

The most important aspect of Daily Fantasy Sports is managing your budget within the salary cap to ensure you are getting maximum value for the salary tokens you have available ( See part 1 and part 2 for how to calculate player value ).


To build a winning team you must be able to picture how your team is coming together on your overall goal of getting the most points for your team.  A Ladder Line – sometimes also called a waterfall chart or an accumulator display – is an important tool to evaluate how one team compares to another. 


A ladder line is a graph that shows the points expected by team member versus the salary expended.  It accumulates the contribution (in points expected) from each team member versus the cost of that team member.  The beauty of a daily fantasy sports ladder line is that it shows the hard line limit of the salary cap while providing a visual indicator of the value of each player.   This is also known as value based drafting.


Here is an example for a NFL Daily Fantasy game with a $60K salary cap.  Per the site rules, we have picked one quarterback (QB), two Running Backs (RB1, RB2), three Wide Receivers (WR1, WR2 and WR3), one Tight End (TE), one Kicker (K) and selected one team for defense (D).  We have pulled down the real Salary Data and average Fantasy Sports points per game from the fantasy site but have not shown the players names.



Column “Player Salary” is the actual salary assigned by the Daily Fantasy Sports site to the players.  At the Fantasy Site, we sorted by salary to find the minimum salary for that role which is listed in column “Salary Floor”.  We then converted to Salary Tokens with the formula Tokens = (PlayerSalary – SalaryFloor) / 100 .  (See part 1 and part 2 for a review on why we use Salary Tokens ).


To construct a ladder line graph, start with creating an origin point of (0,0), which mean (0 salary and 0 points).   Then for each player, accumulate the Tokens and Points  for each player, add the expected points and salary tokens.   In our example, the vertical red line at 180 Tokens is the hard salary cap limit for this game which is ($60,000 - $42,000)/100 .   The blue line shows how this team came together.  The slope of the connecting lines is the value.


The name ladder line comes from the analogy that you are a fixed distance from a hard limit (e.g., 180 Token) and you must connect a number of segments to get the maximum possible height.  You want a line that looks like a ladder that is as steep as possible.


See Daily Fantasy Sports team optimizing – Fanduel NFL NBA Mathematics Part 4 – Using VORP Value Over Replacement Player for instructions on how to fine tune the ladder line to match the competitive scene.


If you have comments or suggestions on this, please ContactMe .   Good picking !