Drafting Fantasy Football Teams: A Comparison Greedy Algorithms
Posted on September 7, 2015
Fantasy football is an increasingly popular game for American football fans. Coaches compete within a league, typically of friends or coworkers. The standard roster of starters includes 1 QB, 2 RB, 2 WR, 1 TE, 1 D/ST (defense/special teams), 1 K, and 1 F (flex: can usually be a WR, RB, or TE). Teams also have bench players (backups for when starters are struggling or on a bye week).
If you aren’t familiar with how fantasy football works, read more here. Even if you aren’t a big football fan, this is worth learning for the exciting strategy behind playing. From here on out, I will assume you have a basic working knowledge of the game.
There are a lot of week to week strategies that coaches employ to pick up the best players off the waiver wire or win week to week, but for now we will just focus on the draft.
Simple Greedy Algorithm
The simplest way to draft is to just pick the best available player. We will call this a greedy algorithm. There is no negative connotation implied here; it just describes the algorithm design: pick the best player available based on projected points.As it turns out, this strategy isn’t too bad; better than wonky strategies like picking only Jets and Chargers players or only from teams capable of flight (both are strategies I've drafted against). Success in a draft is obviously not guaranteed. After all, only one person can draft the best team. As many seasoned coaches suspect, the lucky coaches with early picks (1-3 overall) are more likely to draft teams with the highest projections.
If you are the poor guy sitting in the back with the last pick, it seems like there’s nothing you can do. Even if you know who your opponents are picking, there is not a clear and intuitive way to leverage that information if you stick to just picking the best available. If only there was a way to take advantage of the knowledge of who other players are picking…and that’s where the predictive greedy algorithm comes in.
Predictive Greedy Algorithm
Let’s think through a modification of the simple greedy algorithm by considering the following situation. Let’s say (hypothetically) that you have the QB and WR positions open. Also, Peyton Manning is the best player available and he is worth 500 points, the next best player available is Calvin Johnson, projected to get 475 points. The simple greedy algorithm would tell you to pick Peyton because he is worth more points. When the next round comes around, Calvin Johnson is no longer available at WR so you have to “settle” on 375 from Brandon Marshall.But wait, there’s more! Let’s also say 3 spots behind Peyton (in QBs) is Philip Rivers, a less popular choice, but still projected to get 425 points. And better yet, you know how you’re opponents pick so you know there is a high chance he’ll be available next round. So you can let Peyton Manning go to another team and pick up Calvin Johnson even though he doesn’t have the highest points available, then get Phillip Rivers the next round(Peyton will surely be gone). Some simple math later, you drafted two players worth a combined 475+425=900 points (Johnson and Rivers) instead of 500+375=875 (Manning and Marshall), because you were able to predict what your opponents were going to do, and exploited it.
With that example in mind, let's formally define our new greedy algorithm. Each pick you will follow these steps:
- Determine the best available player and simulate that you pick him
- Determine the best available player at every other position
- Simulate other coaches picking for a round until the pick comes back to you
- Once again, determine the best available player at every position
- Calculate the position with the highest decrease in points and pick that player
There are some obvious shortcomings to this highly trivialized situation, namely the lack of information. You will never know exactly who you’re opponents are going to pick, and risking big by drafting lower rated players earlier can be dangerous. However, in our academically predictable environment, this strategy proves to be quite fruitful.
Comparison
We are going to simulate 66 different drafts: 6-16 person leagues (by 2’s) with everyone picking with the simple greedy strategy except for one person, who will pick with the predictive greedy algorithm. The code is largely unexciting bookkeeping so I won’t walk through it, but you can find it on GitHub.
As expected, the predictive greedy algorithm is quite successful, particularly in larger drafts and for players in the middle of the draft order.
Coaches who picked following this strategy picked the team with the highest projected points 89% of the time.
Other Considerations
This is obviously a drastic oversimplification of the drafting problem, namely because we know our opponents strategy. In reality, coaches’ picks are more sporadic. Some coaches employ strategies like picking 3 RBs in their first 3 rounds, others pick players heavily from their favorite teams.Regardless of how your league tends to pick, a key to success is to get out front of these trends right before they happen (and not too early). We can see the importance of this in the chart below.
Each position has diminishing point value (the slope flattens out) as you go further out in the rankings, some faster than others. You want to pick anytime when the slope is steep, but on the front end (you don't want to pick after the major drop offs). But not all positions are picked at the same time, and this varies by league. In some leagues, quarterbacks go in the 1st round, in some not till the 5th - some leagues pick defenses in the 5th round and some pick defenses in the 8th round. If you know other coach's tendencies, you can get out in front of these major drop offs and take advantage of them.
This overlooks a few other important details - one of which is the bye week problem. Each player has a bye week some time from Week 4 to Week 11 in the 17 week season. Some coaches hedge against this by spreading out the bye weeks among their team – others try to get all the bye weeks at the same time so their team takes only one bad loss.
Another overlooked assumption comes from picking bench players. Consider a 6-team league. There are far more than six QBs that are fairly evenly matched and good enough to start on a fantasy team. Therefore in this simulation, a coach who waits until the last pick to draft the QB does not suffer too much in points lost. However, in reality, some coaches pick their backup QB quite early; some even draft a backup before they fill in all of their starting positions. This decision-making process is hard to predict in these simulations.
With all the assumptions that have gone into this analysis, it’s unlikely that a coach could replicate this success without a little bit of luck and lot of predictable behavior from their opponents. If you did have this information (looking at you ESPN), there is a lot of potential to take this in exciting new directions.