Expected Value, Closing Line and Variance

Terminology

To understand why value betting works, when betting with sports betting software, you need to familiarise yourself with some terms.

Value

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)

Closing Line Value (CLV) is based on the sharp bookmaker’s 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 a 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

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

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 percentage per bet, or per euro staked. ROI (return on investment), is how much your bankroll has increased 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 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 of 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:

Imagine 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 win, your ROI is just +1% but your yield is 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 10 wins in a row with 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 in reducing variance. Here are some tips on how to reduce variance when value betting.