I'm a fantasy basketball player and there is a recurring problem that I have not been able to figure out, and I can't find a similar enough example online that I can adapt for my own usage. For those who don't know, streaming (in fantasy basketball) is when you have an open spot on your individual team that you cycle available / free agent players through, in an attempt to maximize points, based on when they play during the week.
For example, Player 1 has games on Monday, Tuesday and Wednesday, and P2 plays on Thursday, Friday and Sunday. You keep P1 rostered through Wednesday, then drop them and pick up P2 for the rest of the week. Both players' points are added to your total; this allows you to essentially benefit from having two players' scoring for the week while only using one roster spot.
| M | T | W | Th | F | S | S | Avg Pts / Game | |
|---|---|---|---|---|---|---|---|---|
| P1 | x | x | x | 20 | ||||
| P2 | x | x | x | 25 |
The optimal strategy yields 135 points, vs 60 or 75 from just playing one player for the whole week.
The complexity comes from three places.
Players you want to play sometimes overlap on the same day, and their schedules often overlap in a way such that it might be worth it to start a worse player early in the week if it means you get access to a slate of their games later in the week. A player may have a lower points per game than another player, but by virtue of playing more games it’s worth it to start the player with a lower average.
Players can’t be re-added for the rest of the week once dropped, due to the nature of the fantasy sports platform. So you can’t toggle back and forth between two good players if they have complementary schedules. Related to this, there are a set number of “adds” you can use per week. Without this you could just add 7 different players, one each day, and figure out who was going to be the best for each day of the week. For the purposes of this league, the number of adds is 4 per week.
There are lots of available players. Figuring this out manually sometimes means starting players who are ranked far outside the top 130 (the total number of players across all of the leagues rosters) in Points Per Game, but due to their scheduling quirks, offer the best value for the remainder of the week. Trying each combination of players against each other involves a huge number of potential options.
I am a CS hobbyist, but the things I build do not require these sorts of optimizations, and I haven’t been able to find an example that would solve all parts of this problem.
Take the below schedule, for example. An “x” indicates the player is playing that day:
| M | T | W | Th | F | S | S | Avg Pts / Game | |
|---|---|---|---|---|---|---|---|---|
| P1 | x | x | x | x | 20 | |||
| P2 | x | x | x | 21 | ||||
| P3 | x | x | x | 22 |
The points maximizing solution is to start Player 1 Monday, drop them and switch to Player 2 for the next three days, start no one on Thursday (as P1 would not be available after dropping them), and then switch to Player 3 for the last two days.
Start P1: 20 + 63 + 44 = 127
Constraints:
- There are a set number of available days (7)
- Only one player can be played per day
- Each player can only be added one time (but can play consecutive games after being added with no penalty).
- You can only add new players a set number of times: “n”
- There are “p” possible players, each of whom has days of the week they can be played and an average points per game (same across all days)
- The objective is to return the schedule of players in the proper combination that optimizes the total points in a given week.
My (somewhat brief) look through the existing algorithms led me to considering the knapsack problem, optimal scheduling, and greedy. Greedy doesn’t seem to work because it would immediately decide to start Player 3, which would not ultimately lead to the optimal solution, ending up with 125 total points
The scheduling algorithm would seem to require considering the start and end of a “task” as the first and last day a player plays, which creates problems here; Player 1’s “block” or whole week between first and last day would show that Player 1 offers the best total value at 80 points, and that the optimal strategy would be to just play them, but it doesn’t consider prematurely ending the task if something else was available.
Likewise I can’t figure out how to introduce the “switching” element into solutions to the knapsack problem.
There is a related question here but it doesn't include the scheduling aspect: Algorithm to select Player with max points but with a given cost
I feel like there’s a method that I’m not quite grasping, or a simplification that would allow me to use one of the aforementioned solutions. Any help in solving this completely inconsequential problem is greatly appreciated!
