DFS: Analyzing Stacking Strategy (Fantasy Baseball)

Stacking is probably the most common lineup building strategy in the game of MLB DFS. Every day during the season you will see various experts giving their “favorite stacks” and talking all about which players to stack up.

A lot of the time, the most popular conclusion about a question is correct. However, there are times when the consensus is wrong. Identifying these situations provides a huge opportunity to get ahead and really profit, both in fantasy sports and in life in general.

In this post, you will find a few different studies that I really do not know if anybody else has ever attempted.

Over the last couple of weeks, I have assembled a data set of every MLB box score along with each player’s DraftKings salary and points output for the last five seasons. In this data set, I have a row for every individual game each player has played with their full line score and DraftKings information. For hitters, I also have the opposing starting pitcher that hitter faced and that pitcher’s salary. This data set allows us to look back at the last five years of DraftKings data and learn from it.

Just for fun times before we venture into the stacks analysis, let’s check out the top five DraftKings scores of the last five years. Seeing a “NaN” in the salary column means that the player was not on the main DraftKings slate that day.

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Top DraftKings Hitting Performance, Last Five Seasons

Top DraftKings Pitching Performance, Last Five Seasons

Test #1: What Pitchers Should You Stack Against?

Opposing starting pitcher is always the most important variable when considering offensive stacks. Since I had all of the opposing pitcher salaries for the last five seasons, I wanted to see the relationship between DraftKings points generated by an offense and the salary of the opposing starting pitcher. I decided to use just the last three seasons for the purposes of this study since pitcher salaries were pretty inflated in 2014 and 2015.

For every non-extra innings game played where DraftKings salaries were available over the last three years, I did the following:

Rounded each pitcher salary to the nearest $500 mark
Summed up the opposing offense’s DraftKings points

That generated a data set with each team’s offensive output along with their opposing pitcher and his salary. There are 13,449 games represented in the data. The top three scores look like this:

The winning team scored 25, 23, and 23 runs in those games respectively. Needless to say, you would’ve done pretty well if you had a few stacks of those offenses on those days.

To get a feel for the big picture here, I all 13,449 of those rows, rounded each pitcher salary to the nearest $500 and then found the average team DraftKings score against each pitching price point. Here is the plot:

Unsurprisingly, teams do very well against very cheap opposing starters, averaging around 70 team DraftKings points when they face a pitcher priced around $5,000. Along the same vein, they do very poorly against the most expensive starters.

Strangely enough, teams have done much better against starters around the $13,500 mark compared to the $12,500 and $13,000 salaries. There have only been 75 of those instances over the last three years however, so it’s not exactly a huge sample size to learn from.

While there is certainly an obvious downtrend, there does not seem to be much difference at all between pitchers separated by $500-$1000. Teams have performed the same way against $8,000 pitchers as they have against $7,000. The same is true in the $10,000 – $11,000 range, just not much of a noticeable difference there.

If we round the pitchers to the nearest $1,000 instead of $500, here’s what we see:

Once again, the extremes of the plot can be a little wonky because of the lack of data. There have not been many $4,000 or $14,000 starters, so those dots being out of line does not mean much of anything.

To show this a different way with a little more detail, I developed a box plot of the distribution of team scores against each pitcher salary, rounded to the nearest $1,000. For each price point, you’ll see a box, a line, and some dots above the top line.

75% of the data points will be within the range of the box, and 95% of the data points will be inside the vertical line. The dots you see above the top line are the 5% of outliers scores, in this case – very high scores. For more on boxplots, check this out. Here is the plot:

The green line you see is the average team score against each opposing starting pitcher salary. Here are the averages in table form:

What you can see by the box plot is that you typically get those outlier tournament-winning scores from teams facing a pitcher below the $8,000 mark.

Conclusion: No socks will be knocked off by this. Stacking against the cheapest opposing pitchers is a good idea, and stacking against the most expensive is a bad idea. One actually useful thing to notice is that there is not a significant difference in the big picture between stacking against a $7,000 starter and a $9,000 starter. In fact, it may be beneficial to prefer stacking against a pitcher priced near $9,000 – just because you get those outlier performances at about the same rate, and the ownership on that stack will likely be lower.

Test #2: Lineup Spot Correlations

After you have decided what team to stack with, the next question becomes which hitters to choose in your stack.

First, let’s check on the average DraftKings points scored by lineup position over the last five seasons. I have also included the average number of plate appearances and did the division to find points scored per plate appearance:

You can see that the three and four hitters come out on top as the most productive in a per-plate appearance basis, but your cleanup man actually finishes fourth overall in points scored per game because he is giving up those extra plate appearances.

