In fantasy football it is often claimed that a player has a very stable or consistent output while other players are considered unstable or inconsistent. These statements refer to the players point output on a week to week basis. Some people will argue that you're better off with consistent players and thus discount the players with high week to week variation. I'm writing this article to argue that variance should have no effect on your decisions while drafting players and I will give a few arguments as to why high variant players can be to your advantage.
Statistically if both teams have a Gaussian distribution the variance has no effect on the probability of victory for either team. The probability of victory for either team would be...
(E[x] = Expected or mean value of x (essentially points per game), P[x] = Probability that x wins)
P[TeamA] = E[TeamA]/(E[TeamA] + E[TeamB])
This estimation holds up as long as the variance for both teams is high enough for both teams to have a chance to win the match.
As you can see points per game affects the probability of victory for either team while the variance does not. Now the main arguments I to have for drafting variant players is at a premium over consistent players is that making the playoffs mostly depends on your ability to work the waiver wire and trade. I believe that solid owners can make the playoffs almost every year if they really pay attention to fantasy football news and the waiver wire even if they have a weak draft or bad luck with injuries. Drafting is obviously still important in all leagues especially in very competitive leagues (where the free agents are typically of lower quality) but a poor draft can be still overcome (to an extent of course) through free agents, trades, and waiver wire pick ups.
Assuming you do make the playoffs at this point all the teams are likely to be good teams with similar expected values for points per game. It is obviously still advantageous to have the better team but having a high variance could benefit you in the playoffs where you are eliminated with a single loss because whoever wins the league will likely have had blown up in at least a few of their matches and probably didn't have any duds. So basically I'm saying you usually have to get lucky to win your league and having a team that has blow up potential can help you get lucky in the playoffs. Fantasy football in the end is about luck and with multiple players someone will probably get lucky so you might as well have a good chance to get lucky yourself.
You may think that argument is total bs which is arguable but the fact is that expected value is everything in regards to win/loss probability and if you can get a high variance player at a discount because they are high variance don't shy away from the opportunity, its all about points per game.