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Feb 11, 2017
Feb 11, 2017

The Kelly Criterion - A stock trader and betting expert’s perspective

Is the Kelly Criterion appropriate for a professional sports betting fund?

An in-depth analysis of one of the most popular staking methods

The Kelly Criterion - A stock trader and betting expert’s perspective
Wisdom of the crowd insight - based on the Betting Resources list of most popular articles - underlines the perceived importance of staking methods. My experience echoes this, so when invited to contribute a betting strategy article, Kelly Criterion seemed both a natural choice and the perfect way to underline the relevance of what I learned on Wall Street and successfully applied to sports betting.

Relying on my decade-plus experience as a Wall Street equities market maker, I spent time in Trading Bases detailing the similarities I saw between the NASDAQ marketplace I first entered in 1996 and the sports betting industry as it stands today.

Kelly Criterion

Popular staking method which suggests that stake should be proportional to the perceived edge.

In my interview with Pinnacle, it was clear they embraced the attitude I suggested was needed to truly expand the industry as a whole, and, as a result, attract the same type of analytics-based bettor that led to a participation explosion in poker and fantasy sports. There is no better example of this than Pinnacle’s Winners Welcome policy, as well as their cogent explanation of why a market maker in any market should embrace the presence of, what we refer to on Wall Street as, “smart money.” 

The Winners Welcome policy is spelt out in a series of articles in Pinnacle’s Betting Resources section - something that encourages customer participation in sports betting through education. Given the questions that have resurfaced both in the interview and from readers about my bet sizing strategies, this appears to be the perfect forum to formally discuss the topic further.

Wall Street trading applied to betting

Before I get into the merits of the bet sizing method I used versus the widely followed Kelly Criterion (Kelly) it’s important to recognise the importance of the cross-pollination of ideas across different industries or disciplines. 

When I joined the accounting firm of Arthur Andersen, the consulting division illustrated the importance of evaluating best practices across industries by pointing out that Southwest Airlines improved the turnaround time of its fleet between routes not by studying other airlines but instead, the process of NASCAR pit crews.

In the last ten years, a period covering economic booms and historic busts, the value of an investment in the S&P 500 has fluctuated 0.85% a day.

For my part, I bring to this discussion a Wall Street background to managing an investment portfolio, regardless of the underlying assets. First, let’s establish that while everyone wishes to make money when they place a bet, the vast majority of sports betting falls under the heading of entertainment, not investment.

The rest of this piece focuses on sports betting performed by a professional as an investment vehicle, perhaps with others as passive investors, like the fund I ran for the 2012 MLB season in Las Vegas.

The importance of correlation

The aforementioned structure falls under the financial industry heading of an ‘alternative asset’. Like backing a number of aspiring golfers attempting to make the PGA Tour or a handful of poker players on the tournament circuit, these are inherently attractive investments to their backers because the returns of the investment are uncorrelated with traditional stock and bond markets. Hence the term, ‘alternative assets’. 

The appeal of a sports investment fund is that truly uncorrelated investments are difficult to find. Investing in rare wine or comic books may seem uncorrelated to fixed income and equity markets but all it takes is a crisis in the latter for investors in the former to learn that their investments weren’t uncorrelated at all.

Evaluate your betting with the S&P 500

If nearly all financial markets are correlated, what is it exactly that they are correlated to? In America, the market benchmark against which all other assets are measured is the S&P 500. Representing the vast majority of the American economy, the 500 companies that comprise the S&P 500 also make up an investable instrument that is the equivalent to a concept instantly familiar to analytics-based baseball bettors, the replacement player. 

Except for investors, the concept of the replacement player is even easier to grasp than it is in baseball. Buying shares in the S&P 500, through a readily-tradable ETF (Exchange Traded Fund) or mutual fund, can be achieved at virtually no cost. Just as there is a baseline performance expectation for the replacement player in baseball, so is there in the financial markets.

Assuming your 2% edge is exactly correct, there is a greater than 10% chance that your fund will be down at least 40% at the end of one year.

