Mental models in DFS: Part 3, The Gambler's Fallacy

A RotoGrinders post. 

The Story So Far

So far we have explored how the “Availability Heuristic” tricks us into remembering events that are most easily available to our memory, and how the “Liking Bias” clouds our judgement by putting our favourite players ahead of statistical logic. This week we’ll explore The Gambler’s Fallacy, otherwise known as “The Monte Carlo” Fallacy.


Because although DFS is a game of skill, a poorly trained mind that falls trap to the biases that usually befall gamblers then guess what, you’ll end up gambling. Guessing, making rash decisions, panicking & losing isn’t what DFS is about.

What is The Gambler’s Fallacy?

Think of a roulette table in Vegas. The board about the table shows the last 15 spins in a row hitting red. How many times have you thought, “it’s bound to hit black next”? The sequence of events has clouded your judgement, because in your mind it’s increased the likelihood of change.

This is a misunderstanding of the concept of probability. If the two colours on the table (forget 0 for now) are red & black, the probability of either is always 50%. The same with a coin flip.

If you wanted to place a definition on it, you could say it’s “the flawed reasoning that, in a situation of pure random chance, the outcome can be affected by previous outcomes.”

Let’s think about it another way. Would you ever choose the numbers 1, 2, 3, 4, 5, 6 on your lottery ticket? Most people would think that’s stupid. It’s too ordered, a more random sequence like 6, 14, 22, 35, 38, 40 is more likely to come up. However, the order from 1 to 6 is made up in our imagination. We’re the ones that give it any meaning. Random chance is order & sequence agnostic.

The Gambler’s Fallacy in DFS

I don’t want to discredit the importance of a team or player’s form when making decisions in DFS. Clearly past performance can be a good indicator of how well a player will turn up next game. That’s why top players will show consistency in their last handful of games.


As with anything in life however, balance is key. Understanding how probability works & the role of chance in any sporting situations will make you a better DFS player. If you treat each game as an independent trial, you’ll be less likely to allow biases to fool you.

The fact that Giovinco has only scored once in his last five MLS games is not an indication that he’s “due” to score. Similarly, if a defensive player like Nemanja Matic has scored in his last three games, this “hot streak” is likely nothing more than a product of variance.

There are certain players who are more likely to score than others. Sergio Ageuro, Diego Costa, Lionel Messi. However, those players are usually out of most DFS player’s budgets (assuming you’re playing a game that uses salary caps.) So how do you make sure you’re still making smart decisions while trying to find value in lesser known players?

The first step is avoiding gambler’s fallacy. It’s essentially the easiest route to take because you simply look at players on hot streaks.