The Effect of Field Size on DK Quarter Jukebox – A Quantitative Analysis
(Feb 1st, 2018)
With a 5-game slate tonight, a lot of people in slack have been talking about wanting to practice their MME (mass multi-entry) skills tonight. As many coaches have suggested, if you’re new to MME, then start with small stakes. The DK Quarter Jukebox [20 max entry] is a good starting place. The following analysis is from a night back in December when I entered 20 of the same lineups into both a $10K Quarter Jukebox and a $3K Quarter Jukebox ($0.25 x 20 LU = $5 x 2 contests = $10 total).
I. What’s the difference between the Quarter Jukebox’s anyway?
In the morning, the site will release a large field Quarter Jukebox, and then if it fills up fast enough, they release a smaller field Quarter Jukebox, and so forth. The site does this in such a way that it rarely loses any money in these guaranteed prize pools (pretty genius algorithm if you ask me).
DraftKings designs the majority of its various GPP contests to all have the same expected Return on Investment (ROI). You can find this by calculated the expected value of each tournament and seeing how much you’re expected to lose for each entry (which is set at -15.9% for nearly all DK GPP contests).
But despite both of these contests having the same entry fee and same expected ROI, the cash lines for various profit multipliers are NOT the same, primarily due to difference in field size (and in part due to slight differences in payout structure).
II. Comparison of cash lines
This data was taken from the $10K Quarter Juke (47562 entries) and $3K Quarter Juke (14268 entries) on December 5th, 2017. That night was a small 3-game slate, which is perfect for GPP MME and terrible for cash. Here were the actual required scores in those contests on that night required to return 2x, 3x, 4x, 5x, 10x, and 20x your initial $0.25 investment:
(note: when I made all these tables I called it the “Quarter Arcade” which is the old name DK used to call these contests).
As well as the differences between the top 3 scores (and multipliers) between the two:
See any interesting observations? For those of you that are more visual, how about the same info in graphical form?
III. Frequency distribution graphs
The following graph is a frequency distribution of how entry scores are distributed across the spectrum for both the $10K QJ vs. the $3K QJ. In general, a frequency distribution shows you how many entries achieved a certain score. I grouped together 10-pt bands from each contest to count up how many entries scored. So for example, the point in the top graph means that 5800 entries finished with scores from 260 – 269.75 fpts.
The top blue graph is of the $10K QJ and the bottom red graph is of the $3K QJ. The vertical dotted lines on each graph show cash lines for various profit multipliers in that tournament, in order of left to right: Double up (2x), Triple up (3x), Quad up (4x), Quint up (5x), 10x, and 20x
X-axis shows the scoring band (ex: x = 210 is for entries that scored 210 – 219.75 pts)
Y-axis shows the number of entries who scored in that 10-point band
Whoa, because these contests have so many entries, their distributions are very nearly a Normal Distribution.1
[1 – the first time I mapped this out, the math guy in me was blown away… of course, it makes so much sense, but nearly every large field GPP contest in DFS fits a normal distribution or a bell curve. The larger the field, the more the entire distribution tends towards being normal. This is actually an important theorem in Statistics called the Central Limit Theorem.]
Seeing how these thresholds compare is easier if we stack the two graphs on top of each other:
Notice how the majority of payouts are easier to achieve on the blue graph (the larger $10K QJ) than from the red graph (the smaller $3K QJ).
IV. Takeaways
- Cashing for small multipliers is generally easier in the larger field tourney
- The payout lines are generally lower as a result of less variance in larger fields. Variance goes down with more entries, and the distribution tends to shift more and more to a Normal Distribution as the field gets larger.
- A common misconception is that it should be easier to cash in smaller fields since “there are less people to beat”. What might be a better way to think about it is that in a small field a few lucky entries will have a more of an adverse effect on your ability to hit the cash line. For example, 2 entries in a 10-person league hitting the nuts player who goes off in one night is 20% of the entire field; it is far more unlikely 2000 players out of 10000 will get lucky and choose that same nuts player.
- I’ve also read somewhere that there are more dead entries (reserved but never drafted) and lineups affected by scratches in larger fields, but I’d need to look into this statement further to see if it has a big enough effect on the cash line differences.
- If your lineup is a really high scoring one (330 pts+ on this particular night), you’re more likely to snag a top place finish in a smaller field tourney
- While it becomes harder to pass the cash threshold in a smaller field, it is easier to have a nuts lineup land in the top few spots. As contest size gets larger and larger, the top winning score should continue to rise and the closer the top lineup gets to being the “perfect” lineup (best possible lineup on a given night). Think of this like seeing a Royal Flush in poker; you’re unlikely to see one playing in a 10-person game, but at the World Series of Poker with 10,000+ players, the odds of it happening is more likely.
– RJC