Expected value, closing line and variance

Analytics dashboard displaying upward trend lines representing betting value and profit growth metrics

What expected value is and how it works

Expected value (EV) is the average profit or loss a bet would give you if you placed it many times at the same odds and the same probability.

RebelBetting is value betting software that shows the expected value of every value bet.

How expected value works with RebelBetting

Each value bet shows its value: how much better the odds are than the fair odds.
A +5% bet earns €0.50 per €10 staked, on average.
The closing line, the sharp odds just before kick-off, shows whether your bets had value.
Variance decides single results, so expected value only shows over hundreds of bets.

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Expected value, step by step

Three terms come up every time you value bet: value, positive expected value and negative expected value.

Value

Odds of 2.50 imply a probability of 1 ÷ 2.50 = 40%. That implied probability includes the bookmaker's margin. Remove the margin from a sharp bookmaker's odds and you get the fair odds. Value is the percentage next to every value bet in RebelBetting: how much better the odds are right now than the fair odds, also called your edge. It can rise or fall before kick-off as bookmakers move towards the real probability.

Positive expected value

A bet has positive expected value (+EV) when the odds pay more than the real probability is worth. Take a fair coin at odds of 2.10. Bet €10 and you win €11 half the time and lose €10 half the time: (€11 × 0.5) − (€10 × 0.5) = +€0.50 per bet, or +5%.

The formula: EV = (profit if you win × probability of winning) − (stake × probability of losing). As a percentage of the stake: probability of winning × odds − 1. Placing only +EV bets is called EV betting, or value betting.

Negative expected value

A bet has negative expected value (−EV) when the odds pay less than the real probability is worth. A bookmaker that offers 1.90 on both sides of a coin toss gives you (€9 × 0.5) − (€10 × 0.5) = −€0.50 per €10 bet, or −5%.

Most bets at a bookmaker are −EV, because the margin is built into the odds. That's why most bettors lose over time, and why value betting only takes the bets where the odds are higher than the fair odds.

Simulate your betting results

The free profit simulator shows how your results can swing around the expected value, with your own bankroll, stakes and number of bets. Try the simulator.

Closing line value (CLV)

The closing line is the sharp bookmakers' odds just before kick-off. It's the most accurate estimate of the real probability you can get for a match, because it includes all the information and money that came in before the start. We call it the true odds.

RebelBetting uses the closing line to calculate the expected value of your bets. In RebelBetting, CLV and EV mean the same thing.

If you regularly bet at odds higher than the closing line, you have an edge. That's called beating the closing line. More on our page about closing line value.

Beating the closing line doesn't mean you win every bet. Many value bets have true odds above 2.0, which is less than a 50% chance of winning. So your actual profit can be far from your expected value for a long time.

Variance

Variance is how far your profit swings around your expected value. After one coin toss at 2.10, you've either lost €10 or won €11, never the €0.50 you expect on average. The fewer bets you've placed, the bigger the swings.

Variance means you'll have both downswings and upswings when value betting. Read how to reduce variance when value betting.

Profit and closing line value (CLV) — Profit (green) and the closing line value (CLV, in grey). CLV is your expected value, over time.

Profit, ROI and yield

Profit, ROI and yield measure your actual results, which depend on the outcome of the matches. Read more about the difference between ROI and yield. In short, yield is the profit per euro staked. ROI (return on investment) is how much your bankroll has grown since the start.

Flat profit

Flat profit (or unit profit) is used when comparing users, betting systems or tipsters against each other, without taking bankroll size and betting strategy into account. It's the profit you would have achieved if you used a flat staking strategy (also called fixed staking). This means betting one "unit" (1% of your bankroll) at each bet. A unit is different for every user, it can be €10 or €100 – since it's a relative number you can easily compare the results.

Note that betting using the Kelly criterion (a proportional staking strategy) will improve your profits compared to flat staking.

To view your value betting profit and CLV, they are shown at the top of the BetTracker, and also in your detailed reports.

Tom

Value betting user, United Kingdom United Kingdom

It's taken me less than two months of value betting to make as much as I made from matched betting in a year. View the process as more of an investment than betting, think long-term. Trust the system and keep placing bets.

Read the full interview →

Emil

Value betting user, Finland Finland

The only thing you need is a computer and some patience. My starting capital was €2500, and so far I’ve earned +€11000, which is a lot considering it’s tax-free. Use one or two hours per day, and you can make some big profits.

Read the full interview here →

Sam

Value betting user, United Kingdom United Kingdom

I've been using RebelBetting for the past 9 months, and I've seen great results. It's incredibly useful for finding value bets, making it a great way to make extra money on the side. I highly recommend it to anyone looking to start their own side hustle!

