DFS Strategy: Visualizing Player Covariance by Matt Hunter August 5, 2016 In this series, I often talk about player covariance — or the effect that a player’s performance has on his teammates and opponents — and its importance in building DFS lineups. This week, I’d like to expand on some nuances within that topic by looking at a visualization of this phenomenon. First, an overview of the data going into these graphs: using the play-by-play simulator on SaberSim, we have available a full distribution of every statistic for every player within the 10,000 simulations of a game. This data set can be, and is, used to create mean projections (as seen on FanGraphs) but as we dig deeper into the distributions of simulated results, we can isolate games which fulfill certain criteria and see the effect that this has on player distributions. In other words, say that we filter the simulated games to only include games in which the starting pitcher gives up three runs or more. We start by going through the distribution for the pitcher and including only games that fulfill said criteria. This might mean that the distribution goes from [1st game, 2nd, 3rd, 4th, 5th, …] to [1st game, 4th, 15th, 17th, 23rd,…]. Then, for every other player in the game, we similarly filter to match that second distribution. This allows us to see whether and how the criteria affects each player in the game. Let’s take a look at a game from last week, which featured Michael Wacha going up against Jose Fernandez and the Marlins. We’ll isolate the games in which he gave up 0, 1, 2, up to 5 runs, and see how this affects the average DraftKings point values for others in the game. The first observation is that Wacha’s DraftKings points are very strongly correlated with how many runs he gives up. Duh. It’s also completely expected, though not quite as obvious, that Fernandez will see an increase in expected points as Wacha’s runs allowed increases, due to the increased probability of a win. That said, because Fernandez is a pitcher whose value is derived largely from strikeouts, he’s still a good play even if Wacha throws a shutout. Even more interesting is the effect of Wacha’s runs allowed on the opposing batters. As expected, each of Gordon, Stanton, and Yelich see their DK points increase significantly as Wacha allows more runs. However, the effect is not the same. While Dee Gordon’s projection barely doubles between 0 and 5 runs, Stanton’s projection quadruples, going from about three points when Wacha allows no runs to 12+ at five. Yelich is similar to Gordon, but we see his projection increase with Wacha’s RA at a slightly higher rate than Gordon’s. The reason for this difference stems from where each player’s value is derived. Dee Gordon is an elite base stealer and hits for a fairly high average, which means that he can still score points when Wacha gives up a small number of runs, through hits and stolen bases. Yelich derives his value primarily from his excellent on-base abilities. This is more correlated with runs scored than stolen bases, which is why we see Yelich’s projection increase more quickly than Gordon’s, but is still a skill that can provide some value even when Wacha does well. You can probably see where this is going when it comes to Stanton, whose value comes from his elite power. Because home runs are such a large part of Stanton’s DFS projection, and home runs mean runs allowed by the opposing pitcher, Wacha’s RA is very strongly correlated with Stanton’s DFS value, particularly compared to his teammates. These are all fairly intuitive observations, but I find it useful to visually see this effect, and we can take away some useful insight for DFS as well. Because the performance of players like Gordon is more independent of the opposing pitcher’s performance, we might be more willing to play them against highly projected pitchers as contrarian plays. Or, in smaller (2-3 game) slates, we might even consider playing someone like Gordon in the same lineup as the opposing pitcher. While this is still suboptimal from a perspective of maximizing overall points, it can help create differentiation from other lineups in the field, an important factor in these small slates. The other lesson that may not be utilized often is that when you are stacking a lineup, or hoping that a pitcher will give up a lot of runs, you may want to consider playing the opposing pitcher because of their increased chances of a win. While the effect is not large, a few point increase in the projection can bump a pitcher above otherwise similar alternatives. This is just one example of how to use this distribution data from SaberSim to make observations about DFS and baseball in general. You can try out the Conditionals tool, which was used for the above analysis, by clicking here. Please let me know if you have any observations or questions!