Q: What type of discounting is responsible for literally every error ever made in the history of dynasty fantasy football leagues?
A: Hyperbolic discounting!
Now that I’ve made it abundantly clear why I’m a fantasy football writer and not a comedian, let’s talk about one of my favorite cognitive biases.
The Rise and Fall of Draft Picks
Anyone who has been in dynasty leagues for a while has probably observed certain fluctuations in the price of rookie draft picks throughout the season. These fluctuations are sinusoidal. They are also predictable and reliable. We are now reaching the point of the year where future pick values are hitting their nadir, and if this column was devoted to giving you actionable advice, I would probably be suggesting you run buy some right about now.
Instead, I want to look at some theories about why these fluctuations happen in the first place.
From an individual standpoint, it makes perfect sense that the amount of value I place on individual draft picks will change over time. If I open the season 4-0, I will naturally place much less value on my own 2015 picks than I would if I opened 0-4, because the picks I am in line for will be intrinsically less valuable.
From a league-wide standpoint, these individual changes shouldn’t impact the total market. Wins and losses are a zero-sum game, so if I get 4 wins, that means others in my league have accrued 4 matching losses. As my expectations for my own draft picks fall, their expectations for their own picks should rise commensurately.
We established last week that owners are irrationally exuberant, and that this causes them to undervalue future draft picks. The problem is that, while this explains why picks are undervalued in general, it doesn’t explain why they are undervalued by different amounts at different times of the year.
It’s true that, early in the season, more teams are irrationally exuberant. It’s hard for an owner to feel good about his championship odds once he’s been mathematically eliminated from the playoffs. But the teams that remain irrationally exuberant late in the year become even more irrationally exuberant, which partially offsets the shift.
Instead, I have several, (scientifically supported), ideas that help explain the ebb and flow of pick values throughout the year, and I’ll get to them all eventually. For today, as I clumsily alluded to in my opening attempt at humor, I want to introduce the concept of hyperbolic discounting.
The Unexaggerated Truth about Hyperbolic Discounting
The “hyperbolic” in “hyperbolic discounting” refers, not to hyperbole or other gross exaggeration, but to the humble hyperbola. So what is hyperbolic discounting?
Imagine I was offered a choice between receiving $100 today or $250 ten days from now. Imagine I also had access to an amazing investment opportunity that guaranteed me a 10% return compounded daily. If I opt for the $100 today, I could invest it, and after ten days it would be worth $259. $259 is greater than $250, so my strictly rational self should prefer the immediate payoff.
Let’s say my investment opportunity wasn’t expected to pay off quite as well, and I was only anticipating an 8% return each day, (still one heck of an investment opportunity!) In that case, if I invested the $100 today, I would only expect to have $216 at the end of the ten days. This is less than the promised $250, so I would prefer the future payoff.
So far, so good. These are perfect examples of “exponential discounting”. The problem is that, in real-world situations, we often find that our discounting models do not behave exponentially. Instead, we find that the initial discount is too steep- or, rather, that it is “hyperbolic” instead of “exponential”.
Consider the following: a man comes up to you and tells you he will either give you $50 today, or he will give you $100 one year from now. In this situation, most people opt for the immediate $50 reward. Now imagine the same man tells you he will either give you $50 in five years, or $100 in six years. This is the exact same scenario (wait a year to receive double the reward), but in this case, most people opt for the $100 payoff.
Exponential discounting cannot explain this discrepancy, but hyperbolic discounting can. The initial discount from right now to a point a short time in the future is too steep. Later discounts from a point some time in the future to another point even further in the future become even shallower in response.
In fact, this is the key characteristic distinguishing (rational) exponential discounting from (irrational) hyperbolic discounting. Exponential discounting models produce consistent preferences across any range of time spans. Hyperbolic discounting models, on the other hand, are characterized by preference reversals. If presented with a choice, the hyperbolic discounter would prefer one side. If presented with an identical choice over a different time scale, the hyperbolic discounter would prefer the other side.
These preference reversals provide plenty of opportunities for profit. A trade that would be laughed at in May becomes a trade that is eagerly accepted in October. In the most extreme examples, these preference reversals can be exploited on both sides for even greater returns. One could buy first round picks in October when their value is lowest, then sell them right back again in May when their value is highest— often to the same owner who sold them in the first place!
Explaining the Ebb and Flow
“But Adam!”, some among you might interject, “hyperbolic discounting might explain why future picks are undervalued, but how does it explain why the amount they are undervalued by fluctuates throughout the year?”
I’m thankful that I have such astute readers, (who are totally not just figments of my imagination I invented to serve as rhetorical tools designed to provide transitions and advance my thesis). You see, the value of future picks changes throughout the year because the manner in which various assets are perceived changes throughout the year.
In May of 2014, it would have been hard to convince an owner to trade a 2015 first rounder for an expiring asset that was expected to provide some short-term value (such as Pierre Thomas). This is because, in May of 2014, both of those items would be considered “future assets”. The future pick is something that will be valuable in a year, while the expiring asset is something that will put points in the lineup in six months.
There is typically little profit to be made in trading one future asset for another. Remember, the primary feature of hyperbolic discounting is that the initial discount is too steep. Relatedly, one of the secondary features is that, further along the timescale, the discounts become too shallow.
In an extreme example, imagine approaching one of your league mates and trying to trade a 2025 first rounder for a 2026 first rounder. How much extra do you think you would be able to get in such a trade? If your league mate is like most, he’d be unwilling to give much at all to move his gains from eleven years in the future to ten years in the future.
Contrast this with the regular trades involving a team trading a current pick for a pick one year in the future. Typically, these trades command quite the premium, indeed.
Indeed, to take advantage of hyperbolic discounting, one needs to be able to trade assets that are immediately valuable, (the more immediate, the better), for assets that are immediately worthless, but which hold future value. And that particular mix occurs most prominently during the season itself.
Further, to maximize returns, one should seek to buy future first rounders early in the season, before any teams start getting eliminated from the playoffs. This is because once teams get eliminated, expiring assets no longer hold any immediate value. (It’s also because the most valuable picks are from teams that miss the playoffs, and those teams typically aren’t interested in selling once they know for sure they’re going to miss the playoffs.)
Key Points to Remember
Valuing current assets more than future assets is not, in itself, irrational. Current assets truly are more valuable. A 2015 first rounder is absolutely worth more than a 2025 first rounder.
The irrational part is when those preferences become “time inconsistent”. Time inconsistency means that a decision made today might be different from one that would have been made a month ago. In other words, the decisions are subject to “preference reversal”.
Few owners would trade a 2021 first and a 2020 second for a 2020 first today. At the same time, plenty of owners will be happy to make that trade… in 2020. That is an example of a preference reversal. Their preference is not consistent over time.
Savvy owners are able to identify when those preference reversals occur and exploit them for a profit. Much ink is devoted in fantasy football to the concept of “buying low” and “selling high”, but in practice, it’s very difficult to determine when the low point and high point have been reached.
Hyperbolic discounting and other related time-inconsistent biases solve that problem for us, offering a clear and predictable low and high point. The only question left is what we choose to do with that knowledge.
One Final Thought That Likely Offers Little Comfort
Hyperbolic discounting is not strictly a human problem, either. These same results have been replicated in studies of monkeys, rats, and pigeons, too. So when you get right down to it, we’re really not any more illogical than pigeons.
So that’s something to hang our hats on.
