Variance of DFS Tournaments (such as Draft King’s Millionaire Maker)

I was wondering if anyone has a resource for the variance of large daily fantasy sports tournaments such as a DK Millionaire Maker? An approximation would be fine. Just want to compare it to some casino games. With the massively skewed towards the top pay structures, I assume the variance is crazy high. Subjectively, but without data to back it up currently, it seems these games aren’t much better than lotto tickets. For calculation purposes I guess we’d have to make the assumption that there is no “skill” involved and every result (1st place or last) has the same, equal chance of occurring.

Thanks in advance.

Answering my own question but I guess if we assume equal probability for every result it would just be the standard deviation of the mean of these results, squared?

First of all, I am no fantasy expert. I dabble and am ahead in the NFL lifetime.

I'm not sure what you mean by all outcomes, for the sake of calculation, being equal, given the skewing of the prizes.

In any event, you might want to factor in:

1) Back when Fanduel and Draftkings were separate entities, and the NYTimes did an expose on this, the workers at each company were banned from playing the game where they worked. But that didn't stop the people from using beards and in addition, swapping off the info so Draftkings personnel played at Fanduel and Fanduel employees played at Draftkings. Anyway, the point was, economies of scale worked quite well when teamed with insider trading info as to which players were taken by what percentage of contest players. A small cadre of players dominated the prize money, until exposed.

2) Most of the skewed prize money monster pools are still "unlimited entries." But you can go to "single entry" contests to skirt the economy of scale problem to a large extent. The feds made Draftkings and Fanduel institute single entry contests in a legal negotiation.

3) You can always play simple head to head contests. Obviously those contests involve judgement and skill.

Thanks for the response.

Agree with all of the above. For all intents and purposes I know large scale DFS tourneys (especially if playing casually/not maxing out entry numbers/etc) are a sucker bet. I’m actually not even really into DFS, other than the occasional dart throw if nothing else is going on. I mainly wanted to figure some calculations for purposes of my own interest and for discussion amongst friends who are more into DFS.

So for that reason I was interested in calculating variance of the different games. Similar to how the variance of say single hand Jacks of Better VP is around 20, but Multi-Strike JoB is around 300. I wanted to find the variance of a large DK tourney to highlight the point of how sucker-bet-ish/complete flier nature, these tourney are.

By assuming equal probability of outcomes I meant equal chance that your one entry would finish in any of the 200,000ish plus places. Of course, you chance of losing money on any entry is much higher than winning on any entry, but each place would have equal probability.

Thanks for spelling it out for me. What I have found most interesting is the decision-making process of the mass of contest players. I walk away realizing two somewhat different things that relate to what we agree on above. First, I am stunned, as independent as I consider myself regarding most things, how part of a "group mind" we all are. I'm sure this has fascinating political ramifications regarding how we respond to limited media sources, but sticking with the topic at hand -- we and all 200 million adult Americans wind up drawing very similar conclusions regarding what players are worth what and can do what to whom. It's stunning how lemming-like we all are when making choices from limited population pools like these. Second, and this is where the Draftkings and Fanduel employees had big advantages when they were playing and could access percentages when the general public could not, the general public does really gravitate to the name stars as if they were Greek gods. The big names draw action more than their degree-of-being-better suggests. So any week wherein there is some performance variance and the big names don't dominate, the general public does not do well.

All good points.

I think IN GENERAL, the public does not do so well in DFS, at least in these big tourneys.

The more I look into and think about these "millionaire maker" events, the more I believe that these are essentially lotto tickets. At least if you are playing casually and by that I mean only entering one, or a few, lineups. I am at the point where I believe there is almost no skill involved in selecting the players. Well, let me word that different, I believe there's almost no skill that can be reliably reproduced regarding identifying which players will do well enough in any given week to win the tournament. IF there is skill involved, that skill appears to be in lineup optimization and differentiation. Meaning perhaps the skill is not knowing who to play yourself, but knowing who everyone else will be playing, and optimizing lineups which DONT utilize those highly owned players. Which makes sense, if you are in a tourney with almost 250k entries and a limited pool of players to choose from, you aren't going to win the 'ship unless you have a unique lineup. Having uncommonly played players is the only way to stand out. This also highlights your other point, about lack of fair play. This is why that insider info was so important, and why it was so obviously cheating.

Another thing that came up a couple years ago and I am SURE still goes on, is circumventing the max entry limits. Professional DFS guys were pooling lineups, essentially circumventing the 150 max entries by going in pairs or groups and playing different lineups from each other. So instead of having 150 unique lineups you could have 300, or 450, or 600. Depending on how many people you had in your pool. From all reports, the DFS companies were WELL AWARE that this was happening and were turning a blind eye. Yet for a casual player who may only play a couple entries a week, they will lock the account in a heartbeat if he and his significant other log into the app from different locations on the same day. Supposedly the pooled pro players was cracked down on, but I don't buy that.

Interesting discussion, I am still interested in the original question RE: variance of these big tourneys, if anyone has that data or knows how to calculate it. If its just the standard deviation of the mean of all the possible outcomes (i.e. finishing places) squared, that would calculated out to be a variance of like 4 million, which seems inaccurate if you compare it to the variance of commonly played casino games, say VP (where the least volatile games are around 20, and the most volatile VP games, like multi-strike, are around 300). I was not able to find variance of big prize pool lottery but my assumption is the pay structures are similar to these DFS tourneys (huge lean towards jackpot winner, and huge drop off after the jackpot) and thus the variances would be similar.

