# Kelly Criterion Sports Betting Strategy

The Kelly Criterion is a strategy that can be used in several
forms of gambling, including sports betting. It can also be a
resource for various forms of investing too, as its primary
function is to create the right balance between risk and reward
while reducing volatility. In relation to sports betting, it's
about **maximizing potential returns on wagers** and minimizing the
chances of losing an entire bankroll. As these are two of the
fundamental goals when betting on sports, the Kelly Criterion is
a strategy worth exploring.

Although there are some complexities involved in using this betting strategy, it's popular among many bettors. In fact, there are many professional gamblers who swear by it. However, with that being said, there are also many experts who claim that it's useless. In this article we'll try to establish who's right and who's wrong.

To start with, we'll answer two of the most commonly asked questions about this strategy.

- What is the Kelly Criterion?
- How is the Kelly Criterion used in sports betting?

We'll look at the math of this strategy too, explaining exactly how it's used in practice. We'll also examine its advantages and disadvantages and, to conclude, we'll offer our view on whether or not this strategy is worth using.

We've included this article on the Kelly Criterion in our strategy section because using it is widely considered to be a betting strategy in its own right. However, it's essentially just a specific type of staking plan. You might also be interested in reading our article on staking plans and how to use them for supplemental information on the subject.

## The Kelly Criterion & Sports Betting

The Kelly Criterion is basically a mathematical formula that can be applied to determine the optimal sum of money that should be invested or wagered on an opportunity. It takes into consideration the total amount of money that's available to use and the expected return.

In a sports betting sense, it can therefore be used to
**calculate how much you should stake** on any wager you place. The
formula, which we'll explain shortly, will calculate the
"correct" amount of money for you to risk relative to the size
of your betting bankroll.

This probably seems incredibly simple so far, but there's actually more to it than you would expect. In order to use the formula effectively, you have to include the expected chance of a wager winning. This is because the main purpose of the Kelly Criterion as a betting strategy is to make sure that you stake higher amounts when placing wagers with a higher probability of winning and lower amounts when placing wagers that have a lower probability of winning. In theory, doing this means your overall returns will be higher and your overall losses will be lower.

The exact probability of any sports bet winning is uncertain though, as it's based on so many different factors. Working out how likely a wager is to win ultimately comes down to some level of personal opinion, so there's certainly no way of coming up with a definitive, correct answer. This is where using the Kelly Criterion gets more complicated. It doesn't work unless you can assign probabilities with some degree of accuracy. This isn't easy to do, which is precisely why so many people lose money when betting on sports.

For now, though, let's assume that you are able to assign probabilities to your wagers at least reasonably accurately. With this assumption made, you need to learn the relevant math.

For the purposes of the Kelly Criterion formula, it's easiest to use odds in the decimal format. If you aren't familiar with this format, we would advise using our odds convertor tool. This can help you convert odds from either moneylines or fractional formats into decimal formats.

## The Kelly Criterion Formula

To use the Kelly Criterion as a betting strategy, you have to apply the following formula every time you place a wager.

This formula doesn't tell you much by itself. You need to understand what all the components represent, which we explain below.

- "b" is the multiple of your stake you can win from the proposed wager. With decimal odds, b is equal simply to the odds minus 1. For example, a $10 wager at 3.00 returns a total of $30 including the initial stake. The amount won is $20 or a multiple of 2 based on the stake.
- "p" is the probability of the proposed wager winning. For example, a wager with a 40% chance of being successful has a probability of winning of 0.40.
- "q" is the probability of the proposed wager losing. Using the same example of a wager with a 40% chance of being successful, there must be a 60% chance of it losing (assuming no pushes/ties). The probability of it losing is therefore 0.60. "q" can be calculated simply as 1 minus "p".
- "f" is the solution to the formula and provides you with the suggested fraction of your bankroll to stake on the proposed wager.

Let's see how the formula works based on the examples in the above description. We'll say the proposed wager has odds of 3.00, that the probability of it winning is 0.40, and that the probability of it losing is 0.60.

Based on this formula, you should be staking 0.1 (i.e. 10%)
of your bankroll on the proposed wager. Even though the chances
of it losing are greater than the chances of it winning, it's a
wager with **positive expected value** due to the favorable size of
the odds.

## Kelly Criterion & Expected Value

Positive expected value, if you're not familiar with the
term, is when the probability of a wager winning is higher than
the implied probability of the odds. For example, odds of 2.00
have an **implied probability** of 0.50. The implication is that a
wager at these odds has roughly a 50% chance of winning. If your
personal belief is that such a wager has more than 50% chance of
winning, then it has positive expected value.

We've provided a very brief explanation of value here, but this is something you should know all about if you're serious about your sports betting. We strongly suggest referring to our article on the concept of value if this is something you don't completely understand yet.

It should be noted that that the Kelly Criterion formula only really works for wagers that have a positive expected value. This is absolutely correct as, strictly speaking, you should only ever make bets where positive expected value exists. Value is, of course, subjective in sports betting terms, as different people will have different views on the probability of any particular wager winning. However, the point is that you shouldn't place a wager if the odds aren't high enough to compensate for the risk of it losing.

