Quantifying the Impact of Stacking in DFS

by Matt Hunter

July 7, 2016

This week over at SaberSim, I released a tool that allows users to view more detailed projected performance for their lineups. Rather than just adding up projected points for each player, this new Lineup Analysis tool allows us to view mean, median, standard deviation, and percentile projections for the lineup as a whole. In other words, rather than combining each player’s distribution separately, SaberSim analyzes the performance of the entire lineup across each simulated game.

Analyzing the lineup as a whole rather than the players individually is important because of player covariance. When you include multiple players from the same team in a lineup, you’re usually increasing the variance of the lineup’s point total. Even though baseball is a relatively individualistic sport in which each batter acts independently of others in the lineup, opportunity and run scoring depend highly on the interaction of batters. When a player gets on base, it increases the expected number of plate appearances for each other player on the team, as well as the probability that the following batters will get an RBI.

The concept of “stacking” in DFS is based on this player covariance — if you include five batters from a team in your lineup, their overall opportunity for scoring and chances of runs and RBI will be highly correlated. Theoretically, this should reveal itself in the aforementioned Lineup Analysis tool on SaberSim. Lineups with a higher variety of teams included should, all else equal, have a lower standard deviation and lower 75th, 85th, 95th percentile projections, while teams with stacks may sacrifice average score slightly in exchange for higher variance and upside.

Let’s look at tonight’s DraftKings slate as an example. Below is the “optimal” lineup using average points, and the corresponding analysis of the lineup using SaberSim’s tool:

Although there are a few Rockies in the lineup and two Astros, the overall composition is fairly varied, and the pitchers are not on the same team as the batters. Also, notice that because pitching is fairly weak tonight and Hutchison is a value pick, the lineup includes Miguel Cabrera, who is facing Hutchison. While this may not affect median or mean projections negatively, it certainly lowers the upside of the lineup, because any time either of the players has a great performance, it greatly decreases the chance that the other will as well.

Now, take a look at the optimal lineup using 95th percentile projections for each player, and again the corresponding lineup analysis:

In this lineup, we have not only five Rockies batters, but Bettis, the Rockies pitcher. This, along with the fact that we’re using players with high upside *and* we don’t have a batter and his opposing pitcher in Miggy and Hutch, leads to a much higher standard deviation and higher percentile projections. The second lineup has a lower median and mean than the first, but is more likely to score a high number of points than the first because of the correlation between player point totals.

We can also use Conditionals (a topic I’ve discussed in past articles) to create lineups based on isolating portions of projection distributions, which is another way to increase lineup upside. Below is a lineup based on isolating the top quartiles of Gattis and Correa’s projected performance:

Again, we see a low mean and median, but higher 85th and 95th percentiles than the “optimal” lineup due to the correlation between the Houston batters.

This tool is still new to me as well, so I haven’t investigated all types of lineup composition, and the effect they have on the entire lineup distribution. I’d love to hear any feedback from you about strategies that you’ve taken to increase lineup upside, or optimize your lineups for different types of DFS contests.

On to the day’s projections…

DFS Projections: Batters

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