Pinnacle

Bookmaker

As the only bookie to welcome arbitrage action and not limit winning players, we've been working successfully with RebelBetting since 2009. The positive feedback we get from players, is testament to just how good their product is.

James

Value betting user & community member, United Kingdom United Kingdom

RebelBetting is a trustworthy product, and they have a helpful community and customer support. Plus, you’ll probably make a lot more than what you pay in subscription fees – it’s a great investment!

Stefan

Value betting user, Sweden Sweden

The program works and is easy to use. I started with around €1600 and have a €1000 profit now after one month. I'll definitely reinvest my bankroll.

Read full interview →

Tuân

Value betting user, Vietnam Vietnam

I've been using this service for a few months now; starting with the Starter plan and then upgrading to the Pro. The rewards have been worth it – my ROI is over 500%, which is all the proof you need. You should definitely try it.

Rasim Reiz

Reizbet.com, Sweden Sweden

Value betting and Sure betting are two really interesting products tailored for those who want to take betting to the next level. You'll get loads of profitable bets and will learn a completely new approach to betting – a game changer!

Read the Swedish RebelBetting article →

Louis

The Arb Academy

RebelBetting has put together an outstanding arbitrage betting software package. It has a simple, uncluttered interface but is packed with all the necessities for serious arbitrage betting.

Read full review at the Arbacademy →

AzBookmakers

Azbookmaker review, Azbookmaker review Azbookmaker review

RebelBetting is surely the best arbitrage software. It is the fastest and most professional software that directly points out the "mistakes" of bookmakers or the so-called arbitrage bets.

Downswings are unavoidable

Downswings feel unfair, and you can't avoid them. If you keep placing value bets, your results tend to move back towards your expected value.

This video explains how to cope with variance, and why long-term thinking matters for a value betting profit.

Handle downswings

It's easy to get stuck focusing on the downswings. This is because we all suffer from loss aversion – the pain of losing is psychologically about twice as powerful as the pleasure of gaining.

Notice your upswings too: the winning streaks where you're clearly above expected value.
Understand why downswings happen. Let's take the coin toss example.

If you toss a coin 1500 times, there is a 52% chance you will get a streak of 10 heads in a row. This means if you place 1500 bets with an average true odds of 2.0 you have to expect 10 losses in a row. Or 10 wins. See this calculator.
But remember, this is with a 50/50 chance. With value betting you are always tossing a coin that is weighted in your favor, so your wins tend to outweigh your losses over time, by the value of the bets you place.

Your results tend towards your expected value

If you're having a downswing, there's no need to panic. Your results will over time get closer to the expected value. This is because of two statistical tendencies: the law of large numbers and regression to the mean.

The law of large numbers

Explains that the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.

This explains why your results tend to, over time, move closer and align with your expected value. Here are the real -life results of RebelBetting members value betting since 2020:

Of those placing 100 monthly bets or more, 79.7% are profitable
Of those placing 500 monthly bets or more, 90.0% are profitable
With 1000 monthly bets, expect 95% of months to be profitable

Regression to the mean

This is all about how data evens out. It basically states that if a variable is extreme the first time you measure it, it will be closer to the average the next time you measure it. Large downswings from the expected value (a losing streak) is an extreme outcome and will tend to revert back to EV.

So if your expected value is 3%, your actual yield tends towards 3% (profit per euro staked) as you place more bets. Be patient and think long-term.

Variance will be higher in the beginning

Variance is particularly high when the sample size is small, for instance at the start of your value betting career:

Say you place value bets with 4% value at odds of 2.00, staking 1% of your bankroll on each. If the first bet loses, your ROI is −1% but your yield is −100%, because your whole stake so far was lost. If the next two bets win, your ROI is +1% and your yield +33%. Swings this large are normal for the first few hundred bets.

Streaks are more common than you think

After placing 1000 bets at 5% value (with win probability 53%), there is still a 25% risk that you will get 10 losses in a row!

This might make a scary-looking downswing. As bad as that sounds, the upside more than makes up for it. The chance of getting 10 wins in a row with that edge is much more likely; 56% over 1000 bets!

The more bets you place, the variance will have far less effect and your results will over time move closer and align with your expected value. Note that we're not talking about a few hundred bets, it may require a couple of thousand bets. Read more about statistical significance in sports betting.

The importance of thinking long-term

It's important to see value betting as a long-term way to profit. The number of bets, as well as using a staking and max bet strategy, play an important role in reducing variance. Here are some tips on how to reduce variance when value betting.

Learn more on the value betting help page

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