Dynasty, in Theory: What Happens When You Assume?

Little changes in our underlying assumptions can result in big changes in our final results.

Brian Malone is a calamitously clever fantasy football analyst. He’s written smart, thoroughly-researched pieces for a whole passel of sites— DynastyLeagueFootball.com, Rotoviz.com, TwoQBs.com, FootballPerspective.com— and is always active on Twitter at @BrianMaloneFF.

I’ve used him as a sounding board for most of my ideas over the years. He’s extremely analytical and unafraid to probe thought processes for weaknesses. (He’s also one of the participants in the Quarterback Streaming Challenge. I did promise them anonymity, but Brian outed himself first.)

Most importantly, I consider him a friend.

But dynasty owners, fantasy footballers, like-minded travelers, lend me your ears; I come to bury Brian Malone, not to praise him.

In July, reflecting on Calvin Johnson’s retirement and the seeming trend of players walking away early citing— among other things— concerns about brain damage, Brian wondered whether this was going to become a new trend. If so, what kind of impact would it have on dynasty leagues?

To answer that question, Brian referred to my research on the subject of player aging, which is always a cool thing to do. Drawing upon my player mortality tables, Brian concluded that a trend towards early retirement would make older players more valuable, not less. To quote the nut graf:

Most owners’ gut reaction (if any) to the recent spate of retirements was to avoid older players. If Johnson can retire at 30, that means Demaryius Thomas can too. So avoid the fogeys and draft potential, right?

Wrong. To show why, I’m borrowing from Adam Harstad’s argument that we should think about player age in terms of mortality tables. His contention is that each additional year represents a probability that a player’s production will drop (either dramatically or gradually) out of fantasy relevance. Early retirements create more uncertainty at every age, not just at age 29. That increased “career mortality” risk throughout a player’s career means immediate production becomes all the more valuable because it’s the easiest to predict.

Again, it’s a really cool feeling when my research that I’m pretty proud of gets cited by someone who I genuinely admire. I was a big fan of everything about that piece except for just one small detail: Brian Malone is completely wrong.

Well, he’s probably completely wrong, at any rate. You see, Brian’s conclusion is based on the idea that if you take my calculated “death rates” and add a flat “retirement risk” on top— say, an additional 2% at every age— older players lose less value relative to younger players. And he’s not wrong about that.

But the important question is whether it’s at all reasonable to assume that the additional retirement risk would be flat at every age. Chris Borland notwithstanding, I would instead assume that a 22-year-old 2nd-year player would be less likely to start pondering the cost to his future than, say, a 28-year-old veteran who had been in the league a while and already gotten a big signing bonus on a second contract.

And if you assume, as I do, that this new retirement risk would not be flat, but would rather increase with age, then the results completely flip; suddenly the younger players are gaining value relative to the older ones, just like we’d intuitively expect.

When I discussed this with Brian on Twitter, he agreed but added that being a heavy win-now team, (characterized by a very high time discount), would shift things back to the older players. Which I wholeheartedly agreed with... until I ran the numbers. I do so hate it when reality gets in the way of a perfectly good theory.

You see, counterintuitively enough, it’s possible to reach a point where raising our time discount actually makes us prefer the younger players again. After all, if older players are at a much higher risk to retire this year or next, and we’re wildly impatient and cannot stand the thought of losing any value at all in the next two years, it would make sense to favor the young assets who we know are going to stick around in the short term.

Okay, so a trend towards early retirement makes older players more valuable, except that it actually probably makes younger players more valuable. And being in a win-now window shifts your preference towards the old guys, unless it actually shifts them towards the young guys, instead. I’m glad we’ve got all of that settled!

So... what does happen?

The point here isn’t that Brian Malone was wrong. I mean, I still can’t prove that he was. (But he was.) The point is that there are all of these assumptions underpinning all of our conclusions, and minor tweaks to those assumptions can result in categorical changes to those conclusions.

In fantasy football, you can’t get around making assumptions. Is the recent spate of retirements a fluke or a trend? Will heightened retirement risk affect all players equally, or some players more than others? If the latter, who and how much more?

We’re dealing with questions we cannot possibly know the answers to, so we’re forced to predict, or prognosticate, or divine, to forecast, to envisage. These are all just fancy words for guessing that we in the fantasy football industry use to make ourselves feel more important.

And our guesses are going to be shaped by our underlying assumptions and beliefs. But most of the time, those beliefs are invisible. They go unmentioned in our race to the bottom line.

What is the takeaway, here? There are a couple for me. The first is just that this is such a succinct illustration of the fact that most disagreements arise out of the things that went unsaid.

The second is a reminder that I need to do a better job of expressing my own assumptions going forward, because it matters. To that end, I built a fun interactive for you to download and play with, if you’re so inclined, to see just what kind of difference assumptions can make in this problem of increased retirement risk.

The sheet has two tabs, both of which are identical. Each tab has three variables for you to input. The first is your personal time discount rate— e.g. your answer to the question “how much less valuable is next year relative to this year”. This should be expressed as a decimal between zero and 1. So, for instance, if you think next year is 25% less valuable than this year, your time discount is 0.25.

The second variable is flat retirement risk. This is the base increase in retirement risk that applies to all players. Let’s say that because of concussion concerns, every player has a 1% chance of retiring in any given year. (This flat risk is what Brian based his conclusions on.)

The final variable is the accelerating retirement risk. This is how much more likely a player is to retire with every passing year. If you think a 30-year-old is 5% more likely to retire than a 25-year-old, your accelerating risk would be 1%, (or the amount that the risk rose per year over that five-year span).

Once your variables are entered, the worksheet will calculate how this impacts expected career lengths. The “before” column indicates how much longer a player’s expected remaining career is than a comparable 26-year-old’s before retirement adjustments are applied. So, for example, a 21-year-old has a value of “1.5” here. This means we expect him to play 1.5 times as many games in the rest of his career. A 31-year-old has a “0.49”, which means his remaining career should be about half as long as a 26-year-old.

(Please note that these ratios include the time discount; the 21-year-old’s career will be more than 1.5 times as long, but some of that career will be so far in the future that, thanks to time discounting, we don’t value it very highly at all in the present.)

The “after” column shows how these ratios change after our new retirement adjustments are applied, and the “diff.” column shows the difference. A positive difference means that we expect that player’s career to be longer relative to a 26-year-old’s. (Remember, all careers are getting shorter because of the retirement risk, but some players’ careers are getting more shorter than others’.)

I’ve set up conditional formatting to make this easy to read. If the squares turn green, that means under your assumptions players that age became relatively more valuable. (The greener the square, the bigger the boost.) On the other hand, red squares indicate players became relatively less valuable.

And, as I said, the two tabs are identical. This way you can set up two different sets of assumptions and quickly flip back and forth between them to see how things change.

If you like the interactive and want to see me do more things like this in the future, be sure to let me know. Even if you don’t care for the interactive, please know that I’m going to work hard to make my assumptions this clear into the future.

After all, I’m not above getting the math wrong from time to time, but if my outputs are bad, it’s probably much more likely to be the result of faulty inputs than of flaws in my process.

Or, at least, so I assume.

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