DFS Strategy: Boom or Bust and Stacking

Making the perfect daily fantasy picks is different from how it’s done in redraft leagues. Whether it’s hockey, football, baseball, or basketball, though, we suggest that the same DFS strategy will work. It’s all about outlier performance, having a great week not just a good week.

This article contains two DFS strategies which are based on mathematical and statistical principles to help you increase your chance of winning. These strategies will help you make the best daily fantasy picks possible. These strategies aren’t new, our goal is simply to help you sift through the weeds to find the correct daily fantasy sports strategy.

For each DFS strategy we introduce in this article, we’ll give both an intuitive explanation and mathematical reasoning for why this strategy increases your chances of winning.

Most importantly, these strategies are implementable. That is, the strategy isn’t “pick whoever pops out of the end of a formula”. Rather, each DFS strategy in this article can be accomplished with minimal effort.

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The Goal in Daily Fantasy Sports

There are quite a few differences between daily fantasy sports and traditional fantasy leagues. The most obvious difference is that new players are drafted weekly in daily fantasy. However, there is a bigger difference that changes the optimal DFS strategy. The biggest difference is that in daily fantasy, many leagues are much larger than the 8-12 person leagues we see in season-long fantasy.

In 8-12 team leagues, your team needs to be in roughly the top 10% to win. In the larger DFS leagues, your team needs to be better; you might need to be in the top 1% to win! Take a look at the graphic below. On the right hand side, each of the light green dots may have had a good enough team to win a smaller league but only the dark green dot was good enough to win a DFS league.

What this means is that to win a daily fantasy league, you don’t need to have just a good team. You need to have a great team.

Each daily fantasy strategy we suggest in this article is designed to help your team reach the top 1%. It isn’t enough to take the best players, we need to make our team an outlier. The way we propose to accomplish this is to pick teams with extremely high variance in expected performance.

DFS Strategy 1: Boom or Bust

Our first daily fantasy strategy is to focus on the traditional boom or bust players. Boom or bust players are those who are inconsistent; they either have huge games or absolute duds. A boom or bust player who averages about 10 points per game might put up 2 25 point games and 4 2-3 point games. A consistent player with the same average might score between 8 and 12 points in each of these 5 games.

We suggest that in daily fantasy sports, boom or bust players are more valuable than consistent players. When you make your daily fantasy picks, choose the players that have a boom or bust profile.

Intuition

The traditional knock against boom or bust players is that if they put up a dud, a 1 or 2 point game, then your chance of winning your head to head matchup drops dramatically. This is certainly true in traditional fantasy.

In daily fantasy, though, we don’t need average performances from each of our players. We need above average to outstanding performances from everyone in order to beat the huge field. A 10 point performance from an RB1 is just as dooming as a 2 point performance is!

Because we need outstanding, outlier scores, we should pick those players that are most likely to have huge games. Consistent middle-of-the-pack performance from your starters leads to middle-of-the-pack performance of your team.

Mathematical Justification

To win daily fantasy, we need our team’s total performance to be in the top percentile or so of weekly team scores. If our team has a higher variance in how they score, the top percentile actually becomes easier to attain. Take a look at the graphic below.

The black line represents the score we need to attain to win a daily fantasy league. The blue curve is a normal distribution with a small variance while the red curve has a large variance. Remember that probability is area under the curve. The area under the red curve to the right of the black line is larger than the same area for the blue curve. This means that the team with the larger variance has a higher probability of scoring enough points to win.

We can increase the variance of our team’s score by taking boom or bust players.

Daily Fantasy Sports Strategy 2: Stacking/Player Stacks

Our second DFS strategy is to stack players whose performances are correlated. For example, a quarterback and his WR1 will tend to have correlated performances: when one does well, the other probably will too. We want to focus on stacks where player’s points are positively correlated, not negatively correlated. More on that later in the math section.

