German mathematician John von Neumann, widely regarded as the father of game theory, first published works in the field in 1928. He later collaborated with Austrian economist Oskar Morgenstern to develop his theories further, applying them to interactions of competing agents in other disciplines. This groundbreaking publication, titled Theory of Games and Economic Behavior, was published in 1944 and laid the groundwork for the evolution of game theory as we know it today.
John Forbes Nash then contributed to the field of game theory through his 1951 proof of balance in games, labeled Nash equilibrium. An aspect of a game is said to be at Nash equilibrium when no agent or player can gain an appreciable edge over any other by changing one’s strategy, as it would theoretically reduce one’s odds or payout.
While the game of best ball will likely never reach a state of Nash equilibrium due to the borderline infinite potential outcomes, strategies, and variance involved, there are some aspects that are closer to equilibrium than others due to the focus from the industry over the previous five years. In game theory, we label these items as common knowledge. Common knowledge is simply an aspect of information that is known by all players, that all players also know all other players know. Identifying these aspects of a game is beneficial as they will directly influence our decision-making processes as we develop a plan of attack.
Over the previous few years, the industry has done immense work in identifying things like optimal roster construction, expected value (EV), stacking, and positional allocation as it pertains to the EV equation in best ball, effectively decreasing the edge in those areas due to the introduction of common knowledge under the tenets of Nash equilibrium.
In other words, the edges in the game of best ball are shrinking. No longer can we simply “draft better” than the field. No longer can we view Week 17 optimization and roster construction as ways to gain an appreciable edge. This brings us to the question at hand – is there anything we can do to increase our EV in the game of best ball through stacking and correlation, knowing that the largest contributor to EV in playoff-style formats (as found on Underdog) is Week 17? I think there is, and I can prove it with math and theoretical reasoning.
Finally, I can’t get through the entirety of my work in the field of game theory as it applies to DFS and best ball in this piece as it has taken me over three years of work to compile, most of which, until now, has been housed at One Week Season. With that, join me as we work to identify the top best ball stacks on Underdog for the 2024 season.
Framework
The basic principles of game theory involve our own knowledge, our knowledge of the game itself (contest rules), and our observations of the field. From these observations, we can begin to classify various acts or pieces of information as common knowledge, proprietary knowledge, and joint knowledge. These classifications will help guide our decision-making process, allowing us to develop hypotheses based on crowd psychology and other tenets. We call these targeted deviation exploits, or a deviation-based and robust approach for taking advantage of weak opponents while simultaneously maximizing expected value against strong opponents.
To better understand the effects of an exploit on EV, let’s examine a simple zero-sum game like flipping a coin. Let’s say, for example, 100 players offer up $10 to select between two outcomes of a flipped coin. Except this coin is a magic coin, one that lands on heads 75% of the time. A risk-dominant strategy in this game would be to select heads as a three-to-one favorite outcome. As we previously highlighted, natural field tendencies will influence this risk profile, meaning we can expect larger “ownership” on the selection of heads. Say now that 90% of the players in this game select heads.
The EV of heads becomes: [(0.75) * ($1000)] / 90 = $8.33
The EV of tails becomes: [(.25) * ($1000)] / 10 = $25
Mathematically speaking, what would be the better choice if we knew that, going into this game, 90% of the players would choose heads? Over time, we would make more money by always selecting tails.
Realize this is an extreme example to highlight the math behind an exploit, but this is the basic cognitive principle of exploitation in games. As such, our goal in this piece is to identify stacks that the field is underutilizing in best ball tournaments for the 2024 season. Since we don’t have access to site APIs to find the exact ownership of the stacks in play this year, we must first generate hypotheses based on our observations of the field.
Hypothesis One: The field does not utilize QB+RB stacks enough.
My study in DFS yielded similar results, as 22.2% of the GPP-winning rosters over a three-year sample included the a team’s quarterback and running back in their primary stack, yet running backs are not included in primary stacks at a similar frequency in DFS. From my observations, the same can be said for the field’s inclusion of running backs in primary stacks in best ball.
Taking this exploit one step further, let us consider the injury rates at the four major positions at the NFL level. Running back continues to see the highest injury rate of the four major positions, meaning we are likely to see numerous “backup” running backs in the mix for Week 17 (when all the money is won in these best ball contests).
This gives us an opportunity to layer the leverage gained by including a team’s second running back in a primary team stack in best ball. Furthermore, the work done around the industry over the previous five years or so has yielded a blueprint for running back production. The two biggest predictive metrics for running back production in fantasy football are volume (more specifically, weighted opportunities) and touchdowns. This means we can narrow down the search for difference-making stacks further by targeting backups on teams we expect to give one man the bulk of the work, that also play for teams projected to be near the top of the league in scoring.
