Jonathan Bales is the author of the Fantasy Sports for Smart People book series, and most recently Fantasy Football for Smart People: How to Win at Daily Fantasy Sports.


“The wise man is one who knows what he does not know.”
  • Lao Tzu, Tao Te Ching

Okay, I’m about to drop a bombshell. Actually, I doubt anyone will care. Or it could be somewhere in the middle. Yeah—complete bombshell, total indifference, or somewhere between. Solid prediction.

So here’s the thing: I don’t vote. I’ve never voted in my life. I don’t plan on ever voting. I totally get the idea behind it, how it’s viewed as our “civic duty,” yada yada yada. I don’t fault anyone for voting.

There was a presidential election my senior year of high school, and lots of kids in my class who had turned 18 were pumped to vote. I planned on doing it, too, but when the day came, I just sort of thought about it for a second.

What the hell am I doing? I have to drive down to wherever it is people vote, wait in line, and drive back. Okay, that doesn’t really sound that awful, but certainly it would cause me some amount of pain.

And here’s the thing: even if the amount of pain I can possibly feel were theoretically 1,000 (pain units?) and voting is just a 1/1,000 on that scale, statistically I still shouldn’t vote, and it’s not even close.

For me, it was a simple math problem. I thought I would be happier with one presidential candidate over another, sure. Maybe not a lot, but perhaps. But what’s the probability of my single vote being the one that swings Pennsylvania to the candidate of my choosing? Low. Very, very low. And then what are the chances Pennsylvania is the swing state in the election? Decent, but still worse than a coin flip, probably.

So I estimated that because I was (am) a certified loser, multiplied it by the different levels of happiness I’d experience over a four-year period with each presidential candidate, and compared it to the dark, dark place I was in needing to waste perhaps an hour of my day going to vote—a day in which I wouldn’t have been doing shit anyway.

And the numbers weren’t even close. From a utilitarian perspective (which I do realize is not the only way to analyze this situation, and perhaps not the optimal one for a lot of people), the math suggests voting is incredibly stupid. It just isn’t worth it, mathematically speaking.

By the way, I also decided at that time to always lie about voting. So when someone asks if I vote or who I voted for, I just lie. It’s so much easier than dealing with trying to explain myself. I actually think that needs to be part of your calculation when determining if it’s smart to vote; if you’re going to commit to being unpatriotic like me, you also need to commit to being dishonest. It’s the American way. Except now I’m telling all of you about it, so this could really backfire. But I thought it was a good intro, and that’s what really matters here.

Anyway, this is pretty much how I analyze most situations—in terms of expected value—and it requires a basic understanding of probability. Ultimately, our decisions in any area of life are only as good as our ability to predict the future, which boils down to understanding and embracing randomness and probability.

Now let’s talk about daily fantasy football.


Range of Outcomes

The most fundamental way I use probabilities in daily fantasy football is projecting players in terms of ranges. I think there’s some value in traditional median projections and $/point calculations—mostly so in head-to-heads—but for the most part, I want to try to better understand what sort of distribution of potential outcomes a player has. So if we were to simulate this game 10,000 times, how often would he score 20 points? How often would a totally different player with the same median projection score 20 points? How do those probabilities differ and how can I exploit it?

The example I always use to demonstrate this is Vincent Jackson vs. Jarvis Landry. The former player is a big-play guy who can score with consistency. He relies on low-frequency events like deep passes and touchdowns for his fantasy production. Jackson’s average target traveled over 15 yards downfield last season. Thus, he’s super volatile on a weekly basis.

Landry’s average target length was 5.5 yards last year. That’s bananas. He thus has a super high catch rate, and since he relies on pure volume and receptions for his production, he’s quite consistent on a weekly basis.

Every situation is different, but in a typical week, I’d almost never play Jackson in cash games and (rarely) play Landry in tournaments. The former player’s volatility is a negative in cash games, especially in 50/50s in which I’m trying to establish a high floor. Jackson has a super wide range of outcomes—he could have two catches for 20 yards or he could put up a 7/150/2 line—and embracing that variance makes sense only in certain situations.

Landry, on the other hand, has a pretty narrow range of outcomes. He’s rarely going to tank, but—and maybe I’m wrong here since he’s had a couple big games already this season—he also doesn’t have as much exposure to an elite ceiling as someone like Jackson. That doesn’t mean you can never roster Landry in GPPs, but just that statistically I think he’s far less likely to deviate from his median projection than most other receivers.

The overarching idea is to try to view players probabilistically—projecting a range of potential outcomes—and then match up players’ exposure to various levels of production to your goals for a particular league.


A Few Other Quick Notes

I have so much more to say about this topic, but I’m hungry and I have a full box of Peanut Butter Cap’n Crunch calling my name, so here are a few quick-hitters on how a probabilistic approach might affect you as a DFS player:

– I think you could argue that embracing uncertainty and moving away from a black-and-white worldview should increase your pool of potential players and how much you diversify your lineups. The wider the range of outcomes—with MLB being at one end, which is super-random on a nightly basis, and NBA being at the other—the more it makes sense to widen the number of players you’re considering.

– Basically, uncertainty and predictability is fundamentally tied to being contrarian. The philosophy behind my antifragile approach to many DFS tournaments is that others overestimate their ability to make accurate predictions—they don’t fully appreciate randomness and aren’t truly thinking probabilistically—and thus the payoffs for being contrarian are asymmetrical to the risk, i.e. you can have the worst hand but get the right odds to call.

– Finally, it’s vital to understand probability when assessing your performance. I’d argue that the performance of an individual player in a single game tells you almost nothing about whether or not your decision to use him was smart. You can’t grade the value of one player or one lineup based on the results; lots of times, the best lineups perform poorly and the worst do well. Only over the long run do the probabilities “even out,” so to speak, such that you can trust your results.

The End.


“The laws of probability, so true in general, so fallacious in particular.”
  • Edward Gibbon

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