The Kelly Criterion will help you avoid doing that. The
formula will return a negative for a proposed wager where
there's no positive expected value, even if you think the wager
has a good chance of winning. Obviously you can't bet a negative
percentage of your bankroll, so the formula is effectively
telling you **not to make the bet**. We'll use another example to
illustrate this.

For this example, we'll assume that you're looking to bet on an upcoming tennis match between Rafa Nadal and Andy Murray. Your preferred bookmaker is offering the following odds.

Rafael Nadal vs Andy Murray

You believe that there's a 65% chance (0.65 probability) of Murray winning, so you decide to place a wager on him and use the Kelly Criterion formula to calculate your stake. The required calculation would be as follows.

As you can see, the formula has returned a negative value. This means that you shouldn't place the wager, as there's no positive expected value. Despite it having a good chance of success, the odds aren't high enough to justify risking money on it.

## The Kelly Criterion: Advantages & Disadvantages

We can certainly see why the Kelly Criterion betting strategy is so popular. It clearly makes sense to stake higher amounts, relative to your bankroll, on good value wagers. Any technique that can help you to do that must have some merit. This strategy certainly does some have some advantages, although it's not without its flaws either.

One advantage of the strategy is simply that it's a
relatively straightforward way to decide how much to bet.
Although applying the Kelly Criterion to **calculate the size of
your stakes** does take some getting used to, it's not actually
that difficult once you've familiarized yourself with the
formula and how to use it. It's really just a matter of putting
the relevant figures into the formula and then doing some fairly
easy mathematical equations.

The Kelly Criterion also takes the size of your bankroll into
consideration, which is another advantage. With that being said,
**any staking plan** you choose to use should be based primarily on
the amount of money you have to bet with. This is a fundamental
principle of bankroll management. What this particular strategy
does that most other staking plans don't, however, is the
application of the theoretical value of wagers.

In fact, this is probably the biggest advantage of the Kelly
Criterion. It's certainly the main reason for using it in the
eyes of many bettors, as it's essentially what enables them to
get the **right balance** between growing their bankroll and
protecting it. Staking more when the theoretical value is high
and staking less when the theoretical value is low, should
maximize profits in the long run while reducing the chance of
going bust.

The final advantage to mention is that the Kelly Criterion also helps to prevent the placing of wagers where positive expected value doesn't exist. It's not always immediately obvious when a wager is mathematically a bad decision, especially when the probability of it winning is greater than the probability of it losing. As we demonstrated earlier, though, the formula will return a negative when there's no positive expected value. This serves as a useful warning to avoid such wagers.

There are two main disadvantages of the Kelly Criterion. The
first one is something that we've already alluded to; it only
really serves a purpose when you're able to accurately work out
the probabilities of any proposed wagers. If you can't do that
reasonably well, then **the whole concept breaks down**. You'll end
up betting the wrong amounts which will result in you either
losing your bankroll too quickly or hindering its potential
growth. The strategy does nothing to help you find profitable
betting opportunities, which is disappointing.

The second disadvantage of the strategy is that it could be considered overly aggressive. In the example we used earlier, the formula suggested staking an amount equal to 10% of your bankroll. This is a very high percentage to risk under any circumstances. You rarely, if ever, want to commit more than 5% of your bankroll to a single wager and many bettors will never go above 2%.

It's possible to overcome this disadvantage though, by simply
taking a **more cautious approach** and reducing your stakes below
what the formula recommends. A lot of bettors use what is known
as a fractional Kelly strategy, where they bet a fixed fraction
of the suggested stake. This can be any fraction, but half is
common.

Using a fractional Kelly strategy doesn't overcome the main disadvantage though. No matter how much you adjust the formula, it still won't be able to tell you what selections you should make on your betting slips.

## The Kelly Criterion: Our View

When it comes to what bettors and betting experts think about the Kelly Criterion, their views seem to be split from one extreme to the other. Many people firmly believe that the strategy is extremely useful for calculating the optimal stakes to place, while others believe it serves very little purpose at all. Some even consider it to be completely useless.

We are among those who see both sides of the argument. It
clearly makes a lot of sense to stake more money on good value
wagers and the Kelly Criterion can help bettors to do this with
some degree of regularity. It's not some magic system that will
guarantee consistent profits though. Although it's based on
sound logic and reasoning, it still requires the ability to
**find
an edge and identify value bets**.

In our view, the Kelly Criterion has limited use as a betting strategy. It doesn't actually help improve your overall chances of winning money, which is what a good betting strategy should do. We therefore wouldn't actively encourage anyone to use it.

However, we wouldn't talk anyone out of using it either. We strongly recommend using a staking plan and practicing good bankroll management when betting on sports: the Kelly Criterion is a viable option for this. It's up for debate whether it's any better than other methods that can be used in its place.

Article Details

Author: Brad Johnson

Updated: July 2015

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