Using these methodologies, consider the following team stacks in best ball tournaments in 2024:
Miami: Tua Tagovailoa + Tyreek Hill (or Jaylen Waddle) + Jaylen Wright
LA Rams: Matthew Stafford + Puka Nacua (or Cooper Kupp) + Blake Corum
Detroit: Jared Goff + Amon-Ra St. Brown (or Sam LaPorta or Jameson Williams) + David Montgomery
San Francisco: Brock Purdy + Deebo Samuel (or Brandon Aiyuk or George Kittle) + Jordan Mason
Buffalo: Josh Allen + Dalton Kincaid (or Curtis Samuel or Keon Coleman or Khalil Shakir) + Ray Davis
Kansas City: Patrick Mahomes + Travis Kelce (or Rashee Rice or Hollywood Brown or Xavier Worthy) + Clyde Edwards-Helaire
Baltimore: Lamar Jackson + Mark Andrews (or Zay Flowers) + Justice Hill
Cincinnati: Joe Burrow + Ja’Marr Chase (or Tee Higgins) + Zack Moss (or Chase Brown)
Hypothesis Two: The field does not utilize QB+TE stacks enough.
Another data point to come from my study of DFS rosters was the hit rates of certain roster-building techniques on the optimal roster, again over a three-year sample. What I found was that over 23% of optimal rosters during that span included a quarterback and tight end pairing, which makes sense when you consider the fact that there are so few volume tight ends in today’s NFL game.
With fewer tight ends in the league who can be counted on for consistent volume, we see an increased reliance on touchdowns to return GPP-worthy scores at the position. Furthermore, a tight end typically requires two or more touchdowns to find their way onto the optimal roster in a given week, which directly correlates to a higher single-week ceiling for his quarterback.
ADP of the elite tight ends has been more or less tethered to their quarterback if the quarterback is also considered elite (Kelce + Mahomes, Andrews + Jackson, Kincaid + Allen), losing some of the leverage gained by this stacking methodology in the process.
That said, almost every other primary tight end and quarterback pairing has an ADP split that preclude them from being paired often, unless a drafter is specifically targeting the stack. Based on my observations, the pairing frequency of all other tight end and quarterback combinations is far less than its 23% hit rate, making this an easy way to boost EV.
Some of my favorite quarterback and tight end stacks to target in best ball drafts this season are:
Philadelphia: Jalen Hurts + Dallas Goedert
Houston: C.J. Stroud + Dalton Schultz
Green Bay: Jordan Love + Luke Musgrave
Dallas: Dak Prescott + Jake Ferguson
Jacksonville: Trevor Lawrence + Evan Engram
Miami: Tua Tagovailoa + Jonnu Smith
LA Rams: Matthew Stafford + Colby Parkinson
NY Jets: Aaron Rodgers + Tyler Conklin
New England: Drake Maye + Hunter Henry
Minnesota: Sam Darnold + T.J. Hockenson
Hypothesis Three: The field does not utilize team over-stacks enough.
Team over-stacks tend to be underappreciated by the best ball community due to the law of diminishing returns, which basically states that there is a point where you no longer get the same benefit by adding additional assets to something. While that tends to be true in most cases in fantasy football, it neglects to capture bulk upside from the extremes in scoring. As in, that time the Dolphins put up 70 points, or that time the Dolphins and Ravens combined to score 80 points, or that time the Raiders hung 63 on the Chargers. You catch my drift.
We will see teams go absolutely bonkers this season – it happens every year. What if that happens in Week 17 this year? How many rosters will have exposure to that upside in the finals of major best ball tournaments? I would venture a guess that it won’t be many (if any).
This is something that is typically difficult to pull off in best ball drafts because the teams we want to use for this strategy on typically have players with ADPs near the top of drafts, making it even more valuable to us when it does happen. But we see glimpses in time where ADP shifts enough to make it happen. These are the times when we jump into action.
For example, you almost never could grab Christian McCaffrey and one of Deebo Samuel or Brandon Aiyuk in drafts. That is, until Aiyuk’s hold-in. Once Aiyuk’s ADP began to fall, you could pair him with early McCaffrey teams to play into the variance of that situation, basically making the bet that Aiyuk would eventually re-sign with the 49ers. Taking that example one step further, how many McCaffrey + Aiyuk + George Kittle teams do you think have been drafted in BBMV? Not many.
Other examples of team over-stacks to target in best ball drafts when they become available are:
Detroit: Amon-Ra St. Brown + Jahmyr Gibbs + Sam LaPorta + Jared Goff
Miami: Tyreek Hill + Jaylen Waddle + De’Von Achane + Tua Tagovailoa (yes, it happens)
LA Rams: Puka Nacua + Cooper Kupp + Matthew Stafford (requires Nacua/Kupp at the 1-2 turn)
Baltimore: Zay Flowers + Mark Andrews + Lamar Jackson (requires “reaching” on Flowers at the 2-3 turn)
Philadelphia: A.J. Brown + DeVonta Smith (or Saquon Barkley) + Jalen Hurts (requires “reaching” for Smith or Barkley at the 1-2 turn)
Houston: Houston over-stack (requires “reaching” for Nico Collins at the 1-2 turn)
Conclusion
Although the field has largely caught up to the fact that roster construction matters and that stacking and correlating (optimizing) for Week 17 matters,, there are still many techniques we can utilize to gain an edge on the field through game theoretic methodologies.
This was not meant to be an all-encompassing, definitive list on how and who to draft – use these principles to think about the game in a different way than much of the field. The example exploits laid out in this piece are exactly that, examples.
What other exploits do you see in the best ball landscape for the 2024 season? I would love to hear them!
