Using Kelly Criterion for DFS Bankroll Management
USING KELLY CRITERION FOR DFS BANKROLL MANAGEMENT
PART 1 - CASH GAMESKelly Criterion is a tool (math, really) used to help determine how much to bet when you have an edge over the house or another player. The math behind it is complex for the casual player but using “Kelly” essentially gives you the optimal amount of your bankroll to bet in order to maximize the growth of your portfolio, or in this case, your DFS bankroll. The key assumptions that feed into Kelly are 1) what the percent chance is that you win the bet (or cash your DFS contest), and 2) what is the return when that happens. Kelly is an aggressive strategy that assumes the probabilities entered are fact. Because we are often dealing with uncertainty in betting or DFS, many choose to leverage a “Half Kelly” or “Quarter Kelly” strategy, to account for either margin of error in the model or less of an appetite for risk. The basic level of Kelly deals with a single individual wager, and most closely can resemble a cash game or head-to-head format in DFS where the outcome is binary – you are either going to win or lose the result, and the payout is known ahead of time. A lot of previous literature I have read has expressed a “90/10 rule” towards managing your DFS bankrolls, by focusing 90% of your bankroll on cash games and 10% on tournaments. The same articles generally talk about risking 10% of your bankroll on a given day. The truth is cash games have gotten tougher, more casual players play tournaments, and most people reading this enjoy playing tournaments more for the entertainment value. While the 90/10 rule may work for some, it doesn't work for me and may not work for you either. The truth is how much of your bankroll you invest in cash games should be mostly independent on whether you invest it in tournaments. If you are very profitable in cash games, you should be playing those regardless of your tournament exposure. You can also take a look at our initial take on bankroll management. In this article, we will explore how we can use Kelly to guide our cash game bankroll management strategy. But first, the elephant in the room: Your Bankroll! I'd venture only 10-20% of DFS players actually play with a bankroll in mind. Ultimately, your bankroll is whatever you would be willing to lose playing DFS before you stopped playing. If you have $500 in your account, but would snap deposit $500 if you lost it all today, then your bankroll is likely $1000+, while a player who only is willing to play through their current funds would have a smaller bankroll. If you have been playing DFS for two or more seasons than maybe your bankroll is your initial deposit plus profits accumulated, minus taxes and money withdrawn for spending purposes (e.g. paying yourself a salary for living expenses versus withdrawing it just to hold on the side). One of the easiest paths to going busto is to not adjust your bankroll and DFS play for tax consequences. If you are playing this for entertainment, that is fine too, but you should still think about things with some level of understanding of your bankroll.
Head-to-heads and 50/50In order to break this down, we need to understand the items mentioned above – the odds that we win the bet and the return when that happens, and how that changes based on DraftKings or Fanduel game formats. What are the odds that we win the bet? This is a somewhat complex topic but for the purposes of determining your bankroll management, lets assume that you are a seasoned DFS player who can access their results and determine what percentage of games they've won in different game formats. A break-even win rate would be 56%, while a 60% win rate would on average generate an 8% return on investment. Understanding your win rate should be a fundamental starting point to determine if you should play cash games. If you are just getting started, you should set an expectation for your win rate. What is the payout? Understanding the payout for winning is also critical, albeit simple. We will use a head-to-head or 50-50 format to start, where the industry standard rake is 10%. In this type of format, the odds offered are typically 0.8 to 1.0 meaning for every $1 you play, you'll receive $1.80 if you win. A simple Kelly Calculation can then be performed to determine the optimal amount of your bankroll that you should risk, which if you have a 60% win rate would be 10% of your bankroll. Using that we can determine a few options for different players based on Kelly: If you have a 56% win rate you should invest 1% of your bankroll, if you have a 60% win rate you should invest 10%, and at a 65% win rate you could invest 21.25% of your bankroll. And of course, if you have a 94% win rate you should invest 86.5% of your bankroll. However, a full Kelly is aggressive and deals with known probabilities. If you have held a 60% win rate previously, it is possible that your win rate will be lower moving forward either driven by increased rake or more challenging opponents or that you have simply been on the right side of variance. Because of this, it would be risky to use a full Kelly approach. Breaking down cash games further, we need to look at double-ups.
Double-UpsDouble-Ups are similar to the 50/50s discussed above but vary in payout structure. For example, the most recent DraftKings Double-Up for the $25 MLB Single Entry has a rake of 12.97% and pays out 500 of the 1149 participants (43.5% of the field). In order to generate an 8% ROI in that double-up, your win rate would need to be 54%. Running this through the Kelly criterion would identify 8% of your bankroll as the optimal bet size. This is interesting to note because if you have an 8% ROI in both game formats you should be taking a more aggressive bankroll approach and playing 50/50s and Head-to-Heads more regularly (where you can play 10% of your bankroll) versus Double-Ups (where you can play 8%) to maximize the growth of your bankroll despite the same “return on investment” from a percentage basis.
Why you should be careful using full KellyThe items discussed above are “full Kelly” but the truth is most players should be cautious using full Kelly and presuming their historic ROI will stay the same. There are a lot of things that can impact your ROI beyond variance if you overestimate your edge: DFS Contest Profitability = Rake x Your Skill x Opponent Skill x Payout Structure x Field Size x Variance. It all sounds simple, right? The Rake. The obvious one, but the fees DraftKings and Fanduel charge impact the profitability of different games. Increases in effective rake over time would dictate reducing your exposure as a percentage of your bankroll. Looking at your 2016 NFL results as part of the sample for your NFL win rate or ROI will skew the results. Basic Opponent Skill. With the increased DFS content (like ours and dozens of competitors), as well as less marketing being spent on new user acquisition, the average player is simply better than they were before and is getting better each year. The basic skill level is getting sharper and if you're not improving, your results will decline. Quality of Opponents in a Given Contest. Another challenge is that as your results improve and your bankroll grows, you will eventually need to move up in stakes in order to get down the same percentage of your bankroll. The rake at higher stakes is sometimes lower, but the skill of your opponents in that specific contest is higher. The cash line in the smaller field, higher buy-in double ups may be 5-10% higher than the same cash line in smaller field formats. If you are sitting $530 MLB Head-to-Heads with “dandydon” and “papagates” the 5.66% rake may not matter, but if you can find soft games with a lower rake it can be fruitful. Payout Structure and Field Size. This will be covered in a GPP section, but ultimately the profitability of any DFS game and your bankroll approach will be based on the rake, opponent skill, payout structure and field size. Payout structure and field size have some impact on your overall expected profit (since as field size increases, the average quality of opponent may be decreasing) but they mostly impact variance and how long it will take to realize any edge you do have. In Summary.... There is no "rule" that can determine how a DFS player should allocate their bankroll. Even grinders purely seeking to maximize profits will need to find their own path to success. By leveraging our historical results and win rate, and adjusting those for the current rake and skill economics, we can try to get approximate guidelines. For profitable players, these principles would suggest playing 1% to 10% of your bankroll in cash games on a given slate. In Part Two we will discuss things like Winner Take All 3-mans, Leagues and GPPs and how some of the same basic principles can help with your bankroll management...
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