What is the Kelly Criterion?

John Kelly created the Kelly Criterion in 1956 when he was working for AT&T’s Bell Laboratory. Over time, the Kelly Criterion has become increasingly popular across the betting industry and finance sector and is now commonly used by bettors and traders alike (often referenced simply as “Kelly”).

In short, the Kelly Criterion is a formula that calculates the proportion of existing funds that should be risked in order to maximise the potential return of a bet or investment. This means that it takes into account how much money you have to bet with, how likely your bet is to win and how likely it is to lose to help you stake accordingly.

Although it’s one of many tried and tested staking methods, the Kelly Criterion is seen as the best due to the fact that it protects your bankroll while still ensuring you stake funds that are proportionate to the positive expected value (or “edge”) that you have over the market.

How does the Kelly Criterion work?

Staking methods can vary greatly from the straightforward flat or fixed bet staking (betting the same amount every time), to sequential methods like martingale (doubling your stake after a loss) and Fibonacci (moving up one in the sequence of numbers after a loss and down two after a win).

The Kelly Criterion is different to all of the common staking methods listed above in that it is proportional. The amount you bet when you use the Kelly Criterion is always a proportion of your bankroll in relation to your perceived advantage.

The key elements of the Kelly Criterion are that your bankroll should never run out if you lose and that your funds will grow exponentially if you win. If you suffer a series of losses, the advised bet amount will decrease to remain in line with your existing bankroll. The inverse of this is also true. If your bets result in a profit and increased bankroll, the amount you bet moving forward will then also increase.

How to calculate the Kelly Criterion

The Kelly Criterion formula might seem confusing to some but once you break it down, it is very easy to understand and apply to your own betting.

f is the amount you should bet (fraction of your bankroll).

b is the decimal odds on your prospective bet – 1

p is the probability of winning (as calculated by you)

q is the probability of losing (1 – p)

We can now use a practical example to help make this clearer. Let’s say Roger Federer is playing Rafael Nadal in the Wimbledon final. Federer is listed at 1.598, while Nadal is 2.490. The odds are giving Nadal around a 40% chance of winning, but you think he has a 48% chance of winning.

This means:

b is the decimal odds on your prospective bet (2.49) – 1 = 1.49

p is the probability of winning (as calculated by you) = 0.48

q is the probability of losing (1 – 0.48) = 0.52

Therefore, in the example provided above, the Kelly Criterion would suggest staking 13% of your bankroll on Rafael Nadal to beat Roger Federer.

While it is important to understand how to calculate your stake amount based on the Kelly Criterion formula, you can use tools such as Excel to automate this process or any number of the free Kelly Criterion calculators available online.

What are the criticisms of the Kelly Criterion

The most common criticism of the Kelly Criterion in a betting context is that it fails to account for the volatility of the betting market and impact that variance can have on results.

This means you could build your bankroll with several small stakes on bets at high odds where the edge you have is perceived to be small. However, if your model finds a big edge on a small-priced option in the market, your work in building your bankroll could be undone in one fell swoop were that bet to lose.

There have been numerous studies into this issue and the solution appears to be a fairly simple one – a fractional version of the Kelly Criterion. Bettors will now adopt a 1/2, 1/4 or 1/8 Kelly Criterion bankroll strategy (consistently using the same fraction as part of the method). This means if the Kelly Criterion advises a bet at 10% of your bankroll, if you’re using 1/2 Kelly it would be 5%, 1/4 2.5% and 1/8 1.25%.

Another common complaint about the Kelly Criterion is how to manage multiple edges on concurrent bets. There is a potential scenario where a bettor finds an edge on Team A vs. Team B while also having and edge on Team C vs. Team D with both events taking place at the same time. Additionally, using the 1X2 market or a long list futures market as an example, it could be possible that two, three or even more of the outcomes in a multi-way market provide a bettor with an edge.

In both of these scenarios, the popular complaint levied at the Kelly Criterion comes back into question. Depending on the number of concurrent events and the size of the perceived edge, using the Kelly Criterion could result in a stake suggestion that will wipe out the bulk of a bankroll. In some extreme cases, it could result in a suggest stake amount that even exceeds the current bankroll.

It is also worth considering whether the Kelly Criterion is the right staking method based on your betting profile. If you are disciplined and commited to developing an edge and putting in the time it takes to build your bankroll then Kelly is probably the right way to go. If, however, you’re merely betting as a mean of entertainment or the process behind placing a bet is not a thoroughly calculated one then a sticking to relatively small stakes from your overall bankroll (if you have one) is advised.

If you would like to learn more about the Kelly Criterion criticisms (and the potential solutions), then I would suggest reading a previous Betting Resources article by @PlusEVAnalytics.

Final thought: Work on your edge

One final thought for bettors using the Kelly Criterion or a fractional version of it is that this method is based on your calculation of outcome probability. Optimising your bankroll management in relation to your edge is all well and good, but you also need to put work in to ensure it is a legitimate edge you have over the market.

There is a lot of work involved in producing more accurate outcome probabilities than those available in the betting market, but you also need to dedicate time to refining your model and continuously testing to eliminate the influence of luck and randomness in any positive results.