Basic Probability and the Concept of Value

It would be reasonable to assume that the way to win money
from sports betting is to accurately predict what will happen in
sports events. While this is technically true, you might be
surprised to learn that simply getting your predictions right isn’t necessarily enough to consistently make a profit.

This is because, no matter how good you are, you won’t get
your predictions right every time. There are simply too many
variables involved in sports events. No one is always right, not
even the most successful gamblers in the world.

Although it obviously helps to be right as often as you can,
a more important aspect of betting is to actually find value.
Value is a term you’ll hear sports bettors use often, and it’s one that you absolutely have to understand if you are going
to be successful.

On this page we explain what value is, and how it relates to
probability. First, though, we must explain what your hit rate
is in sports betting terms, and why it may not be enough to
simply get your predictions right more often than you get them
wrong.

When betting on sports, your hit rate refers to the number of
bets you win in relation to the number of bets you place
overall. It’s typically expressed as a percentage. So, for
example, if you place 100 bets and win 50 of them, then your hit
rate is 50%.

If every single wager you placed was a winner, then you would
have a hit rate of 100%, and would clearly make plenty of money.
This is entirely unrealistic though, as we have already stated.
You should, of course, try to be as accurate as possible with
your predictions, but a high hit rate doesn’t guarantee a
profit in the long term.

We’ll demonstrate this with a hypothetical scenario, based on
betting on the results of tennis matches. For the purposes of
this example we’re going to use the first day of the US Open in
2013. In the early round matches of a tournament, it’s
reasonable to expect most of the favorites to win, so you could
be pretty confident of a high hit rate if you chose to back them
all.

Let’s see what would have happened if you decided to bet on
all the favorites in the men’s matches taking place on the first
day.

# of Matches Favorites Won Favorites Lost Hit Rate
19 15 4 79%

As you can see, you would have had a hit rate of nearly 80%.
On the surface, winning nearly four bets out of five seems
excellent. However, the average odds for the favorites that won
on that day were 1.25. Based on those odds, if you had bet \$10
on each match your 15 winning bets would have returned \$187.50
in total (including stake), for \$37.50 in profit. You would have
also lost four bets, at \$10 each, for an overall loss of \$2.50.

You’ve only just made a loss, and on another day the same
strategy may well have returned a small profit. We haven’t used
this example to discuss the pros and cons of betting on the
favorites in tennis matches though, and this is a very small
sample of relevant data anyway. The point we are trying to
illustrate with this example is simply that a high hit rate by
itself doesn’t automatically mean you’ll make a profit.

To put it another way, your hit rate doesn’t reflect your
chances of winning money. It simply reflects how many wagers you
win relative to how many wagers you place. As we have just
shown, winning a high percentage of your wagers doesn’t
necessarily equate to making money. It isn’t the number of
predictions you get right which determines your success, it’s
the relative quality of your predictions.

This is where value comes into play, because it’s the value
associated with your predictions that determines their quality.
We’ll get onto exactly what value is in sports betting terms
shortly, but first we will look at the role probability plays.

Probability in Sports Betting

Basic probability is really quite straightforward. It is a
measure of how likely something is to happen, and is usually
expressed as a decimal between 0 and 1.0 in which 0 indicates
impossibility and 1 indicates certainty. Probability can also be
expressed as percentage, where 0% indicates impossibility and
100% indicates certainty. In many circumstances, probability can be calculated
precisely. Take the toss of a coin, for example. There are only
two possible outcomes, and each is equally likely. The
probability of the coin coming up heads is therefore 50%, and
the probability of it coming up tails is also 50%. The roll of a
die is another good example. There are six possible outcomes,
and again each one is equally likely. So the probability of any
one number being rolled is always 16.66% (100% divided by six).

Probability in sports betting is not quite so
straightforward. It is impossible to calculate the precise
probability of any outcome in a sport event, as there are so
many factors involved. You can apply all the statistics you
want, and take all the factors that can affect a result into
account, but you simply cannot determine a definitively accurate
probability.

All you can do is calculate what you believe the chances of
any particular outcome to be. This is all the bookmakers can do
too. While the odds they set do reflect the relative likelihood
of the possible outcomes, they are not necessarily completely
accurate representations of the probabilities involved.
Ultimately they are based on the bookmakers’ assessment of what
they think may happen, adjusted to make sure there is a built in
margin for them.

While bookmakers do put the odds in their favor, it is
possible to overcome their advantage. This is not easy to do,
but it is certainly possible. Ideally you need to really know
your sports, and you definitely need to understand implied
probability and expected value.

