This is the 148th installment of The Labyrinthian, a series dedicated to exploring random fields of knowledge in order to give you unordinary theoretical, philosophical, strategic, and/or often rambling guidance on daily fantasy sports. Consult the introductory piece to the series for further explanation.
Over a year ago I wrote a couple of pieces that apply paradoxes, problems, riddles, etc., to DFS:
- The Monty Hall Problem, Anchoring, Late Swap, and The Panopticon
- Pearl Jam, The Missing Dollar Riddle, and The Double-Counting Error
Those Labyrinthian titles are sooooooo last year, amirite? At least I no longer write fantasy articles about Pearl Jam (cough, cough).
Anyway, I’m returning to my paradoxical roots. This piece is about the ancient conundrum of Achilles and the Tortoise — and DFS.
Zeno of Elea
Unlike FantasyLabs Co-Founder Jonathan Bales, I didn’t major in Philosophy in college. I figured it was better to major in Biology, Chemistry, and English and — instead of going to medical school — enroll in a Ph.D. program in literature, get to the dissertation stage, and then drop out so I could write about fantasy sports and eventually work for Bales.
Anyway, I didn’t major in Philosophy in college, so until I recently read the book Paradoxes: Adventures in the Impossible (#WorkExpense) I had no idea who Zeno of Elea was.
It turns out he was a guy from Elea.
Born 490 BCE, Zeno was a philosopher and disciple/possible lover of the slightly more famous philosopher Parmenides, with whom around 450 BCE he traveled to Athens, where he met Socrates. Like a lot of bad-ass ancient philosophers, Zeno was killed by people in power. Following in Parmenides’ footsteps, Zeno (more or less?) believed that the universe is a unified and changeless entity and that time and motion are illusions perpetrated by our deceptive senses.
I think Zeno’s ideas are pseudo-intellectual bullsh*t, but I’m probably never going to hang out with Socrates and get executed by a tyrant, so what do I know?
Still. one of his paradoxes is worth considering, not because it’s illuminating but because a philosopher in the 1960s responded to it in an instructive way.
The paradox is typically called “Achilles and the Tortoise.”
Achilles and the Tortoise
Little of Zeno’s writings have survived, so many of his paradoxes come to us through Aristotle, who attributed them to Zeno. Here’s a loose paraphrase of Achilles and the Tortoise (per Aristotle):
There’s a race between Achilles and a tortoise. In order to make the race fairer, Achilles gives the tortoise a significant head start since it’s a long race. While it seems inevitable that Achilles will win, think about this a little more: In order to win the race, Achilles first must pass the tortoise, and in order to pass the tortoise he must catch up to it — and Achilles will never be able catch up to it. Why can’t Achilles, one of the greatest athletes of all time, catch up to the tortoise? Achilles needs time to catch up to where the tortoise is, and in the time it will take Achilles to reach that point the tortoise will have moved to a point farther along the course — and in the time it will take Achilles to reach that new point the tortoise will have moved to yet another point farther along the course — and on and on the process goes ad nauseam. So, as you see, Achilles cannot catch up to the tortoise, and so he won’t win the race.
You don’t have to tell me: This paradox is f*cking stupid.
Achilles at the Gun Range
A lot of thinkers over the last 2,500 years have taken Zeno to task. One of them is the philosopher Alan R. White, who in 1963 wrote this exercise (which I’m paraphrasing):
Achilles and Zeno are at the gun range. Achilles is shooting at the center of the target, but he always misses his mark because the target is continuously moving to the right. Zeno tells Achilles to continue to aim at where the target currently is, and Achilles continues to miss, no matter what type of gun or ammunition he uses. After a while, Socrates shows up, sees what’s happening, and tells Achilles to aim slightly to the right, where the target will be whenever the bullet reaches it. Achilles takes his advice and hits his mark on his next shot, just like Tom’s daughter.
We can get to some DFS now.
Mathematics > Philosophy
Clearly, Zeno was more of a philosopher and less of a mathematician. If he had put numbers to his paradox, then it wouldn’t have been a paradox. It would’ve been a simple f*cking problem that anyone with a basic understanding of math would’ve been able to solve. For instance:
- Achilles can run 10 miles in the time it takes the tortoise to run/crawl one mile.