I did just find a pretty good statistics article talking about variance in Powerball. Variance will of course depend on the jackpot value, which changes in powerball, but SD seems to be around 9,000, which would mean a variance of around 81million. Powerball has the highest jackpot (and to my knowledge most skewed distribution of total payout towards the jackpot) of any lotto game, but it puts the 4mil for DFS millionaire maker in perspective. My guess is that the 4mil variance for DFS Millionaire Maker is accurate, and is probably around that of a scratch off lotto ticket with a similar cost/pay out (say a $20 ticket with a Million Dollar top prize), although I can't find data on scratch off lotto tickets.

If anyone is interested the article is here:
/doi/full/10.1080/10691898.2005.11910555

Quote: handsNftRmangos

All good points.

I think IN GENERAL, the public does not do so well in DFS, at least in these big tourneys.

The more I look into and think about these "millionaire maker" events, the more I believe that these are essentially lotto tickets. At least if you are playing casually and by that I mean only entering one, or a few, lineups. I am at the point where I believe there is almost no skill involved in selecting the players. Well, let me word that different, I believe there's almost no skill that can be reliably reproduced regarding identifying which players will do well enough in any given week to win the tournament. IF there is skill involved, that skill appears to be in lineup optimization and differentiation. Meaning perhaps the skill is not knowing who to play yourself, but knowing who everyone else will be playing, and optimizing lineups which DONT utilize those highly owned players. Which makes sense, if you are in a tourney with almost 250k entries and a limited pool of players to choose from, you aren't going to win the 'ship unless you have a unique lineup. Having uncommonly played players is the only way to stand out. This also highlights your other point, about lack of fair play. This is why that insider info was so important, and why it was so obviously cheating.

Another thing that came up a couple years ago and I am SURE still goes on, is circumventing the max entry limits. Professional DFS guys were pooling lineups, essentially circumventing the 150 max entries by going in pairs or groups and playing different lineups from each other. So instead of having 150 unique lineups you could have 300, or 450, or 600. Depending on how many people you had in your pool. From all reports, the DFS companies were WELL AWARE that this was happening and were turning a blind eye. Yet for a casual player who may only play a couple entries a week, they will lock the account in a heartbeat if he and his significant other log into the app from different locations on the same day. Supposedly the pooled pro players was cracked down on, but I don't buy that.

Interesting discussion, I am still interested in the original question RE: variance of these big tourneys, if anyone has that data or knows how to calculate it. If its just the standard deviation of the mean of all the possible outcomes (i.e. finishing places) squared, that would calculated out to be a variance of like 4 million, which seems inaccurate if you compare it to the variance of commonly played casino games, say VP (where the least volatile games are around 20, and the most volatile VP games, like multi-strike, are around 300). I was not able to find variance of big prize pool lottery but my assumption is the pay structures are similar to these DFS tourneys (huge lean towards jackpot winner, and huge drop off after the jackpot) and thus the variances would be similar.

Now that I have a better handle on what you mean, I can agree with you. As I said, I'm no DFS expert, but I have managed to grind out a small profit, all of which is from the NFL. I usually stick to "single entry" tournaments just because of the mass coordinated entries of the unlimited entry contests. So this week, I played about a dozen entries in one of those millionaire maker type deals. I was a little shocked at the pay structure with the lotto first place, as you say, and then the huge drop-off. You have to be correct in that the variance is lotto-like.

My initial take is that the way to have a chance to win one of these is to commit to some far fetched scenario and invest 10K or so in going after it. Like being a team doctor and knowing certain players have covid and backups will play against a shoddy defense like, say, the Falcons.

As you mention, I'm sure the max entry limits are circumvented. As someone who coordinated small cartels in the old Boyd NFL no-spread contests, I can assure you that Boyd didn't care about the circumventions either. The per person limit was five entries. I coordinated maybe 80 at the most any given season, and managed a profit all but two season. I know for a fact that out of the 30K entries, one group coordinated 1100 entries, making my little group look like nothing. The only way that 1100-entry outfit missed out on the weekly first place was if multiple touchdown-plus underdogs won. I'm thinking that DFS works the same way. The only way the coordinated cartels fail to snag the weekly million is if multiple sleeper players hit the top 10 leaderboard for scoring.

I had to share this player summary from Fanduel for the Broncos/Jets game tonight. Very rarely do you read something this subjective and LOL tilted-but-accurate regarding any of these teams. It's about Jamison Crowder for the Jets:

"Pelissero says Crowder isn't 100% healthy, but he'll be giving it a go to try to help a desolate Jets offense that has been a wasteland for fantasy football production through three games."

Now understand that thousands of DFS players read these summaries each week. A little influential, wouldn't you say?

So of course I used him. And other Jets. They really are desolate and a wasteland, but tonight a movable object meets a resistible force, so anything can happen.

That’s some really good data on the Boyd contest, not surprising but a good confirmation.

Also, I like your idea of going contrarian with the DK recommendations. I still don’t think it will matter much if it’s one of those huge tourneys unless you are optimizing the max 150 entries (even then it’s somewhat of a dart throw especially with the likely max entry circumvention), because what’s somewhat unique in these is you often have to have a combination of the chalk plays and the fliers that hit. Like you probably couldn’t win the millionaire maker last week without Kamara. But even if you played him you’d still have to hit on the deep fliers that went off to bring down the ship. If you have one team and played him , odds of hitting the flyers are very slim. if you max out 150 and play him say at 30%, at least that gives you 50 chances to hit on that deep cut flier. 200 chances if your circumventing rules and entering 600 total with 3 of your buddies. You get my point haha.