Dynasty, in Theory: The Difference Between Contending and Rebuilding

Using game theory and economics to explain the different preferences of rebuilding and contending teams.

What is the difference in preferences between a rebuilding team and a contending team?

I don’t mean this rhetorically, or as the opening to some sort of Socratic debate where I convince you through a series of probing questions that there’s no difference at all. Clearly there is a difference between how rebuilding teams and contending teams value players. But precisely what is the difference? And what accounts for it?

I wrote two years ago that dynasty is essentially a game of limited resources. The key to winning was growing your resource pile bigger than everyone else’s. But beyond that, the key to winning was concentrating your resources in the right place.

In game theory, there’s something called a “Blotto game”, which like dynasty is a game where players are tasked with distributing limited resources to achieve victory. As a simple example of a Blotto game, imagine that you and a partner are generals, and you each have five soldiers. You will dispatch your five soldiers to three different battlefields. Whoever sends more soldiers to a battlefield wins it, and whoever wins more battlefields wins the war.

One could assemble an overwhelming force, sending all five soldiers to a single battlefield. Doing so, however, would all-but assure defeat, as the other two battlefields could be stolen with just a single soldier.

One general might decide to send three soldiers to one location, hoping to win by superior force, while sending one soldier to each of the other two locations, hoping to steal them while they’re undefended. Another might counter by deploying 2-2-1. The 2-2-1 owner would be guaranteed a draw at worst (with a guaranteed loss against the other owner’s “3” territory and a guaranteed win against one of the other owners “1” territories), but would occasionally win, too. Therefore, 2-2-1 would be the superior strategy.

To win a Blotto game, one must deploy the smallest number of resources that is still greater than the number that his or her opponent deployed. And while it may seem like a silly kids’ game like Tic-Tac-Toe, Blotto games are actually very powerful tools with a broad range of applications.

Football play-calling, for instance, is an example of a Blotto game. The offense has five eligible receivers to deploy. The defense has 7 defenders to drop into coverage. Good offensive play design should get one of those receivers into an area not occupied by a defender. Good defensive play design should prevent that from happening.

Dynasty leagues, as I mentioned, are another powerful example of a Blotto game, with every “battlefield” being a season. Except instead of five soldiers, teams have 20+ rostered players of varying value. And instead of two generals competing over three battlefields, you have ten, twelve, fourteen, or even more owners competing over potentially limitless battlefields.

Winning the Blotto Game

The simplest way for owners to win the Blotto game is to have more resources than the competition. For instance, in our three-battlefields hypothetical, if one general had six soldiers and the other had only three, the first general could guarantee a victory by sending two soldiers to each territory. And if one general managed to get twelve soldiers while the other was stuck at three, he could deploy four soldiers to all three locations and guarantee a clean sweep of all battlefields.

In dynasty terms, this means increasing the total value of the assets on your roster. If you could trade one first rounder for two others, then your pool of resources just got bigger, and you would be closer to your goal of sweeping all battlefields.

But until an owner accumulates an overwhelming advantage, the fate of the battlefields will be decided by how smartly owners deploy their resources. And this, at its heart, is the difference between a contending team and a rebuilding team.

A contending team recognizes an advantage at the current battlefield and seeks to reinforce it to guarantee the day. A rebuilding team recognizes it is unlikely to win the current field and withdraws, deploying its soldiers elsewhere and hoping to steal a different battlefield while everyone is contending over this one.

Or, to step out of our Blotto game framework, contenders value this year more than future years, while rebuilders value future years more than this year.

So tell me something I don’t know.

My readers are pretty sharp guys and gals, so I’m sure you realized this already. So why am I going to the trouble of spelling it out like this? Let me answer that with another story.

In some of the poorest places in the world, electricity and even windows are a luxury. Housing is packed so closely together that, during the day, no light can enter, leaving dwellings as dark at noon as they are at midnight.

