Fantasy football game theory
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Luck, Probability and Variance in Fantasy Football


It’s an old story in fantasy football. The 4-player defensive block has kept a clean sheet for 90 minutes, tournament victory is within reach – and then your defence lets this incredibly stupid goal slip through in stoppage time, your tournament is left in ruins and the world goes to wrack and ruin.

A very disappointing day, when everything went wrong for your team. All fantasy football managers are faced with the same problem; Lady Luck is fickle and often changes her mind about who she favours.

Is fantasy football, therefore, simple a matter of luck? The idea is plausible, but it does not fully address the situation. Let’s take a closer look at some key terms to see what light they can shed on the topic.

In this article, we’ll examine the terms luck, probability, variance and expectation and show you the correct approach to fantasy football tournaments.

Game Theory: Luck

The word luck is generally believed to derive from the middle-low German “g(e)lucke” or “lucke”.

According to Wikipedia: “The definition of luck (or chance) varies by the philosophical, religious, mystical, and emotional context of the one interpreting it; according to the classic Noah Webster’s dictionary, luck is “a purposeless, unpredictable and uncontrollable force that shapes events favourably or unfavourably for an individual, group or cause”. Yet the author Max Gunther defines it as “events that influence one’s life and are seemingly beyond one’s control”.” (https://en.wikipedia.org/wiki/Luck)

You will probably be familiar with the expression “s/he has all the luck” or “s/he’s a lucky one”, which refer back to the original meaning of the word. But is fantasy sports simply a game of chance, in which luck is all that really matters? Is the outcome of a tournament all that’s important? How can it be that some people win more often than others in so-called games of chance such as poker or even fantasy football? This brings us to another concept in the game.

Daily Fantasy Football Game Theory: Probability

There are very few certainties in football. The trainer and football philosopher Sepp Herberger has summed up a few of them. Many of his sayings have become popular expressions in the world of football: “The ball is round”, “The game lasts 90 minutes.” and “As one game ends, another begins.

In addition, there are few guarantees in football. However, security is not really what football is all about, because at the end of the day, football is a game and an element of luck makes games more fun. It would be boring if Bayern were to win each and every match. They are always favourites in the league and it is also very likely that they will win. But it is not absolutely certain.

In daily fantasy football, you work on the basis of probabilities trust less to luck or chance. A solid analysis of the relevant probabilities on any given match day should be more important to you than hanging your horseshoe the right way up or putting a lucky charm on your computer.

Probabilities are a mathematically quantifiable value with which you can understand the probability of certain events and you can apply them to your profit (literally).

Probabilities can be given in percentage form or in the form of odds and are always the starting point for your line-ups.

The bookmakers play a very important role here as they calculate the probabilities of many events according to statistical analyses and mathematical models.

Learn more about match day preparation with a statistical preview for a matchday.

Variance in Fantasy Football

All this leads us nicely to the important concept of variance. Variance is the distribution of probability by means of random variables. You must put your team together in view of certain probabilities. Your defence and your goalkeeper have a 60% chance of keeping a clean sheet. Your striker has a 63% chance of scoring and so on for your entire team.

These probabilities are then put to the test on match day, because many random events determine the outcome of the game and thus whether or not the probabilities hold good. Of course, it could come about that your prolific striker has a bad day or even gets injured, that’s just how it is sometimes. It does not change the fact that he was very likely to score a goal.

The deviation from the predicted probability is called variance, and is also a computable value.

We’ll skip the in-depth mathematical details here and go straight to what fantasy football managers need to understand.

Expected Value

All important decisions revolve around the central concept of expected value. In fantasy sports, this could also be called a team’s point potential.

The expected value is only determined by the probabilities, and ignores the effects of luck or the events in the actual, physical match.

The expected value thus reflects the mathematical potential of your team how many points they can theoretically achieve. Because of this luck is ignored, since expected value holds sway over the long term.

An Example:

Let’s say Barcelona play against Legia Warsaw in the Champions League. It may well be that Legia beats them in one specific game when they are running unbelievably well. But what sort of outcome would we expect if they played against each other 100 times, or even 1000 times? Without much hesitation, we can say here that Barcelona will win far more often than Legia Warsaw. The greater the number of games played, the closer the outcome will be to the expected value, which is to say the odds. Luck, therefore, always plays a minor role.

In terms of fantasy football, this means that if you only play one, single tournament with a line-up which has a high expected value, the outcome is very much dependent on chance. But if you play 1000 tournaments where your team has a bigger point potential than the other players, then the swings and roundabouts of luck will steady out, just like it did in the example above. Most of the time, the better team will win and luck will play an ever-decreasing role in your overall tournament results.

The Successful Fantasy Football Manager

If you want to be successful at daily fantasy football, you should look less at the short-term results and focus your attention on your teams’ expected value.

If you set up good teams with good chances, then sooner or later you will be successful.

Even if you have a bad run, which lasts for a few weeks or months, you should always look at your teams and ask yourself if they had solid probabilities and if they were used in an appropriate formation. If you can answer both of these questions with a yes, then you are doing everything right and should keep calm and carry on. Success is only a matter of time.


Herbert is a doctor of philosophy, speaks 5 languages fluently and moved to Barcelona to be close to good football... Herbert was Head of Education at Pokerstrategy and responsible for ensuring that 8 million members successfully learned poker. He discusses Instructional Design and Learning Theories on Griffl.org.
As a founding member of 11Heroes, Herbert plays a similar role as at Pokerstrategy.com. You can find him on Twitter as @DrFantasy11

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