Variance and Expected Value In Sports Betting

Variance is one of the most important things to think about when it comes to sports betting. In essence, variance is a posh way of saying that you’ll win some and you’ll lose some, being the expression used to explain the fact that you will suffer some downswings in your betting history just as you will enjoy some periods of being in profit. It’s why it is so important to think about things over the long-term when placing bets.

Expected Value, often expressed simply as EV, is a way of measuring what you can expect to win or lose when you place a bet over the long-term. Unlike variance, Expected Value doesn’t show any wild movement because it’s showing the average over a period of time, as opposed to the spread of how far out your betting results are from the mean. Variance can be used to describe any numbers and isn’t limited to sports betting.

What Is Variance?

trading analysis chartLet’s imagine for a moment that you’re measuring a group of 20 people. You’ve discovered that the average height of those twenty people is 180 centimetres. You could pick the shortest person and the tallest person in the group, knowing that the average height would be about 180 centimetres but the difference between them both would be quite large, meaning that it would fluctuate.

The variance of the group would be quite high, going up and down depending on the height of the person that you were measuring at any one time. This is in spite of the fact that you know that the average height in the group is 180 centimetres. Imagine that instead of having them in one group of 20 people, you instead split them up into two groups, one with everyone of roughly the right height and the other all the extremes.

You can pick any two people from group one and know that they will almost certainly measure in at about 180 centimetres, given that that is the average height and you’ve chosen them from the average group. The variance in that group would be limited, whereas the variance in the group of people made up of the extremes would be much more wild, even though everyone in the group’s height would average out at 180 centimetres.

Why It Matters In Sports Betting

Instead of imagining people of different heights, imagine that those same values were applied to bets that you’ve placed. Anything above £180 is profit, anything below £180 is a loss. Suddenly we can see that our profit and loss in the given circumstance can vary wildly from one minute to the next. This is why it’s important to think about our betting over a long period of time, meaning that we’re less likely to panic when we hit a big loss.

Alternatively, imagine the following two betting opportunities:

Bet 1

Profit Probability
£0 25%
£200 50%
£400 25%

Bet 2

Profit Probability
£199 25%
£200 50%
£201 25%

In both cases, the expected value is £200, but the variance in the first case is much larger than the second. The result of this is that placing the first bet is much more risky than the second, with any intelligent bettor always looking for a case of low-risk, high return when placing their bets. Variance is another word for risk and you want to reduce it as much as possible when looking into the bets that you can place.

Variance is the difference between the results that we’re getting and the results that we are expecting. When you’re looking at your sports betting over a period of time, you’re going to be looking at the variance compared to your expected value. That is to say, you should expect your profits to end up around the expected margin over time, rather than wildly one way or another.

Large Numbers Of Bets Are Important

time money balance man standing between them

The outcome of a single bet is negligible when you’re looking at your betting over a long period of time. If you were to place 100 bets of roughly the same amount, whether a single one of those bets is a winner or a loser is essentially irrelevant when it comes to looking at your betting as a whole. Let’s say that you expect your average profit to be about £20. After one bet you might be £40 up. That isn’t telling is much.

What you want to know is how close to your £20 profit you can be over a solid number of bets. Looking after, say, ten bets might put you in a situation where you’re well over your £20 average, but that doesn’t mean that you’ll end up there after 100 bets. Equally, it’s entirely possible that you could lose your first five bets and begin to panic, but it’s not relevant to the overall look of your betting pattern.

Betting Isn’t Just About Picking Winners

winner signWe’d all love to be able to pick a winner with every single bet that we place. In truth, many of us would also love to be able to walk away the second we had a losing wager, but that’s beside the point. The reality of betting is that we’ll all have some winners and some losers, with the ability to understand that that’s the case being an important part of our betting experience. You can’t throw the baby out with the bathwater.

Successful sports betting is as much about doing some maths as it is about the bets themselves, especially if you want to do it seriously. It’s why those that consider themselves to be serious bettors get obsessed with the notion of finding value in their betting, looking to see whether the odds offered actually match the probability of the outcome in question actually occurring.

To put that another way, the probability implied by the odds of an event doesn’t always match the actual likelihood of that outcome being true. Understand that notion is the first step towards getting your head around variance and Expected Value. In order to understand that, you need to think in terms of probability. Imagine that Liverpool are playing Everton 100 times. How many times would you expect Liverpool to win?