Over the last decade, an ingenious solution has been devised to this problem. Residents drill a hole in the roof, plug it with a 2-liter bottle, and fill the bottle with purified water and a small amount of bleach, (to prevent algae growth). The sunlight shines down on the bottle, which then refracts it 360 degrees, providing for no additional cost as much light as a 55-watt bulb.

This is a really cool story about the triumph of human ingenuity and the small ways we can find to make others’ lives better. But buried within that story is a parable. 2-liter bottles have been around for decades. Water has been around for eons. Billions of humans have existed on this earth alongside both and never once thought of combining them to make a light bulb.

Creating the solution took one clever individual looking at bottles and water as more than just bottles and water, but instead as unique components with a series of properties. Bottles aren’t just bottles, they’re impermeable containers capable of preventing the passage of a liquid. Water isn’t just a drink or something to wash with, it is a clear liquid capable of holding the shape of its container and refracting light. Combined, they provided an impermeable barrier capable of dispersing light without letting in rain.

When faced with a tough problem, it’s important to know what tools you have available to you. But it’s even more important to look beyond our preconceived notion of those tools and take a good stock of their fundamental properties.

Rebuilders value future years more. Contenders value current years more. This is an obvious and fundamental difference between the two types of teams. But by expressing it this simply, we discover an elegant answer to a pernicious problem in dynasty: how do we compare values for rebuilders to values for contenders?

Marshawn Lynch is more valuable to a contender than a future 1st. A future 1st is more valuable to a rebuilder than Marshawn Lynch. But is trading Marshawn Lynch for a future 1st a “fair” trade? What if the rebuilder sees only a slight gain, while the contender sees a huge gain, or vice versa? Should one side or the other be adding more assets to the trade to achieve balance?

A Tool To Answer The Question

In economics, there is a principle called “time preference” or “time discounting”. In a nutshell, it's the idea that an asset today is worth more than an equivalent asset a year from now. Or, perhaps, that a bird already in the hand is worth more than two otherwise equivalent birds that still reside in the bush.

On the whole, it makes sense for dynasty leagues to have some degree of time preference. No dynasty team would trade its 2017 first rounder for a 2027 first rounder straight up. A lot could happen in the intervening decade; the league could fold or the owner could quit, for instance. The sooner an asset produces, the more valuable that production is.

But there’s nothing that suggests all owners should use an equivalent time discount. A balanced dynasty team might estimate that each future season is worth 10% less than the season before. A contender might put that estimate at 25%. A rebuilder might not have any time discount; if his team is bad enough, he might even have a negative time discount, valuing each season as 10% more valuable than the season before.

To answer the initial question, then, contending teams and rebuilding teams are both playing a resource allocation game, but they’re trying to allocate their resources to different “battlefields”. Differences in their preferences are entirely explained by how much they value each battlefield relative to the others.

Or, to put it more succinctly, the difference between rebuilding teams and contending teams is that contending teams have a steeper time discount.

Okay, but what does it MEAN?

So let’s say you’re on the same page with me so far. The difference between contention and rebuilding is simply one of time preference. What does this mean for how we run our dynasty teams?

By itself, this idea won’t change how you do anything. The stated goal of “Dynasty, in Theory” is exploring abstract concepts with little direct practical application. This idea that the only difference between how teams value assets boils down to differences in time preference certainly fits that bill.

If we had some sort of formula to estimate a player’s value over various seasons, however, suddenly the concept of variable time discounts would be quite powerful, indeed. One could create a single global dynasty value, and then merely alter the time discounts one way or the other to make it broadly applicable to teams in every stage of the contention/rebuild cycle.

In fact, one could even place a thumb on the scale to differentiate between types of contenders. Perhaps a heavy contender has a 30% time discount, while a borderline contender is at 15%. Each different discount would alter the global rankings, resulting in different player values perfectly customized to a team's preferences.

But again, without some sort of global dynasty values, this is all just interesting theory. If only someone had a way to generate dynasty values, though, the practical applications would be limitless. It’s a shame that there’s not anything like that out there…

Yet.

Follow @AdamHarstad


More articles from Adam Harstad

See all

More articles on: Dynasty

See all