I'm considering a normal fantasy football season one that lasts 12 games and awards 1 point to the winner of each game. The 6 teams with the most points make the playoffs. This is equivalent to saying the 6 teams with the best records make the playoffs.

Assume you have 12 teams and they are all exactly equal in quality. That is, assume that they will each score the same number of points each week on average. What is the likelihood of a given team making the playoffs in this situation? It should be obvious that it's 50%. We can plot this also. Below are the results of simulating 100,000 seasons assuming all teams are equal:

This gives you some idea of the spread in results. Even though all teams are exactly equal in quality each week, roughly 20% of teams will finish 4-8 or worse, and roughly 20% of teams will finish 8-4 or better.

Now, imagine 1 of the 12 teams is clearly better than the others. Assume that this team will average 5% more points each week than the other 11 teams. This team should make the playoffs something like 90% of the time right? If we assume the typical spread in points scored per week is 30 points (this is lower than my league the last two years), the team that is clearly better than all the other teams will make the playoffs...

63% of the time

That's low. Here are the results for this team after simulating 100,000 of these seasons:

What if we go crazy and say one team is 10% better than every other team in the league? Does that get us to 90%? No...it gets us to 74%. That means in roughly one fourth of seasons where the best team is 10% better than every other team, the best team by far in the league does not make the playoffs. Here is the distribution of results:

There are a lot of different ways you can do this. I tried a number of them. Every time, I got that the luck factor in fantasy football is enormous, and it's a bit disheartening.