Are we alone in the universe? It's a question that has fascinated everyone from academia to Hollywood, one that some hope to answer with... math. Enter the Drake equation, created by Dr. Frank Drake in 1961.
N = R* x fp x ne x fl x fi x fc x L
N = the number of active, communicative, detectable extraterrestrial civilizations
R* = rate of star formation
fp = fraction of stars formed that have planets
ne = for stars with planets, the average number that could potentially support life
fl = the fraction of potentially-habitable planets that develop life
fi = the fraction of planets with life that develop intelligent, civilized life
fc = the fraction of civilized, intelligent lifeforms that develop communications
L = the length of time over which such civilizations release detectable signals
Drake originally estimated the following values for each term:
R* = 1 per year
fp = 0.2 to 0.5
ne = 1 to 5
fl = 100%
fi = 100%
fc = 10 to 20%
L = 1,000 to 100,000,000
Using all of the minimum and maximum values, Drake concluded that there should be between 20 and 50,000,000 detectable civilizations in the galaxy. After discussion, he modified that to estimate that there were probably between 1,000 and 100,000,000 civilizations in the Milky Way. And the sinister question then becomes: why can't we find them?
Astronomy has come a long way since 1961. Perhaps new science reveals that his values were wildly off? Yet futurists routinely revisit the Drake equation, estimate the factors, come up with a value in the thousands, and then ask "so where is everybody?" This "where is everybody?" question is famous enough that it has a name: the Fermi paradox.
Of course, one resolution to the Fermi paradox is to say that everyone is being wildly optimistic and overestimating the value of one or more terms in the Drake equation. And it's true that futurists are certainly an optimistic bunch. But a more interesting response is that even using the optimistic estimates provided by the most optimistic futurists, the Fermi paradox isn't much of a paradox at all.
Futurist A and Futurist B might both provide a set of estimates that suggest there should be 10,000 civilizations out there, for instance. But perhaps Futurist A assigns a relatively low value to fl (the probability that life develops) and a relatively high value to fi (the probability that, once life develops, intelligence develops). And perhaps Futurist B does the opposite, assigning a low probability of life developing, but believing once it does that intelligence is a near-certainty.
If you tossed Futurist A's estimates in a bag with Futurist B's estimates and selected them at random, about a quarter of the time you'd pair Futurist A's certainty that life is inevitable with Futurist B's certainty that intelligence is inevitable, producing in a result to the Drake equation that's astronomically higher. But a quarter of the time you'd pair Futurist B's doubt that life is all that common with Futurist A's doubt that intelligence is all that common, producing a much smaller estimate for the Drake equation.
Indeed, a rigorous survey has found that if you take all published estimates for the Drake equation, scramble all the terms together, and select them at random, there's an 8% chance that the resulting outcome is N = 1 or less. Which means even if you listen only to the optimists, there's a staggeringly high chance that we're alone in the universe!
What does the Drake equation have to do with fantasy football? Absolutely nothing. But this criticism of the Drake equation is everything.
Here at Footballguys, we create player projections. We do this because we believe they're the absolute best way to forecast fantasy production, and industry results bear this out. If you look at the kinds of people who routinely dominate industry-wide fantasy leagues, or who win expert accuracy contests, every single one of them is creating or using player projections.
But player projections are point estimates not at all unlike the output of the Drake equation. For instance, a receiver's projected yards can be described by the following equation:
Yards = np x fp x fc x ny x G
np = number of passes per game attempted by the receiver's offense
fp = percentage of the offense's passes directed to the receiver
fc = percentage of targets that the receiver catches
ny = number of yards gained per catch, on average
G = games played
Let's say that Cleveland will throw 35 passes per game, and Josh Gordon will secure 21% of their targets, which is 7.35 targets per game. His career-average catch rate is 52%, and he averages 17.3 yards per reception. Plug in all those values, and you're projecting Josh Gordon for 3.8 catches for 66.1 yards per game.
Over a full season that would be 61 catches for 1059 yards, but let's say to reflect the heightened suspension risk let's project him for 12 games played. Suddenly my Josh Gordon projection is just 730 receiving yards-- not a very compelling argument for drafting him.
But this is a point estimate, and as we saw, point estimates miss a huge range of possibilities. So let's add some uncertainty to the mix and convert these estimates to a range of plausible outcomes. For example, one might think that 35 passes per game is the most likely outcome for Cleveland, but you wouldn't be surprised if they threw three more or fewer passes, instead. If we do this for every term, perhaps we get something that looks like this:
np = 35 +/- 3
fp = 21% +/- 4
fc = 52% +/- 3
ny = 17.3 +/- 1
G = 12 +/- 4
Using the low range of every estimate, no one would be truly shocked if Josh Gordon played half a season and had just 350 yards. After all, in his last 8 games, Gordon has just 443 yards, and that was before Cleveland brought in Jarvis Landry to compete for looks.
But on the other hand, if the high end of each of those estimates comes through, people likewise wouldn't be surprised if Gordon played 16 games and finished with 1530 yards. That may not be the most likely outcome, but it's certainly a reasonable one given that we already saw him once lead the NFL with 1646 receiving yards (and 1734 yards from scrimmage) in just 14 games.
Take a second to draw your attention to just how massive this range is. This is basically projecting Josh Gordon for somewhere between 350 and 1530 yards. But huge ranges are what you get when you multiply uncertainties!
Each individual term only varies a little bit. It's reasonable to be projecting his yards per reception to be between 16.3 and 18.3, which is a very tight range. One might think his catch rate will be between 49% and 55%, which again is a small spread. But when you multiply together five different variables with a relatively tight range, you wind up with an answer with a huge potential spread.
You don't need to make any unreasonable assumptions to create this huge spread. In fact, we have four different staff members who create preseason projections. you can just take each of their projections for each individual term, scramble them together, and that alone is sufficient to create a wide range of outcomes. If you mix David Dodds' target share estimate with Maurile Tremblay's catch rate estimate, Bob Henry's yards per reception estimate, and Jason Wood's games played estimate, you might get a value that his dramatically higher or lower than any of those individual projectors' actual projections taken in isolation.
This process of multiplying uncertainties is a large part of how we project player upside for Footballguys. But it doesn't explain why we project player upside at Footballguys.
To answer that, return to the Fermi paradox. These futurists who are estimating the number of alien civilizations in the galaxy aren't really concerned with how many alien civilizations there are, per se. It doesn't make a huge difference whether there are 100 others or 100,000 others. Obviously, it would be easier to find them in the latter situation than the former, but otherwise, the extra 99,900 civilizations aren't changing much.
But it makes a dramatic difference whether there are 100 others or 0 others. It's the difference between being alone and being not alone, which is what this gets down to. The Drake equation, the Fermi paradox, they're all driven by a need to answer the fundamental question: are we alone in the universe?
Similarly, when we create projections for Josh Gordon, we're not really all that concerned with exactly how many yards Josh Gordon is going to finish 2018 with. Instead, all of this is an attempt to answer the bigger question: how likely is it that Josh Gordon wins you your fantasy league?
A projection alone isn't enough to answer that question, though it's certainly a good start. But if we really want to know, we need to embrace uncertainty, too.