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, 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.

The Standard Line on Luck in Fantasy Football

As the season draws to a close, I hope as many of my readers as possible are still alive for a championship this weekend. Doubtless many more have been eliminated, but the bright spots always stand out more. Often, the conversation at this time of year turns to the role of skill and luck in fantasy football.

I've shared many times over the years how abysmal the odds can be in fantasy football. The higher-seeded team in dynasty leagues tends to win about 58% of matchups even in the semifinals, where the disparity in team quality is typically the greatest. The best team loses in about two-thirds of leagues. This could lead one to believe that this hobby was predominantly driven by luck.

Personally, I take the standard position: fantasy football is about 50% skill and 50% luck. The 50% of the time when I win, that's skill; the 50% when I lose is luck. (The corollary to this is that there's no such thing as good luck. Listen to a hundred fantasy managers speak, and you'll hear a hundred stories about how they got screwed by luck and not a single one about how they only won because of their incredible good fortune. Success has many fathers, but failure is an orphan.)

(My lone championship match this weekend is projected about as close to 50/50 as it gets-- 185.92 points to 185.34 points. I think the Fantasy Gods knew I planned to write this column this week and decided to have some fun at my expense.)

But if I were ever feeling particularly serious and someone asked me what percentage of fantasy football was inherently driven by luck, I'd say they were fundamentally understanding just what exactly luck is, here.

First, To Distinguish Luck from Variance

If I have a coin that's weighted so that it comes up heads 58% of the time, I flip it, you call "heads" in the air, and it comes up tails, that's not really bad luck. The nature of the game is such that we need that coin to come up tails some of the time still. (42% of the time, to be exact.)

If I flip that coin 100 times and it comes up tails 50 times, that's not really bad luck, either. The odds of getting exactly 58 heads on 100 flips are quite low. Some small deviation from that total is only natural and expected.

These short-run deviations are variance, and the solution to them is quite simple: more trials. If you flip that coin a hundred times, you probably aren't going to see 58% heads. If you flip it a million times, you'll almost certainly be within a couple of decimal places of it.

Fantasy football has a lot of variance. At Footballguys, we've tracked our weekly projections over the last two decades and found that depending on the position and the projection, they typically have a coefficient of variation (or CV) of between 0.35 and 0.65. Let's call it 0.50 to keep it simple. CV represents the size of fluctuations as a percentage of the mean. This means that 68% of the time, a player scores within +/- 50% of his weekly projection. Of course, this also means that 16% of the time, that player scores 50% more points than we projected, and another 16% of the time, he scores 50% fewer.

Over a lot of observations, players projected to score 15 points do average 15 points. But over a single week, there's about a 1-in-6 chance they'll score 22.5 and a 1-in-6 chance they'll score 7.5, instead. And there are even smaller chances of larger deviations; about 1 in 50 times those players should double their projection and score 30. Another 1 in 50 times, they should go bust and score virtually nothing.

In the fantasy playoffs, these deviations can mean the end of a season. If your Jordan Addison gets hurt after his first catch and your opponent's Amari Cooper has 11 catches for 265 yards and 2 TDs, you might easily be joining 42% of the other higher seeds in defeat.