I’m fond of saying that thought experiments are my favorite kinds of experiments, because they’re basically like science without all of that messy gathering and analyzing data nonsense. Obviously this quip is meant humorously, but my love of thought experiments is completely serious.
You might think that, with no real work required, thought experiments would be easy. But the good ones are hard, sometimes crushingly so. Thinking rigorously about a subject can be difficult, overcoming your innate biases is daunting, and few things are more painful than facing your own errors and shortcomings. But this is what makes them so valuable.
Last week, I used my friend Brian Malone as a bit of a punching bag to prove a point, but a big reason why I respect Malone so much is the he approaches fantasy football with the same level of intellectual rigor that I aspire to. So when a thought experiment I was grappling with kept ruining my day, I decided it would be fun to toss it to him and completely wreck his day, too.
The experiment is simple. I asked him to complete two very simple statements.
1. In a typical year, I value a perfectly random 1st round rookie pick the same as __ perfectly random 2nds.
2. I would value a perfectly random 2nd in 2017 the same as a perfectly random 1st in 20__.
And here was his response:
@AdamHarstad 1st = 3x 2nd. 2017 2nd = ... I see what you've done here.
— Brian Malone (@BrianMaloneFF) September 15, 2016
So what’s going on here? Brian, like myself, believes in the importance of using something called “time discounting” to reduce the value of future production. Basically, it’s the idea that points next year are less valuable than points this year.
Why would this be the case? For one thing, dynasty leagues are not permanent. Sometimes they fold. And even if they don’t fold, there’s no guarantees that you won’t leave. Even if you have no intention of leaving today, things can happen— births, deaths, marriage, divorce, promotions, or any number of other things that can impact our free time and our desire.
Heck, there’s no guarantee there will even still be football in five years. It’s incredibly likely there will be, but who knows, maybe former players allege in a lawsuit that the NFL covered up the risks of brain injury and the league is forced to settle for such a large sum of money that it goes bankrupt. Again, the chances of this are exceedingly small, but they are not zero.
As a result, the further out in the future production is, the less likely it is that you will actually benefit from that production.
Even if there was no risk of your fantasy league folding or you leaving, I would contend that the value of winning championships is your ability to enjoy them afterwards. A championship this year is better than a championship in thirty years because you have thirty years more to enjoy it. And if you play for money, a big payout today is better than a big payout several years down the road because you can invest it and earn compound interest on your winnings.
Everyone already time-discounts intuitively. If you think you don’t, ask yourself: would you trade your first rounder in 2019 for a first and a second in 2073? If you answered no, you time discount. The size of the time discount can vary, but the appropriateness of having one in the first place does not.
This thought experiment is insidious because it’s asking you to give an explicit value on two factors, but those explicit values can be combined to give an implicit value on a third factor— namely, what kind of implicit time discount you’re using.
Let’s say that I say a 1st rounder is worth 2 second-rounders, and I’d trade a 2nd-rounder in 2017 for a 1st rounder in 2018. What I’m saying is that I would trade something 50% as valuable in two years for something 100% as valuable in one year, meaning the value decreased by 50% in just one year. That’s a 50% time discount.
In the past, I have operated under the belief that a small time discount was most appropriate. Specifically, I advocated for a 10% time discount. Brian has likewise advocated for a 10% time discount. But his intuitive fill-in-the-blanks on my two statements were that a 1st was worth three 2nds and a 2017 2nd was worth a 2020 1st.
Those two statements imply a 30.7% time discount. (A quick aside for those interested in the math: The value of a 2nd relative to a first equals one minus your time discount raised to the number of years you would move back to move from the 2nd to the 1st. Once we know two of the three terms, we can solve for the third.)
This 30% implied time discount was a far cry from his stated preference of 10%. And the thought experiment was bedeviling me for exactly the same reason— I had that a 1st was worth 2.5 2nds and a 2017 2nd was worth a 2020 1st, which implies a 26% time discount, despite my stated preference for 10%. In short, I was simultaneously holding three positions that were completely irreconcilable.
So, what does one do when three key beliefs are completely irreconcilable? The only option is to change one, two, or even all three of them so that they are consistent and compatible. (This is not entirely true; another option would be to continue on with three incompatible beliefs and just exist in a state of cognitive dissonance. For obvious reasons, this choice is sub-optimal.)
So how have I reconciled them? I’m not sure yet— I’m still in the process. It’s clear to me that maybe my time discount needs to come up, but going all the way to 25-30% produces different results which I find intuitively untenable. Perhaps the takeaway is that I’m undervaluing 2nd round picks, or that I’m not sufficiently willing to trade them for firsts over a longer timescale.
For instance, combining Brian’s belief that a first is worth three seconds with his stated preference for a 10% time discount, he should be willing to trade his second for a first rounder in 2027, which… is a long time out. Again, this is the problem with a 10% time discount. It’s just too low.
Given the popularity of last week's interactive feature, I've whipped up a quick interactive tool for you to download, (File > Save As), and enter your own stated preferences for all three values. The sheet will then automatically calculated the implied value for each calculated from your stated values for the other two. If your implied values align with your stated values, congratulations on having a consistent and coherent belief set! If they don't... welcome to Cognitive Dissonanceland, population: me.
Why Does This Matter?
One could say that nothing about our silly little hobby truly “matters” in the grand scheme of things, but in terms of producing optimal decisions to maximize long-term winning, the time discount you use can change things a great deal. Using a 30% time discount and holding all of my other assumptions constant, Antonio Brown is about 7% more valuable than DeAndre Hopkins. Using a 10% time discount and holding all else constant, DeAndre Hopkins is worth about 18% more than Antonio Brown. That’s a huge swing.
Like I said, I’m still searching for the right answer right now. But more importantly, I’m always working hard to find places like this where I was giving the wrong answer. That’s the value of thought experiments like these. They’re not just science for lazy people, they’re also an invaluable tool for holding ourselves accountable.
Not to mention that, if you know a thoughtful and analytical fantasy football player, they’re a fun way to ruin his or her day.
