# Expected Value, Closing Line and Variance

Variance means you will experience both downswings and amazing profits when value betting. Here we explain variance and the importance of thinking long-term.

### Terminology

To understand why value betting works, you need to familiar yourself with some terms.

**Value **is the percentage you see beside every value bet in RebelBetting. This is the value (also called edge, ROI or yield) of this particular odds right now compared to the “true odds”. Note that a value might decrease or increase closer to match start, as the bookmakers converge closer to the true probability. This is called the closing line.

**Closing Line Value (CLV) **is based on the sharp bookmakers odds just before match start. We call this the *true odds*. This is proven to be the best predictor of the outcome of a match, with accuracy uncannily close to 100%.

We use CLV as the predictor of your **expected value (EV)**. Both these terms can be used, and they mean the same thing in RebelBetting.

If you regularly bet on odds higher than the closing line, you will be profitable. This is called *beating the closing line. *ValueBetting customers beat the closing line over 80% of the time.

Note that even though the sharp bookmakers make extremely accurate predictions, this does not mean you will win every bet. You often bet on value bets with true odds over 2.0 (lower than 50% chance of winning), and often the underdog wins. This means your actual profit will at times differ a lot from the profit predicted by the CLV. This is called variance.

**Variance** measures the difference between your profit and the CLV. Or how far a set of numbers are spread out from their average value.

**Profit, ROI and Yield ** measures your actual results, which depends on the outcome of the matches. Read more about the difference between ROI and Yield. In short, yield is the profit percentage per bet, or per euro staked. ROI (return on investment), is how much your bankroll have increased since the start.

**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 ValueBetting profit and CLV, they are shown at the top of the BetTracker, and also in your detailed reports.

### Coin toss example

The probability of a coin to land on Heads is 50%. But assume you get the odds 2.10 on Heads and bet €10.

- If you win you profit €11
- If you lose you lose €10

To calculate the **expected value** of the bet you can use this formula:

*(profit per bet * probability of winning in decimals) – (loss per bet * probability of losing in decimals)*.

In this case: (€11 * 0.5) – (€10 * 0.5) = €0.5

Therefore you would expect to make an average profit of €0.5 (or 5%) for each €10 bet, because *the odds offered are better than the implied odds* of the coin toss.

However, after only one toss you would have either lost €10 or earned €11, not won €0.5. So if you only place 1 bet, the **variance** will be huge.

### 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:

Imaging if we place value bets with 4% value, at odds 2.00 with 1% of our stake. If the first bet loses your ROI is -1% but your yield is a scary sounding -100% (because your first and total stake was lost). If you then place two more bets which wins, your ROI is just +1% but your yield a fantastic +33%. This high variance will continue for some time, usually for hundreds of bets, especially if you have a streak of bad or good luck.

## 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!

As bas as that sounds, the upside more than makes up for it. The chance of getting 10wins in a rowwith that edge is more likely than not; 54% 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 to reduce variance. Here are some tips on how to reduce variance when value betting.

### Downswings are unavoidable, but temporary

Downswings can feel disheartening and unfair. But it’s something you will have to handle, because they are unavoidable. But if you don’t give up, you will also overcome them all.

**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.

- Take note and celebrate of your
*upswings*– your lucky winning streaks when you’re clearly over expected value. - Understand why downswings happen. Let’s take the coin toss example again.

If you toss a coin 1500 times, there is a 52% chance you will get a streak of 10 heads or tails. 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.

**You will overcome all downswings**

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 numbersexplains 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 meanis 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 you have an expected value of 3%, your actual results will, over time, even out to 3% yield (profit per dollar spent). Once again, have patience and think long-term.

Author:** Simon Renström, **RebelBetting founder

*Simon is the chief architect behind the sure betting and value betting products. **A veteran software developer and entrepreneur that founded RebelBetting in 2007.*

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