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Understanding Game Variance

bripc23 (bripc23)

BriPC23 is a GrindersU instructor and was the 2013 StarStreet PFBC Runner-Up.

This article explores the variance in the three most popular types of games in DFS: head to head contests, 50/50s a.k.a. double-ups, and large field tournaments. Since each game is structured differently, different variance results. Let’s look at each game individually:

Head-to-Heads

I propose that H2H games have the least variance in all of DFS. This is because H2H pays you according to your “fair share.” Let me explain:

Let’s assume you enter one million H2H contests against one million different opponents. Now let’s say you are lucky enough to produce a 80th percentile lineup on that day. This means you will win 80% of your H2H games and lose 20% of them. On the flip side if you have a bad day and produce a 20th percentile lineup you will lose 80% but still win 20% of your games to people who had an even worse lineup than you. Of course in any one game or any one day you can lose with a good lineup or win with a bad one. However if you enter enough games the odds of losing with a good lineup or winning with a bad one approach your actual percentile rank over time.

That decreases the variance of H2H leagues in such a way that if you are a long-term profitable player and play heavy-volume H2H you can afford to wager more of your bankroll in any one day. You will always win some and always lose some. They key is just to be a profitable player and produce more higher percentile lineups than lower percentile ones over the long run.

Double-Ups

Let’s contrast this with 50/50s. At first glance it would appear that 50/50s offer less variance than H2H because there are more opponents in each game. However I propose that they are actually slightly riskier.

Let’s assume again that you hypothetically enter one million 50/50 leagues. This time when you produce a 80th percentile lineup you will win virtually all of your 50/50s. Conversely, if you produce a 20th percentile lineup, you will lose almost every game. As you can see, there is more variance in both the upside and downside compared to H2H. You are fully rewarded for a good lineup and fully punished for a poor one, not just mostly fully rewarded and mostly fully punished like in H2H.

For further reading I encourage you to check out the below article I wrote that simulates variance in 50/50s.

Tournaments

Neither H2H nor 50/50s hold a candle when it comes to the variance of tournaments, however. Tournaments have two major distinctions compared to H2H and 50/50s: a much smaller percentage of players get paid (anywhere from 10%-25% usually), and those that do get paid get multiple times their buy-in. Because of this, variance is much higher than either H2H or 50/50s and is heavily driven by how often you win the top prize and how often you cash. Much of the value of a tournament is contained in the first few slots of the payout structure. It is entirely possible to play tournaments regularly and cash in them regularly but still be a loser if you never take first place. The implication is two-fold. First, you should build lineups that embrace variance and give you a chance to take first place, rather than just merely cash for the minimum. Second, you should wager a smaller percentage of your bankroll in tournaments than other game types.

For further reading I encourage you to check out the following article I wrote that simulates the variance in a typical large field tournament.

GrindersU Videos: Variance in H2H/GPP Play with CSURam88 and BriPC23

Final Thoughts

I am a huge fan of game diversification. I think you should enter all three of the type of games that I described every day. This is for diversification purposes but also for emotional purposes. There is nothing worse than putting up a big score in a 50/50 but realizing that you didn’t play a single tournament that day and thus missed out on a big score. Similarly, it is a bad feeling putting up a score that doesn’t cash in your tournaments but would have cashed in every single 50/50 that night. By playing all three games at the same time you get the best of all worlds, the lower variance and opponent diversification that comes with playing H2H and 50/50s, and the chance of a big score that comes with playing tournaments.

It should be noted that over the really long term variance washes away and you should be concerned about playing whichever game you believe offers you the highest ROI. Often this is tournaments since they contain the most “bad money” of newer players looking for a big score. For most of us, however, we are concerned about both maximizing profits and minimizing risk in the meantime.



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About the Author

  • bripc23 (bripc23)

  • BriPC23 is a GrindersU instructor and was the 2013 StarStreet PFBC Runner-Up.

Instructor

BriPC23 is a GrindersU instructor and was the 2013 StarStreet PFBC Runner-Up.

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