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.

But if you get a lot of higher-seeded teams into the playoffs, then over a large enough number of observations your long-run winning percentage will tend to converge on 58%. Sometimes you'll catch the low side of variance and lose a matchup you "should" have won. Other times, you'll catch the high side and win matchups you "should" have lost. Luck is sometimes just what we call variance that hasn't had a chance to wash out of the system yet.

Once You Get Past the Variance, How Much Luck Is Inherent to Fantasy Football?

The answer here is "none", and that answer hinges on one specific word in the question: "inherent". This can be illustrated by a simple example: My youngest son is 7 years old and has no interest in football. Variance or no variance, if he and I played in a league together, what are the chances he beats me? He can't name a single player; he could probably only correctly name three or four teams. On the rare moments a game catches his interest, he chooses his rooting interest based on a simple heuristic: cool animals trump lame animals and lame animals trump non-animals. Other than John Wolford, I'm not sure who he'd even draft.

On the other end of the spectrum, over a long timeline, Footballguys staffers win 50% of the time in our staff leagues. (Over a short timeline, they win 50% of the time, too; this is tautological. But even for individual staff members, as the variance washes out, everyone's performance trends fairly close to 50%. Wins and losses become a coin flip.)

This is the result of something called the Mauboussin Paradox of Skill (after Michael Mauboussin, who has written at length about it): as the disparity between skill decreases, the role of luck increases. I would beat my 7-year-old son every time because the skill disparity between us is huge. Matchups between Footballguys staff members are a virtual coin flip because the skill disparity between them is small.

This is true in the NFL, too. The gap between teams is large enough that the better team usually wins but small enough that luck plays a significant role. The New York Jets, after all, beat both the Bills and the Eagles this year. Pair the Jets against a college team -- any college team -- and their chances of winning are virtually 100%. The skill disparity would be too great.

(This is also why no team outperforms the average in the NFL draft over a long timeline. All 32 teams are skilled enough at picking players that any short-term variation in results is almost entirely driven by luck.)

Pick any field, and you'll see the paradox of skill in action. Have a chess player with a FIDE rating of 2500 play another chess player with a rating of 1800, and the grandmaster will win every time. Have him play against someone rated 2450, and that falls to 55%, barely better than a coin flip despite chess not typically being an endeavor we think of as driven by luck.

If it feels like luck plays an outsized role in your fantasy football leagues... you're probably right. The proliferation of quality fantasy football advice over the last decade means there's never been a higher baseline level of skill. Even a completely inexperienced player can just draft and start the players recommended by the league host and still do fairly well for themselves. If everyone is good, then everything is a coin flip.

For a while, dynasty leagues were a haven from these forces. Since dynasty was less popular, dynasty resources were less common, and there were larger gaps between good and bad dynasty managers. There were more opportunities for skilled managers to separate. But the popularity of crowdsourced tools like KeepTradeCut and FantasyCalc means these gaps are narrowing, too.

For some people, this can be a troubling realization, the idea that every year a greater and greater share of their success or failure will be determined by random chance. You can get better and better at the hobby, but if your leaguemates improve as well you won't gain any ground.

But I think fantasy football is beautiful and worthwhile nevertheless, not because it's an opportunity to demonstrate my superiority, but because it creates stories that tie us together. As a wise man famously said: