Dynasty, in Theory: Random is Random

On Finding the Noise in the Signal

Let’s talk about the nature of randomness.

There’s a well-known demonstration given in statistics classes where half of the class is assigned to flip a coin 100 times and record the results while the other half is asked to create a fake string of 100 random coin flips. The statistics professor, with no knowledge of which students belonged to which group, will glance through everyone’s results and deduce whether that student was in the “actual coin-flip” group or the “fake coin-flip” group. An experienced professor can usually guess with astounding accuracy, typically well north of 80%, a rate far above what would be predicted by chance alone.

The giveaway in the exercise, it turns out, is the length of the “runs” of either heads or tails. Our minds intuitively expect sequences of eight consecutive heads or tails flips would be rare— and indeed, they are. Given a perfectly fair coin, the odds that the first flip will be followed by the exact same outcome seven more times are 1 in 2^7, which works out to 0.78%. It is certainly an outlier event.

But those are the odds within any specific 8-flip sample; a 100-flip sample will naturally contain 93 different 8-flip samples, each with its own 0.78% probability. The odds that one of those 93 sequences features all heads or all tails are much higher— 16%, in fact. That’s still unlikely, but more in the realm of “uncommon” than “rare”.

And a run of 8 is relatively extreme; runs of 7 should occur in 32% of truly random samples, runs of 6 should occur in 55%, and runs of 5 should occur in a striking 81% of truly random 100-flip samples.

On the other hand, when asked to fake a string of coin flips, most people will be loathe to put such long strings into their results. Our conception of “randomness” is really closer to “alternating”. And alternating is actually the opposite of random; if a coin truly alternated heads and tails perfectly, then every flip could be predicted with perfect accuracy.

Indeed, this notion of “random” as “alternating” is one of the key drivers behind the Gambler’s Fallacy, or the idea that certain outcomes in a random process eventually become “due”.

If we assume that 90% of the “faked coin flip” students are unwilling to put a run of 5 or more in their string, then 82% of papers the professor saw that lacked a run of 5 would have belonged to the “faked flip” sample. At the same time, 89% of the papers that included a run of 5 would belong to the “genuine flip” sample. Simply scanning for the longest run and guessing accordingly easily explains the aforementioned success rate.

What does this have to do with fantasy football? Nothing, and everything.

I mentioned the Gambler’s Fallacy, or the notion that in a truly random process, streaks indicate that some other outcome is coming “due”. That plays out when we know for sure that the process is random; roulette, blackjack, or other games of chance. But what about when we aren’t so sure?

In that case, streaks and runs will cause us to reject our belief that random chance is at work, often far quicker than we should. If a player has three bad games in a row, we think he is cold and trending down. If a player has three good games, we think he is hot and trending up.

In his four games from week 4 through 8, Todd Gurley averaged over 150 yards per game and 6.4 yards per carry. At that point, he was viewed as a white-hot, sure-fire fantasy star who would carry his teams to championships.

Over his next four games, Todd Gurley’s yards per game and yards per carry were both cut by more than half, to 74 and 3.1, respectively. At that point, he was viewed as someone who couldn’t overcome his supporting cast, and relegated to many teams’ benches.

In the three games since, Gurley’s yards per game hovered around 90 and his yards per carry rose back up to 5.0. Suddenly, in the playoffs, he’s back to carrying fantasy teams, (albeit not quite as much as he was early in the season).

So who is Gurley? The scorching-hot back from early in the year? The ice-cold back who followed? The solid-but-unspectacular back of the last couple weeks? He’s none of the above; he’s a typical NFL player whose good performances and bad performances were relatively randomly distributed. He's most likely as good as his entire sample indicates, rather than one specific slice of it. Random is streaky, and those streaks got mistaken for trends.

Our tendency to mistake streaks for trends is behind some of the gravest errors we’ll make in fantasy football: applying the “injury-prone” label too liberally; overestimating championship odds based on regular-season performance; overrating players with early-season breakouts; assuming that an influx of talented tall receivers means that taller receivers are now undervalued by the NFL; underrating the predictive power of preseason ADP once the season is underway; trying to “buy low” and “sell high”; overrating the predictive power of touchdowns; trying to stream players based on perceived matchups. And that’s just the ones I’ve written about so far.

This year, we saw an unprecedented rash of injuries at the running back position. I already see many touting this as evidence that running back is too volatile to invest in. Historically, however, running backs have typically averaged just one fewer game per year than their wide receiver counterparts. Is this year’s carnage really a harbinger of things to come? Or is it just the latest example of flipping “heads” 8 times in a row?

Randomness— true, genuine randomness— is practically unfathomable to the human mind, which craves patterns and works tirelessly to find some hint of order amidst the chaos. Not every streak is a trend, however; sometimes it’s simply randomness being random.


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