In fantasy sports, you have a budget of \$60,000 and 9 roster positions. Each player to choose from has a given salary. Better performing players are usually priced higher than lower-performing players. This is based on fantasy points scored. How could I determine when a player's salary is too high to justify rostering in my lineups? For example, if a player has a salary of \$14,000 and his projections are 50 points then my remaining 8 players need to score around 44 points each, but my average salary per player is \$5750. What type of math could I reference to better make decisions on what the threshold should be?

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    $\begingroup$ We use dollar signs to set off MathJax. You need to escape them with backslashes to avoid the formatting problems, or just delete them because the unit of currency does not matter. $\endgroup$ Commented Nov 5, 2019 at 3:21

1 Answer 1


This is a game theory problem, which is why I added the tag. It sounds like you believe you need $94$ points to win. This is a case of the knapsack problem, which is known to be NP-complete.

The first simple thing is to list all players by points/salary ratio. You want to find the nine players you can afford that give you the most expected points. This is a discrete integer programming problem.

The next layer is to think about how big a crowd are you competing with. Some players will have more dispersion on their points scored than others. This could come from a higher chance of injury, or that they tend to do riskier plays, or whatever. If you are competing against a large crowd that has some sense, they will use this approach as well. You need to be lucky as well as skillful, so higher variance is good for you if your goal is to be the winner and don't care about placing otherwise.

It is hard. Good luck.

  • $\begingroup$ I have an optimizer that does most of the heavy lifting. I’m just struggling with how many high salary players I can pick before I cross the threshold where my lineup is made up of all high salary high output and low salary low output $\endgroup$ Commented Nov 5, 2019 at 3:46
  • $\begingroup$ That gets into the details of the optimizer. If you can solve that problem you have an opportunity in the hiring of sports players in leagues with a salary cap, among other things. I think it is hard. $\endgroup$ Commented Nov 5, 2019 at 4:03

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