Implied Probability and Expected Value

In sports betting, implied probability is what the odds
suggest the likelihood of an outcome happening is. It is
calculated by dividing one by the decimal odds. So, if the
Chicago Bears are given odds of 2.50 to win a match, their
implied probability of winning is 0.4, or 40%. If they are given
odds of 1.50 to win a match, their implied probability of
winning is 0.67, or 67%.

To easily convert odds, in any format, into implied
probability, you can use
our odds converter tool.

Expected value relates to how much you can expect to win from
a wager. It is a theoretical measure that is based on the
overall probability of it winning. Let’s use an example of
betting on the Chicago Bears at 2.50 to illustrate expected
value.

If you placed a \$10 wager on the Bears to win at odds of 2.50
then you stand to make a return of \$25, including your stake.
Assuming the implied probability of them winning (which we’ve
already established is 40% based on these odds) is an accurate
reflection of their real probability of winning, you will be
paid \$25 40% of the time that you make this wager. You will lose
\$10 60% of the time that you make this wager.

The calculation for expected value is as follows.

Expected Value = (Probability of Winning x Amount Won Per
Bet) – (Probability of Losing x Stake)

Let’s use this calculation to work out the expected value of
this wager.

(40% x \$15) – (60% x \$10) = \$6.00 –\$6.00 = \$0.00

The expected value of this wager is therefore zero, meaning
it should break even in the long run. Obviously it will always
win or lose in practice, but expected value is basically used to
measure how much theoretical value a wager offers over the long
term.

The expected value of a wager is in fact always zero when you
assume that the implied probability is an accurate reflection of
real probability. However, the implied probability that
bookmakers’ odds suggest is usually higher than the real
probability. When the odds are 2.50 on the Chicago Bears winning
a match, then the real probability on them winning is actually
likely to be less than 40%.

Let’s do some sums based on the real probability of the Bears
wining being 35%, and the real probability of them losing being
65%.

(35% x \$15) – (65% x \$10) = \$5.25 – \$6.50 = -\$1.25

We can see that, based on these probabilities, a wager on the
Bears winning at 2.50 actually has negative expected value. This
means that you would expect to lose money on this wager in the
long run.

We mentioned earlier that it’s the value associated with your
predictions that determines their quality. If a prediction
involves making a wager where the expected value of a wager is
less than zero, then it’s technically a low quality prediction.
You may be right sometimes, but the expectation in the long run
is that you will lose money.

High quality predictions involve making wagers with positive
expected value. These might be wrong sometimes, but the
expectation is that you will win money in the long run. To find
positive expected value, you have to find opportunities to place
a wager where you believe the real probability is higher than
the implied probability that the odds suggest.

Let’s use the example of betting on the Chicago Bears to win
at 2.50 again. This time we’ll do the sums based on you
believing the real probability of them winning to be 45%.

(45% x \$15) – (55% x \$10) = \$6.75 – \$5.50 = \$1.25

We can see that a wager on the Chicago Bears at 2.50 now
appears to offer positive expected value.

The examples we’ve used here are somewhat simplified. We have
used them purely to illustrate the concept of value in sports
betting. We have also demonstrated one very important aspect of
value – that it is ultimately a matter of opinion.

The fact is that a bet on the Chicago Bears to win a match at
odds of 2.50 might be a good value bet in the eyes of one
bettor, and a bad value bet in the eyes of another. It basically
depends on how you assess the relative probabilities of the
possible outcomes. This is very much an individual thing, and
there is no particularly right or wrong way to do it.

Summary

There are three key points that you should take away from
important as some would have you believe. Of course you want to
get as many of your predictions right as you can, but you have
to consider the odds of your selections. It’s no good winning
80% of your wagers if you still lose money overall.

The second point is that the odds that bookmakers set do not
necessarily accurately reflect the real probability of possible
outcomes. They are usually pretty close, but you must remember
that there is always the built in margin to consider. It is also
quite possible for bookmakers to make mistakes, and offer odds
that are actually higher than they technically should be.

The third point is that assessing the value of any particular
wager is an excellent way to decide which bets to place, but
offers no guarantee of success. In theory, if you only ever
place bets that have positive expected value then you should
make money overall. It is important to recognize, though, that
value is subjective. Making bets that you perceive to offer
value will only prove to be profitable if your perception is
correct.

Identifying opportunities which do offer genuine value is not
easy. If you can do it consistently though, then you stand a
very good chance of becoming a successful bettor. This is where
sports knowledge, an ability to analyze data and statistics, and
an understanding of various betting strategies are all useful.

In our sports betting strategy section we provide a range of