- Achilles gives the tortoise a one-mile head start.
- The raise is 26.2 miles.
Question: Will Achilles win the race?
Answer: Are you a moron? — or just a philosopher named Zeno?
Achilles will pass the tortoise before he hits even the two-mile mark. How do I know this? Because I’ve put numbers to the philosophical problem.
In philosophy, life, and DFS, it’s easy to get facts confused when you don’t consult the data. Whenever you have a DFS idea, go to the numbers. Use the Labs Tools to find out what the numbers say. Use our Trends tool — preferably the right way — to discover quantifiable reality (via our Plus/Minus and Consistency Rating metrics). Use our Player Models to see for yourself how all of the numbers fit together.
When we fail to attach numbers to our thoughts, we risk reaching illogical (or at least impractical) conclusions that can lose us money as DFS players. Of course, as Zeno might say, it’s impossible to lose money — because it doesn’t exist.
That makes sense from a certain perspective.
The perspective of a loser.
The Moving Target of DFS
Like Achilles at the gun range, you are firing at a moving target. Life moves. The world moves. The universe moves. The target — and the target is a metaphor for basically everything — is always moving.
In DFS, the target is game theory. How sharp players approach contests is always changing — but the one constant is this: They are ahead of the change. They anticipate it. They herald it. They create it. In effect, they are the change. If you look at the members of Team FantasyLabs, what you’ll see are players who lead the industry by firing bullets where the target isn’t.
Last year, Bryan Mears wrote a piece about Heisenberg’s Uncertainty Principle and DFS strategy. For those who never took physics: Heisenberg’s principle states that there’s a limit to the precision with which one can know certain information about the physical properties of a particle, such as its position and momentum. Bryan applies this concept to DFS:
So what’s the position and momentum that’s impossible to define in DFS? I believe that it’s game theory. Finding the ‘edge’ is much like locating our physics particle: The moment you define it, it’s probably gone. There is no general ‘DFS Tournament Strategy’ in any sport. There are general heuristics — you want to target high-upside, under-rostered players who give you the best chance to win a tournament — but the actual process of making that happen constantly changes, whether you are utilizing stacks, paying up for a specific position that is undervalued in tournaments, and so on. It may seem silly to try to figure out where strategy is going (instead of where it is) yet I think that doing so is precisely how to be a profitable DFS player. It’s much better to be ahead of game theory than behind it, and, as we already said, it’s impossible to be on it.
Why is it that DFS game theory must change? For one, the marketplace of industry participants is always changing. With new blood come new ideas and strategies. On top of that, the industry itself is still relatively young. It’s evolving and growing. FanDuel and DraftKings are still in the process of tweaking their contests. They change rules. They create new formats — such as FanDuel’s Mixup games. The platforms themselves are maturing. Also — and this is a big factor — salaries change. Salary dynamics change, because teams, players, and slates change.
Still, even if all of those factors were static, game theory would continue to evolve in the DFS marketplace, because life isn’t a play in which Rosencrantz and Guildenstern are the would-be stars. People develop, learn, and adapt — or they die and quietly exit the market.
Achilles the DFS Warrior
DFS players can never know exactly where game theory is headed and how quickly it will get there. At the same time, it’s possible to get a sense of game theory’s present momentum and future position if you . . .
- Review tournament ownership patterns across various buy-in levels with our DFS Ownership Dashboard.
- Watch the model previews and lineup reviews on our Premium Content Portal, where players like Bales, Peter Jennings (CSURAM88), Adam Levitan, and Kevin McClelland (The Sports Geek) share their thoughts.
This week is the U.S. Open. It’s a big deal. FanDuel and DraftKings have some great guaranteed prize pools available, and we have a U.S. Open Dashboard so you can access in one place all our content for the event.
I have no idea which strategies will put DFS players in position to take down GPPs this weekend — listen to this week’s Daily Fantasy Flex to hear what CSURAM88, Colin Davy, and Bryan think — but I’m sure of this:
The people who win U.S. Open GPPs won’t be aiming directly at the cup.
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The Labyrinthian: 2017.53, 148
Previous installments can be accessed via my author page or the series archive.
