# 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.

## Your Hit Rate

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

this article. The first is that your hit rate is not as

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

information and advice that will help you to identify good

betting opportunities, but for now we suggest continuing with

this beginner’s guide. In the next article we provide our top tips for beginners.