Dynasty, in Theory: the Law of Total Expectation

There's a lot of strong dynasty analysis out there, especially when compared to five or ten years ago. But most of it is so dang practical—Player X is undervalued, Player Y's workload is troubling, the market at this position is irrational, and take this specific action to win your league. Dynasty, in Theory is meant as a corrective, offering insights and takeaways into the strategic and structural nature of the game that might not lead to an immediate benefit but which should help us become better players over time.

Overview of an inefficiency

Two weeks ago, I discussed Platonic realism—the theory that concepts exist in their purest forms—and exhorted us to imagine what the Platonic ideal of "player value" might look like. Last week, I examined how that ideal would move over time and contrasted that with how actual value moves. If we had perfect information, every big game a player had would cause their value to drop, as that represents production we could no longer stand to benefit from. In the real world, though, player values rise rather than fall after a big game.

I offered an explanation for this discrepancy: we don't operate in a world of perfect information, and we largely don't know how good players really are. When someone like Oronde Gadsden has a big game, it might mean there are fewer career points left in front of him, but it causes us to revise our opinion of how good he is (and therefore how large the pool of available points truly is), and the latter effect largely swamps the former. Players move as we reevaluate who they are, and (especially for younger players), the "fewer career points remaining" effect is treated as a rounding error.

(Which, in fairness, it largely is. Though it must be noted that the market more than makes up for lost time once players reach an age that is considered concerning.)

That is all perfectly rational for players with a large degree of uncertainty, such as rookies or players in new circumstances. But I suggested that the better we know who a player is, the more of a market inefficiency this represents. We already think Patrick Mahomes II is a multiple-MVP in his prime, a slam-dunk first-ballot Hall of Famer with plenty of career left in front of him, so what new information are we really gaining from his latest 4-touchdown performance?

Because of this inefficiency, it is often possible to acquire a young, proven player for cost N, start them for several years and benefit from their production, then sell them at the end for a cost approximately equal to N, making all the intervening production functionally free.

A clever rebuttal

A reader reached out to me to push back on this framing. He suggested that when Patrick Mahomes II has a big game, we are still gaining new information; many star players decline before we expect them to, and every big game suggests the player in question is less likely to be among them.

Russell Wilson, for instance, was a Top 12 fantasy quarterback in each of his first nine seasons. His (lowercase-v) value finally peaked in 2020, at age 32, when a hot start to the season pushed him to the #2 or #3 quarterback in dynasty leagues. (Let the record show that I found this a ridiculous valuation for a mobile quarterback who was already 32—the perfect example of a player whose lowercase-v value was somehow rising, even in the absence of any significant new information, while their capital-V Value was drying up.)

In the last few days I have learned that some are valuing Russell Wilson above Lamar Jackson in dynasty. In light of this new evidence, I am regretfully forced to retire my “Russell Wilson will always be underrated in dynasty” take.

I appreciate your support in this trying time.

— Adam Harstad (@AdamHarstad) October 16, 2020

Wilson faded down the stretch, finishing as the QB15 over the last third of the season and never again cracking the Top 12. Dak Prescott is the same age, so big games from Prescott serve to increase his value because they reassure us he is not yet mirroring Wilson's decline. 

Odell Beckham Jr began his career as impressively as Ja'Marr Chase and Justin Jefferson, but because of injuries and unexpected decline, he never finished higher than WR16 after Age 24. Chase and Jefferson are now the age when Beckham declined, so production is valuable insofar as it signals that they will not likewise leave us in a lurch.

This is a great point, and it's one I'm sympathetic to; I've been writing for a decade now that we underrate the possibility of careers ending earlier than expected. And I love when smart people push back on my arguments, because it's the most efficient way to realize I'm wrong and correct my beliefs. If this was how the market was operating, that would be wisdom, not inefficiency. But I don't think that's the case.

To see why, we need to discuss the Law of Total Expectation, which is the entire basis for the argument.

What do (lowercase-v) values represent?