Let’s imagine that you think Liverpool will win 72% of the time, you now know that you’ve got a base for looking at the odds offered by a bookmaker and deciding whether they’re fair or not. When the next match between Liverpool and Everton rolls around, you want to treat it as its own even and figure out what the odds are on that specific match. Say that Liverpool are missing two key players and Everton’s striker is in red hot form.

In that instance, you might decide that, actually, Liverpool have got a 57% chance of winning. You now know that, as far as you’re concerned, the chance of Liverpool winning this specific Merseyside derby is lower than your average percentage of them being victorious. Do the odds offered by the bookmakers reflect that fact? If the bookmakers seem to suggest that Liverpool are a shoe-in, you know that they’ve got their odds wrong.

In that case, the value bet will likely be on Everton winning rather than their city rivals. You might still lose your bet, but at least you managed to find the expected value in the wager that you’re looking at placing. On the other hand, the bookies might have got too carried away with Liverpool’s injury situation and decided that Everton are as good as guaranteed to win, meaning that there is some expected value in betting on Liverpool.

How Expected Value Works In Your Favour

Man holding bet slip looking at the skyUnderstanding the world of Expected Value is the first step on the road to successful betting. Figuring out what you think the actual value of a sports team is at any given moment is crucial in betting. Having a figure in your head of the chances of a team or player winning or losing will then allow you to compare and contrast that with the odds that are being offered by a bookmaker.

This will allow you to find value bets, which are bets that offer a positive expected value rather than a negative one. This is also where we come back to talking about variance, with the long-term being crucial to your finding Expected Value. You will lose some bets that you thought at a positive Expected Value, but as long as you’re always on the lookout for a value bet then you’re likely to be in the black overall.

You need to know what your winning edge is as a bettor. Let us imagine that you’ve worked it out to be about 5%, meaning that you’ll win 5% profit on your wagers. This allows you to not panic when you’re going through a period of losing bets, knowing that they will come back around and put you in profit at some point. Equally, it’s important to not get carried away when you’re winning, instead using the profit to cover future losses.

Starting with a bankroll of £100 and placing bets of £20 a time, you only need to lose five bets in a row and your bankroll is wiped out. This is why it’s important to allow for variance and take that into account when you’re figuring out your bet size. Placing bets of, say, £5 will allow you to gamble for much longer if you hit a losing streak, giving you a chance to get back on track with the aim of finishing the year with £105 when you’ve got a winning edge of 5%.

Is The Bet Worth Placing?

Betting Slip AccaThe big thing that understanding Expected Value does is it allows you to work out whether a bet is worth placing or not. There is no hard and fast rule on this front, with different bettors having different approaches. Some will only place bets if their perceived edge is 10% or higher, whilst some will opt for a 3% edge. Once you’ve figured out what yours is, you can explore the bets you want to place and decide whether to do so or not.

It is often the case that wagers with a positive expected value come with long odds. As a result, they are risky short-term bets even if they promise long-term value. That is to say, if you place ten bets with a 10% edge, you could lose four of them but still make a profit if you win the other six. Again, this is why the best punters tend to think in the long-term rather than the short. You want to shift the odds in your favour, but this take time.

The key to successful betting is in combining a solid handicap with good mathematics. You want to think carefully about your Expected Value and work hard to not get too carried away in either direction when it comes to the variance of your betting. Sticking to the plan is key when things go well just as much as it is crucial when things go badly. You don’t want to start increasing your stake size or reducing your edge just because you’ve had a few unexpected winners.

Can you be patient enough to see how much your variance is over a prolonged period of time? Can you place a year’s worth of bets, ensuring that they are all offering you a positive expected value, then look back at the end of it all and see whether you got your maths right or not? Not only that, but a crucial part of taking advantage of the world of Expected Value and variance is being able to adjust your maths based on those results.

What we mean by that is that you might get to the end of the year and have made a profit of 3%, rather than the 5% that you were expecting. Can you work out where the 2% drop has come from? If so, what can you change in order to get closer to 5%? By the same token, if you end up with 7% profit, is that because you got your maths wrong or was it just a matter of being a bit lucky with a few of your wagers? They’re key thoughts for long-term betting success using Expected Value and variance.