Utilizing stacks will help you make the best daily fantasy picks. Let’s look at the specifics

How to Use Stacks in Daily Fantasy

Stacking players helps you win your daily fantasy leagues by increasing the variance of your team’s total points. Remember, a high variance makes it more likely our team will explode for a huge total. Two examples of stacks in different sports that we condone include:

• A quarterback and his best receiver.
  • If the receiver has a good game, it is likely the QB will too and vice versa!
  • We’ve written about why this is a great strategy in season-long fantasy as well in this article.
• The two best hitters on a baseball team
  • The opposing pitcher may have an off-day or they might be able to bat each other in; they will have more correlated performance than two batters on different teams

Some stacks are actually detrimental to your team’s total, though. We want our player’s performances to be positively correlated, not negatively correlated. That means when one player does well, the other does too.

Some sports might have negatively correlated performances which you should avoid in your daily fantasy lineups because they decrease variance! Two examples include:

• Two receivers on the same NFL team
• Teammates in the NBA

These are probably anti-stacks because when one guy does well, it is because of an abundance of opportunities. These opportunities are often taken away from their teammates leading to decreased performance.

Anti-stacks lead to more consistent, middle-of-the-road performance and less consistent combined boom performances. We need both players to boom, so the safety is actually a detriment. Before explaining why stacks make sense in daily fantasy, let’s look at how to identify when players’ performances are positively correlated.

Identifying Stack Opportunities

Identifying stacks in daily fantasy is as simple as looking at the correlation between two player’s fantasy performances. This can be done extremely easily using either excel or your favorite coding language.

To identify stacks, we want to make a scatter plot with one player’s score on the x-axis and the other player’s score on the y-axis. There are a few ways to determine whether the data is positively correlated. In excel, you can simply compute a line of best fit (a least squares regression line) and look at the corresponding R value. If R (not R^2 ) is close to 1, then the data are positively linearly correlated.

You can also do this graphically! First, take each player’s scores and subtract their mean score – this is called centering the data. Then, plot the data. If more of the points lie in quadrants 1 and 3, then the data are positively correlated. For example, the plot below shows (weak) positive correlation between two fantasy scores!

A line like this with a positive slope and a large R/ R^2 value indicates correlated performance and players who are stackable. Be careful to take this to the extreme though. Sometimes player’s will “accidentally” have correlated performance because of random statistical noise. A way to avoid this is to make sure it makes sense that our player’s performance should be correlated. A QB/WR1 combo for example makes sense.

Intuition Behind Daily Fantasy Stacks

Remember the goal of our DFS strategy: achieve an extreme outlier score. When we have players whose performances are correlated, when one of them booms, the other has a good chance of booming too.

In order to win a daily fantasy league, you need multiple players to have very, very good games. When you have two players whose performances are correlated, this becomes much easier. Instead of getting lucky twice, we now need to get lucky only once.

The mathematical justification between stacking in your daily fantasy picks is just as interesting.

Mathematical Justification Behind DFS Stacking

Our team’s score is a random variable. To win a daily fantasy league, we need our score to exceed some critical threshold \rho . Player’s are, in general, priced according to their expected production. This means we can’t really increase the expected value of the random variable very much. What we can do, though, is maximize the variance of our lineup.

Consider two player’s scores denoted by X and Y. The variance of the sum of these two random variables satisfies the well known decomposition Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y) where Cov(\cdot, \cdot) is the covariance between two random variables.

For independent random variables, their covariance is 0. This means that for two players with uncorrelated performances, the variance of their sum is the sum of their variances. But we can do better with stacking.

If two players have correlated performances, then their covariance is nonzero! In fact, we want to pick players whose performances are positively correlated so that Cov(X,Y) >0 . This essentially gives us a variance boost in our team’s total score. This makes it more likely that we will exceed the critical threshold \rho .

On the other hand, players whose performances are negatively correlated will decrease our team’s overall variance. This is a net negative in our ability to win.

Summary of Findings

Going into a DFS draft, of course you want to find underpriced players and diamonds in the rough. But you can also increase your odds by making daily fantasy picks that increase the variance of your team’s total score.

We suggest two ways to do this: taking boom or bust players and stacking players with positively correlated performances. These two strategies are easy to implement and will give your team a better chance of winning regularly in DFS.

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