Investors should expect the S&P 500, based on decades of performance, to return 8% a year over the long-term1. Of course, the returns won’t be smooth; market fluctuations and economic cycles introduce a high degree of variance in the short- and medium-term returns of the stock market and result in a measure of quantifiable risk.

Essentially, across the entire spectrum of financial investments, higher expected return comes with more short-term risk. Fortunately, we can measure that risk, or variance, exactly. In the last ten years, a period covering economic booms and historic busts, the value of an investment in the S&P 500 has fluctuated 0.85% a day - data provided by Bloomberg from over nearly 2500 trading days from 2007-2016.

So an 8% expected annualised return has a recent historical variance of 85 basis points a day. If you can find an investment that returns 8% with less variance, or ideally, find an investment that returns more than 8% a year with the same amount of risk (as the world’s most popular benchmark for stock market investing) you’ve created a superior alternative to equity investing that you can legitimately market to others as a viable investment.

What's wrong with the Kelly Criterion?

The problem with using Kelly is that no matter what you calculate your expected return to be, your variance will be ridiculously, and to my eye, “uninvestably” high.

Take, for example, the most common illustration of the Kelly approach to bet sizing, the ability to lay even odds on a coin flip featuring a weighted coin with a 52% chance of landing on heads. Kelly suggests a bet on heads of 4% of your bankroll. It is empirically correct that this wager size maximises profit but it results in an unacceptable level of variance if you are endeavouring to professionally manage a sports betting fund for others.

Go back and look at your log of bets of a long period of time, ideally something around 250 betting days, and calculate what bet size would produce a daily variance of 85 bps.

The stock market is open 250 days a year and if you bet baseball on a daily basis from Opening Day through the World Series, you’ve got a season approaching that length with nearly 2,500 games to choose from. Imagine spotting a 2% game each day to invest in. After 250 days, assuming your 2% edge is exactly correct (much more realistic in say, blackjack card counting than modeling sporting event outcomes, but that’s a topic for another discussion) there is a greater than 10% chance that your fund will be down at least 40% at the end of one year. That is, to repeat what I wrote in the preceding paragraph, unacceptable as an investment vehicle.

I can’t tell you what your exact bet size should be; correct staking varies by expected edge, the variance of that edge, and the number of bets placed etc., but I can tell you how to evaluate your results from a post-mortem perspective. Go back and look at your log of bets of a long period of time, ideally something around 250 betting days, and calculate what bet size would produce a daily variance of 85 bps. If your return under that sizing strategy is greater than 8%, you may truly have created an alternative asset suitable for soliciting outside investors. 

The Kelly Criterion and risk management

One more thought on Kelly as it relates to the business of risk management. A 2% edge is meaningful – entire casino empires have been built on a similar edge. For example, the standard, 38-slot roulette wheel offers the house an edge of 2.6% on a bet that pays even money. In this case, Kelly suggests the optimal bet size is not 4% but 5.2% of bankroll!

The Wynn Resorts Corporation is worth more than $9b based on its stock market capitalization; MGM Resorts International is worth in excess of $16b. 
Ask yourself this: Would Steve Wynn ever let someone come into his casino, walk up to a roulette wheel, and bet $500 million on black? Could Warren Buffet place a nearly $1b roulette bet in an MGM-owned casino? No. And it’s the same reason you, if you are seriously betting on sports as an investment for yourself or others, should never rely on the Kelly formula to determine your bet sizes.

References:

1. 20 year return of the S&P 500 showing an annualised return of 7.59% 
- it's generally regarded that an 8% return is the industry standard expectation.

Apply the Kelly Criterion to betting now
Joe is a former Wall Street trader and author of the bestselling non-fiction memoir, Trading Bases: A Story About Wall Street, Gambling, and Baseball. His book examined the data analytics overlap that exists in the financial industry, sports betting, and, as made famous in Moneyball, Major League Baseball. The book received substantial critical acclaim and was a best-seller in a number of seemingly disparate categories; during 2013 Trading Bases was named a Top 10 Business book by Amazon.com, a Top 10 Sports book by Publisher's Weekly, and a Top 10 Non-Fiction book by Fortune.
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