Understanding Variance in the Context of Daily Fantasy Sports
I’m a member of Rotogrinders.com and I frequent the forums there. Recently there was a thread posted on the topic of variance, and being statistically minded my interest was naturally piqued. I started writing a response on the thread, but it turned into such a rambling dialog that I decided I’d just make it a blog post, and provide a link to it on the forum for anyone who was interested (God help them). So here it is…
I’m glad I found this thread. My background is computer programming, physics and finance (and the intersection of those things) so when I see a forum post with ‘variance’ in the title I can’t help but get interested.
But now that I’ve read through most of the comments here, I’m starting to think that ‘variance’ is almost never used correctly in the context of DFS. What is being discussed here is, almost universally, ‘diversification’ – in finance diversification is any attempt to remove unsystematic risk from a portfolio. It’s buying hedges against heavily owned positions, or simply owning multiple stocks in different industries that typically zig when their counter parts zag.
This is very different from variance. The most diversified bag of equities is a bag that includes every stock in the world. To approximate this bag, let’s just use the S&P 500. So, owning the S&P 500 is, in theory, taking the most diversified equity position possible (notice I’m intentionally leaving out bonds, cash, and alt. investments for simplicity here). That ‘most diversified bag’ will still experience the *statistical phenomenon of variance* in it’s measured performance; that is systematic real-world effects which cannot be diversified away will impact it’s ROI.
Are there a corollaries between finance and DFS? Well, they may be strained, but I think they exist. In DFS the most diversified portfolio would be having every possible team playing against every possible opponent. The expected return of a fully diversified DFS portfolio is probably *very* negative – as you are always paying the rake, and most possible teams are degenerate and would easily lose to anyone who thought about their team-construction seriously.
So I think the best way to understand diversification in DFS is based on one’s projected player performance. Since, theoretically speaking and ignoring bankroll and game-selection issues for a moment, the ROI for someone in DFS is based on their skill level at projecting player performance – ‘investing’ in DFS is really an investment in one’s ability to predict the fantasy performances of athletes. Diversification then refers to one’s financial exposure to athlete risk. Even if, based on your projections, there were only 15 golfers (pardon me, PGA is my sport) projected to be great picks for the week, there would still be 5,005 unique teams of 6 to construct using only these top 15 projections.
Undoubtedly some combinations wouldn’t fit within the salary cap, but perhaps 2,500 of the 5,005 teams them are actually affordable Complete diversification would be owning all of those teams – and playing them in equal measure against every opponent. Diversification in DFS is much more expensive than it is in finance exactly because you can’t simply buy an ‘index of reasonable teams’ in the same way that the S&P 500 is an ‘index of reasonable stocks ‘- there is a combinatorial explosion of player combinations and there’s no chance to get equal exposure even to the subset of combinations you think are ‘good’ (i.e. projected to perform).
In as much as I’ve thought about diversification in DFS I think it comes down to one basic tenant: play your best projected teams, no more, no less (if you can afford it).
Variance is something wholly different from diversification. I’ve noticed that there’s a grinders norm that says something like: if you’re practicing proper bankroll management you should never invest much more than around 10% of your bankroll in a given night. This is a strategy to handle variance. Most nights in DFS, assuming you are playing a diversified bag of your top teams, are still either going to be great and you win everything (your player projections were more right than the next guy), or not so great and you lose most contests (your player projections were less right than the next guy). It’s OK to talk about having an ROI of such-and-such, but this ROI should not be viewed like the ROI of the S&P 500. The S&P 500 never goes to 0 (it’s possible, but hasn’t happened yet).
If I had to describe the behavior of DFS players in the terms of finance I’d say we are all a bunch of options traders – we have most of our money in cash, and only put a little bit of it at risk at a time because the odds of losing all of it are relatively high. If you’ve never read books like The Black Swan, Fooled By Randomness, or Anti-Fragile you probably should (they are all by an insane financier named Nassim Taleb, but the are fun reads and the ideas are directly applicable to both finance and DFS). But variance describes the risk in your DFS matchups that is un-diversifiable – the risk that your projections/thought process for the week are just wrong. Anyone who plays DFS knows this feeling. This week, for instance, my top projected golfer is Hunter Mahan, who is entering into Sunday tied for 58th! It’s not that my projection methodology is wrong, most golf minded DFS players would have put Mahan at the top of the projected pack this week (though admittedly I was higher on him than most). It’s that sports really are unpredictable, there’s nothing you can do to change that, so even using fully diversified rosters of your most sound and highest quality picks you will lose often.
That’s variance – not who do I put on my team, or who do I go H-2-H against (diversification) – but rather given that I’m using the soundest strategy possible to me, some weeks I will be highly profitable, others I’ll fall flat on my face. Some years the S&P is up, other years it’s down. So variance isn’t something you can actively work to get rid of – in DFS your variance is largely determined simply by how good of a player you are. If you’re really, really good your variance is going to be lower (because, while you will still lose, you will lose less often than you win). Similarly, if you’re really, really bad your variance will be lower (because, while you will still sometimes win, you will win less often than you lose). The person who has the hardest time with variance is the average player – week to week they are not sure if they are more likely to be up than down. It’s very difficult to try and tease out whether you are slightly above average or slightly below average, variance is a sneaky bastard in that way. But it’s not diversification. Even a diversified set of teams will experience variance – IMO, in the context of DFS we should be talking about variance as a statistical phenomenon based in the undiversifiable component of risk, and diversification as a method for smoothing out non-systematic player-risk.
Anyway – I wanted to bring up this subtle distinction so that we can talk about diversification vs variance more clearly. They are two important topics, and to have dialog on these subjects it would help to tease them apart and have clear definitions of what each one represents… Hopefully I’ve added a modicum of clarity here, rather than muddying the waters further.