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.
(bp – q) / b = f
This formula doesn’t tell you much by itself. You need to
understand what all the components represent, which we explain
“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.
( (2 x 0.40) – 0.60 ) / 2 = 0.1
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
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
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 Match Result
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.
( (0.50 x 0.65) – 0.35 ) / 0.50 = -0.05
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
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
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
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.
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