Daily Fantasy 50/50 Variance
This article is part 2 of my series on variance. Last time we took a look at Daily Fantasy Tournament Variance, and this time we will explore 50/50s. The question once again is what does variance look like and many games do we have to play until we have a good idea of our real ability?
Daily Fantasy 50/50 Variance: Example 1
I will use a $22 50/50 game with a $40 prize as an example. I created a hypothetical player to play in this game. This person cashes 60% of the time for a long-term ROI of 9.1%. Again whether or not you agree with this number is not that important – what is important is the variation around the number, which I will demonstrate.
I simulate my hypothetical player in the 50/50 as follows:
- Generate a random number from 0 to 1
- If this number is below .60, consider it a “cash,” if above .60, a loss
- Repeat this process one million times
I did this and got the following graph. The blue line is cumulative ROI across all trials up to that point, and the red line is the 9.1% long-term ROI that I referenced earlier.
ROI stabilizes at around 500 trials. If you recall when I did this for tournaments things didn’t stabilize until around 1,300 to 6,000 trials depending on what “stable” meant to you.
[It is worth noting that this assumes all trials are completely uncorrelated with each other. If you are entering multiple lineups with similar core players across many lineups, than these volatility figures would be higher for you.]
Daily Fantasy 50/50 Variance: Risk of No Profits
Although in statistics it is not really defined this way, when people talk about variance in DFS, they typically are referring to a risk of losing money. Therefore, I approached the analysis from another angle. I broke my sample into intervals and analyzed profitability (or lack thereof) over these smaller samples. You can then ask yourself the following question: given a certain number of 50/50s, what is the percent chance of losing money? For example, for a range of 100 consecutive games, the picture looks like this (ROI on the x-axis):
In this case there is a 23.4% chance of losing money over any 100 game period. If we extend the sample period out to 1,000 trials the picture looks like this:
Here there is only a 1.0% chance of losing money. In fact at 550 trials is when I first had less than 5% chance of losing money. Recall from the tournament example that the 5% threshold occurred at 2,600 trials.
Thanks for reading and let me know in the comments if there is anything you would like to see from me in the future.