There's a lot of really 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, 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. (Additionally, it serves as a vehicle for me to make jokes like "theoretically, this column will help you out".)

Let's Get Blotto

Here's a game to play with a friend. Imagine that you two are generals, and you each have four units under your command. You are tasked with conquering three battlefields. If you send more units than your opponent, you win the field. If you send fewer, you lose. If you both send the same, the field remains neutral.

The catch is that it takes time for your army to travel, so you must give your marching orders in advance before you know what your opponent is going to do. You assign your armies, your friend assigns his or hers, and then you reveal your choices and figure the results. Whoever ends the game with more captured battlefields wins.

Let's think through the strategies of this game. There are only four ways to divide your units: 4/0/0, 3/1/0, 2/1/1, and 2/2/0. Obviously, if you and your opponent each select the same strategy, the net engagement does not favor one side or the other. But we can evaluate each strategy against each other one.

4/0/0 is obviously a terrible strategy, never capable of taking more than a single battlefield. There is literally no way for it to win; the best it can hope for is a draw. It can be safely discarded.

3/1/0 will lose 33% of the time against 2/2/0 (when your 3 faces off against their 0), win 33% of the time (when your 1 faces off against their 0), and draw 33% of the time (when your 0 faces off against their 0), so neither strategy dominates the other. It will win 0% of the time against 2/1/1, lose 33% of the time, and draw 66% of the time, so it can be said that 2/1/1 "dominates" 3/1/0 (meaning 2/1/1 is strictly better and cannot lose if your opponent selects a 3/1/0 strategy). Since 3/1/0 does not dominate any other strategy and is dominated by another strategy, there is no reason to ever use it. It can be safely discarded.

2/1/1, as has been mentioned, will dominate 3/1/0. Against 2/2/0, it will win 0% of the time, lose 33% of the time, and draw 66% of the time. So 2/1/1 dominates 3/1/0, but 3/1/0 is a failed strategy and that domination is pointless. Meanwhile, it will be dominated by 2/2/0. 2/1/1 never produces a winning result against a top strategy, so it can be safely discarded.

2/2/0 dominates 4/0/0 and 2/1/1, and it breaks even against 3/1/0, (and, of course, against another 2/2/0). At best, it's a win, and at worst, it's a tie. Under the terms of the game, it is the optimal strategy.

Congratulations, we've just walked through something called a "Blotto game", which is a 2-player, zero-sum "game" that game theorists use to entertain themselves at parties. (Game theorists are a wild bunch.)

If this Blotto game seems relatively simple, that's because it is. But Blotto games can get unbelievably complex. Both sides can have a different number of units at their disposal (if one side has six units and the other has four, there's a deployment strategy that guarantees victory; I'll leave it to the reader to puzzle it out). They can gain additional points for every enemy unit they defeat, or the different battlefields can be worth a different amount. If one of the battlefields was worth five points and the others were worth one, smart players would send four units to the important field every time and damn the rest.

Demonstrating how deceptive their simplicity is, after being invented in 1921, it took nearly 100 years for Blotto games to get fully "solved".

What Does This Have To Do With Fantasy Football?

They may seem pointless, but Blotto games have a shockingly large number of potential applications. Beyond the obvious troop deployment considerations in war, Blotto games have been used to estimate optimal research and development spending, allocation of marketing budgets, political campaigning tactics, salary cap spending, and more. Any time you have direct competitors operating in conditions of limited resources, Blotto games apply.

That includes fantasy football in general, and especially dynasty leagues in particular.

Consider: every team in a dynasty league gets one first-round pick a year. If your league starts one quarterback, two running backs, three receivers, and one tight end, every team gets seven player-starts a week. Waiver claims and roster spots are also limited resources. You can't just play everyone you think will have the best week (regardless of whose roster they're on), you have to manage your limited resources to coax out the most points possible. The manager that does the best at the task wins.

Just like in Blotto games, it's easier to win if you have more value on your roster than your opponent. If you consistently pick good players in the rookie draft while your opponent consistently picks bad ones, you'll have more good players, and things will become more similar to the hypothetical version where one general gets six units, and the other only gets four. Most dynasty advice tends to tilt in this direction, focusing on how to get the most value out of your scarce resources.

This is complicated by the nature of dynasty leagues, which tend to give the most valuable rookie picks to the worst teams, and the least valuable rookie picks to the best teams. It's also confounded by the nature of NFL careers, where the most productive players are often near the end of the line and carry less future value than many of their less-productive peers.

But even if you can't manage to increase your roster value beyond the other teams in your league, you can still win by allocating the roster value you do have more efficiently. A team that featured Geno Smith, Derrick Henry, Austin Ekeler, Davante Adams, Stefon Diggs, DeAndre Hopkins, and Travis Kelce would be incredibly well-positioned to win a title this year. But it also would have essentially allocated all of its value to 2022 and would have a much-reduced chance of competing in future seasons.

One of the lessons of the Blotto game is the optimal strategy is to win each battlefield by the narrowest margin possible to ensure you have the maximum amount of leftover resources to allocate elsewhere; swapping Derrick Henry and DeAndre Hopkins for Najee Harris and Marquise Brown would still leave that team a strong title contender this year but would also spread some more value into 2023, 2024, and beyond.

And just as individual seasons can be viewed as distinct battlefields, individual positions can be as well. One interesting thing about trade markets is that two leagues with identical rules might see players at a specific position trading for wildly different costs. Quarterbacks especially seem to have wild swings in value from league to league, with some leagues treating them as a virtual afterthought and others treating them as cornerstone assets.

If a position is especially expensive in your league, often the best play is to just cede that battlefield to your competitors, spending the bare minimum amount of resources that is necessary on it and leaving yourself with more resources to outbid your competitors at other positions where points are cheaper to acquire.

At the end of the day, viewing dynasty leagues as a Blotto game is just another paradigm. It doesn't change who wins or who loses. But considering your options through the framework of resource allocation can lead to better decisions and more wins.