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Bullet Holes, Survivorship Bias, and Why We May Be Analyzing DFS Lineups Incorrectly

The daily fantasy landscape has grown a tremendous amount since people first started playing in the mid to late 2000’s. Along with that has come massive tournaments, crazy prize pools, and awesome live finals. It has also brought with it a great surplus of information.

Much like in seasonal fantasy leagues, finding the best DFS plays is now easier than ever, and you could argue there are no true “sleepers” outside of what a few sharp players come up with in the dark alleys of their internet browsers. However, I think that it is possible we are analyzing a lot of our information incorrectly, particularly with respect to how we evaluate lineup success.

Where Are the Missing Holes?

Before I get to my DFS hypothesis, let’s first start with an interesting story I read about in How to Not Be Wrong – The Power of Mathematical Thinking by Jordan Ellenberg.

It’s World War II and the Americans are trying to armor their planes in the optimal way. They want to protect their planes as much as possible without weighting them down or making it too difficult to maneuver. When American planes came back from Europe, there was data compiled on the bullet locations on them. Here is what the data looked like.


Seems pretty simple right? Just armor the planes where the bullets were most often hitting, and protect them from taking on serious damage. However, renowned mathematician Abraham Wald, a member of the Statistical Research Group for the Americans (though he was a native Romanian), had a different idea.

Armor the planes where holes are missing.

Wald’s simple, yet accurate conjecture was that the reason so few planes were coming back with holes in the engine was that the planes with holes in the engine weren’t coming back! The ample amounts of shots being taken to the fuselage and other parts of the plane simply weren’t as important to armor, because clearly planes could survive after taking damage there.

This is a perfect example of survivorship bias, which is, per Wikipedia, “the logical error of concentrating on the people or things that “survived” some process and inadvertently overlooking those that did not because of their lack of visibility”.

How it Impacts DFS

Now to circle back to daily fantasy, it appears, to me, that we are encountering a lot of survivorship bias when we analyze lineup construction. It is typical, for example, for us to see statements like “60 percent of winning lineups this weekend had Adrian Peterson“. Here’s why those statements are flawed.

Suppose a particular DFS slate has just finished. Below are two players with their ownership in lineups that cashed in a big double up. Who was more valuable?

PlayerWinning Lineup %

Again, just like the bullet holes problem, this seems obvious right? Player A was obviously more valuable. But what if I gave you some more data?

PlayerWinning Lineup %Overall %Difference

Now that we know that Player A was significantly higher owned than Player B, and more owned than he was in winning lineups, we know that Player B was more crucial to creating a winning lineup than Player A was. But by just looking at who was in winning lineups, or reading an article that does, you would never know that. All you are doing is letting survivorship bias impact how you look at things.

For another example, you may recall my NBA DFS Primer, in which I referenced a numberFire piece that analyzed perfect lineups, and how they were constructed. There were conclusions that the piece, and myself, made such as “pay up for point guard.” But really, such claims are just infused with survivorship bias without more information.

Even though 76 percent of perfect FanDuel lineups contained a PG1 in the $7,100 and up range, we don’t know how truly valuable that is because we don’t know what percent of the public paid that for PG1 in the overall data set. Perhaps that mantra of “pay up for PG” is so commonly spoken that 90 percent of the field is paying up for PG! Then there really isn’t any additional value being gained by doing so. We may, in fact, be better off looking for mid-range PGs if only 10 percent of the field is doing so, but 24 percent of perfect lineups contain a mid-range PG.

What Does It All Mean?

Similar to the bullet holes problem, we believe that we need to prioritize positions like RB because we see that many winning teams are strong in these spots. But that doesn’t make them the most valuable DFS position.

Ellenberg mentions that a good strategy to use when trying to understand survivorship bias is to “set a variable to zero”. In the case of the bullet holes, that meant assuming that if the planes were hit in the engine, that they wouldn’t survive. In other words, they had a survival rate of zero. That would explain why so few planes were coming back with engine holes.

Relating this to DFS is a little easier because the idea of a variable being equal to zero is easier to use (since we have actual points data to deal with). Assume that your stud RB, the chalk, gets hurt in in his game, scoring zero points. Because he is so highly owned, that actually doesn’t knock you out of your cash games, and a good bit of lineups with that RB still cash.

However, instead assume your TE gets hurt, and he scores 0 points. You went stud RB…but so did the rest of the field. In other words, you received no edge at that position. But your TE, who is less chalky, is supposed to differentiate you from the field. His injury doesn’t appear to cost you as much, and when healthy he may actually score less points than the RB, but it hurts your team more because now the field is able to one-up you in an area of your lineup. In other words: the TE is more valuable to your lineup than the RB is.


When setting DFS lineups, people often revert back to what has worked for them in the past, or what they have read has worked for the field. When they do that, they are just ending up on the same chalk plays as everyone else. However, where your lineups are really made or broken is in the ancillary plays, the guys who are not going to be as owned by the field.

Instead of using up all of your time to figure out who the chalk is, and just filling out the rest of your roster, DFS players would be best suited by finding the best plays available at the non-chalk spots. Even in cash games, where you differentiate from the field is going to matter the most. So avoid survivorship bias, find the missing bullet holes in every slate, and dominate daily fantasy.

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