Note that the #9 spot in this study is destroyed by pitchers who only get two or three plate appearances in most games. I used the starting lineup for this purpose, so if a pitcher gets two plate appearances in a game and then pinch hitters get two in that spot, only the starting pitcher’s two PA’s will count for these purposes. The actual plate appearances that the #9 spot gets is 3.48.

Checking the correlation between different pairs of lineup positions is a pretty tough thing to do responsibly since there are a lot of zeroes in the MLB DFS game. I went about this in a couple of different ways.

First, I tried it the old fashioned way. I picked ten different pairings of lineup spots and made two lists of all of the DraftKings scores that those lineup spots have produced over the last five years, and I saw what the correlation coefficients were. With so much data, these numbers should be somewhat reliable. I did not expect any real correlation to develop, but we can learn something just by how they fared against each other. Here are the results:

In statistics, you would not say two variables are correlated at all until you saw a coefficient of 0.3 or so, but that does not mean that we can’t learn something here. The order of the pairings does make sense. The most correlated pairs are closer in the batting order to each other than the least correlated. The 1-2 pair is the clear winner here, with a big gap between it and the second-place pair. The 1-3, 4-5, and 2-3 are all tied for second.

The second way I tried this out was to isolate each of the top five lineup spots, find the games where that spot did very well, and then see how that big game affected the lineup spots around it.

First, I checked what happened to each position’s average DraftKings score when each spot went over 10 DraftKings points. Here are the results:

So the way to interpret this is to look at the first grouping of color numbers there. That box tells you that when the lead-off scores more than 10 DraftKings points, the #2 hitter sees the biggest benefit, jumping up 1.79 points over the average for #2 hitters. You can see how the numbers all descend in order after that.

In every case but the #4 hitter, the biggest beneficiaries of a hitter going off are the hitters immediately before and after him, and it’s a significant difference from the hitters more than one spot removed.

Interestingly, the #3 hitter doesn’t get much of a benefit when the #4 hitter has a big game, probably because of a lot of three-up three-down first innings.

I did the same thing again, but checked when each hitter went over 14 DraftKings points:

The #2 hitter really thrives when the #3 guy has a big game, going 2.18 points over his average. Interestingly, the players that hit before the guy that goes over 14 DK points actually see a bigger boost in scores than the player who follows him in the order. Typically, if you’re going to get 15 DK points or more, a home run is involved – so this makes some sense because a home run never helps the guy batting next.

Conclusion: Keep it simple, stupid. If you are going to stack an offense, do it with hitters batting consecutively in the lineup. The 1-2 is your best pair. Always consider the base rates – the #1 and #3 hitters score the most points per game on average, so they also stand to benefit most from a whole team busting out. Your best stack is just starting at the top of the lineup and working your way down in order, however far you want to push it.

Test #3: How Often Do Teammates Finish Near the Top of the Daily Leader Board?

I will save you all some verbiage here. All I did, in this case, is loop through every day last year, using only days that had 10 or more games on the slate, and check to see how often teammates were in the top __ of hitting scores for the day. Here are the results for 2019:

Percent of the time that two or more teammates finished in the top 20 hitters: 100%
Percent of the time that three or more teammates finished in the top 20 hitters: 86%
Percent of the time that four or more teammates finished in the top 20 hitters: 33%
Percent of the time that five or more teammates finished in the top 20 hitters: 6%

Percent of the time that two or more teammates finished in the top 10 hitters: 94%
Percent of the time that three or more teammates finished in the top 10 hitters: 28%
Percent of the time that four or more teammates finished in the top 10 hitters: 5%

Percent of the time that two or more teammates finished in the top five hitters: 46%
Percent of the time that three or more teammates finished in the top five hitters: 7%

Percent of the time that the top two hitters of the day were on the same team: 10%
Percent of the time that the top three hitters of the day were on the same team: 2%

I checked these numbers for 2018 and 2017 as well, and the percentages were basically identical.

Conclusion

It is largely what we all suspected in the first place, stacking is a super viable DFS baseball strategy. Here is this article’s main takeaways in bullet format.

On any given day (on a normal-sized slate), there is a 94% chance that two or more teammates will find themselves in the top ten hitters of the day.
There is a 46% chance that two or more teammates will find themselves in the top five.
There is a 10% chance that two teammates will be the top-scoring hitters overall.
If you want to win a tournament, your best statistical odds are to do with a stack.
The best two-man stack is to do a 1-2 stack.
The best three-man is a 1-2-3 stack.
The best lineup positions to be in are the lead-off and #3 spots.
Target the cheapest opposing starting pitchers
If targeting a more expensive pitcher, lean towards the $8000-$9000 pitchers as they give up about the same scores as the $7000-$8000 pitchers and ownership will likely be lower

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