The Law of Averages Doesn’t Exist: A Lesson from Fantasy Basketball

Pretty late to the party, but I recently joined my first fantasy basketball league. I’ve been hooked since draft day.

Had I known how close it was to feeling like Billy Beane from Moneyball, I would’ve started years ago. More than the games, I enjoyed the numbers and the trends. It was essentially playing with data, and I always loved data.

If you aren’t familiar with how fantasy works, it’s basically managing a hypothetical team made with players from real life. The better players perform in real life, the better your team performs in the game. You trade players, drop underperforming players, and add players who are performing well.

As a beginner, you could imagine, I was on my heels for every game.

On an almost daily basis, I would be trigger happy on adding and dropping players. After a bad game by a pick on my roster, I’d almost immediately consider dropping him. Luckily, my friends who were also playing in the same league would advise me to go easy on the drops; it may have just been a bad game. And so I heeded their advice. I’d wait a game or two to observe.

Trust in the law of averages, I’d remind myself. But over the next few days, again and again, I would find myself disappointed. A bad game today did not mean a good game the next day. More often, it just meant another bad game. There was no “averaging out” going on. The law of averages seems to have been failing me over and over again.

It turns out, there was no such thing as the law of averages.

This “law” wasn’t an actual mathematical theory to begin with. Also known as the “gambler’s fallacy,” we usually invoke the law of averages when presented with an undesirable situation or outcome. We tell ourselves, if today has been a bad day, then chances are, tomorrow will be better. “It should average out.”

Of course, it rarely happens this way. There are exceptions, yes, but that isn’t quite the point. The fact is, given all other variables are held constant, the probability that tomorrow will be a good day is the same probability that today had been a good day. If it’s 20% today, it’s still 20% tomorrow, not 80%.

Probability knows no history in the short term.

In the short term, spikes in data, in days, in moods, these are highly unpredictable. No one can predict tomorrow. We don’t see the waves that come. And if we let every single blow hit us, it will hurt. Every bad game, every bad decision.

The long term, however, is a different story.

In the long term, the Law of Large Numbers applies. Now this one is backed by real math. Simply, given a large enough sample size, things do average out. In the long run, things are more predictable and smooth. But as the name suggests, this only applies to large enough numbers. Big picture. Long game. Only in the long term are the numbers “balanced.”

Going back to my short stint as a fantasy team general manager, it wasn’t the averages that were killing me, it was my lack of patience. I was feeling every single up and down beat.

And we see this happening outside the hypothetical world of fantasy as well.

In the volatility of the short term, it’s easy to keep looking at tomorrow. Even on our best days, we await the end of it. We preempt the Mondays that follow long weekends and the last day of a trip. To be in the present while playing the long game, that’s life’s true balancing act.

Fortunately, the numbers don’t lie, time does most of the balancing for us.